Excesso De 128 Opções Binárias

Class PoolingOptions. Options relacionadas ao pool de conexões. O driver usa conexões de uma forma assíncrona Significado que várias solicitações podem ser enviadas na mesma conexão ao mesmo tempo Isso significa que o driver só precisa manter um número relativamente pequeno de conexões para cada Cassandra Host Essas opções permitem que o driver controle quantas conexões são mantidas exatamente. Para cada host, o driver mantém um núcleo pool de conexões abertas em todos os tempos determinado por chamada Se o uso dessas conexões atinge um limite configurável, mais conexões são criadas acima Para o número máximo configurável de conexões Quando o pool excede o número máximo de conexões, as conexões em excesso são recuperadas. Cada um desses parâmetros pode ser configurado separadamente para hosts LOCAL e REMOTE HostDistance Para hosts IGNORED, o padrão para todas essas configurações é 0 e Não pode ser changed. Constructor Summary. Constructor e Description. Method Summary. Modifier e Type. Method e Desc Ription. Returns o número central de conexões por host. Returns o intervalo de batimento cardíaco, após o qual uma mensagem é enviada em uma conexão ociosa para se certificar de que ele ainda está alive. Returns o tempo limite antes de uma conexão ociosa é removed. Returns o executor para usar Para inicialização de conexão. Retorna o número máximo de conexões por host. Returns o número de solicitações simultâneas em todas as conexões para um host após o qual mais conexões são created. this opção isn t usado mais com o atual pool de redimensionamento algorithm. Returns o tempo limite ao tentar Para adquirir uma conexão de um pool do host s. Solicita ao driver para reavaliar o HostDistance para um determinado node. Requests o driver para reavaliar o HostDistance através do configurado para todos os hosts conhecidos e para soltar adicionar conexões para cada hosts de acordo com A distância calculada. Sets o núcleo eo número máximo de conexões por host em uma chamada. Sets o número de núcleo de conexões por host. Sets o intervalo de batimento cardíaco, após o qual um Mensagem é enviada em uma conexão ociosa para se certificar de que ele ainda está vivo. Method Detail. Deprecated esta opção isn t usado mais com o atual pool de redimensionamento algorithm. Returns o número de solicitações simultâneas em uma conexão abaixo do qual as conexões em excesso são recuperados. Se Uma conexão aberta com um host à distância de distância trata menos do que este número de solicitações simultâneas e há mais do que conexões abertas para este host, a conexão é fechada. O valor padrão para esta opção é 25 para LOCAL e REMOTO hosts. Parameters distância - O HostDistance para o qual devolver este limite Retorna o limite configurado, ou o padrão se nenhum tiver sido set. Deprecated esta opção isn t usado mais com o algoritmo atual de resizing pool. Configura o número de solicitações simultâneas em uma conexão abaixo da qual as conexões em Excesso são recuperados. Parameters distância - o HostDistance para o qual a configurar este limite newMinSimultaneousRequests - o valor a definir entre 0 E 128 Retorna este PoolingOptions Throws IllegalArgumentException - se a distância ou se minSimultaneousRequests não estiver no intervalo ou se newMinSimultaneousRequests for maior que o valor máximo para esta distância. Retorna o número de solicitações simultâneas em todas as conexões a um host após o qual mais conexões são criadas. Se todas as conexões abertas a um host à distância distância conexão estão manipulando mais do que este número de solicitações simultâneas e há menos de conexões abertas para este host, uma nova conexão é open. Note que uma determinada conexão não pode lidar com mais de 128 pedidos simultâneos Protocolo. O valor padrão para esta opção é 100 para LOCAL e REMOTO hosts. Parameters distância - o HostDistance para o qual retornar este limite Retorna o limite configurado, ou o padrão se nenhum tiver sido set. Sets número de solicitações simultâneas em todos Conexões a um host após o qual mais conexões são criadas. Parameters distância - o HostDista Nce para o qual configurar esse limite newMaxSimultaneousRequests - o valor a ser definido entre 0 e 128 Retorna este PoolingOptions Throws IllegalArgumentException - se a distância ou se maxSimultaneousRequests não estiver no intervalo ou se newMaxSimultaneousRequests for menor que o valor mínimo para esta distância. Retorna o número do núcleo De conexões por host. Para a distância fornecida isso corresponde ao número de conexões inicialmente criadas e mantidas abertas para cada host dessa distância. Parameters distância - a HostDistance para o qual retornar este limite Retorna o número de núcleo de conexões por host à distância. Sets o número de núcleo de conexões por host. Parameters de distância - o HostDistance para o qual definir esse limite newCoreConnections - o valor a ser definido Retorna este PoolingOptions Throws IllegalArgumentException - se a distância ou se newCoreConnections é maior que o valor máximo para essa distância See Also setConnectionsPerHost HostDistance, int, int. Returns O número máximo de conexões por host. Para a distância fornecida isso corresponde ao número máximo de conexões que podem ser criadas por host a essa distância. Parameters distância - o HostDistance para o qual retornar este limite Retorna o número máximo de conexões por host em Distância distance. Sets o número máximo de conexões por host. Parameters distância - a HostDistance para que para definir este limite newMaxConnections - o valor a ser definido Retorna este PoolingOptions Throws IllegalArgumentException - se distância ou se newMaxConnections é menor que o valor central para essa distância Veja Além disso, setConnectionsPerHost HostDistance, int, int. Sets o núcleo eo número máximo de conexões por host em uma chamada. Parameters distância - a HostDistance para o qual definir esses limiar núcleo - o núcleo número de conexões max - o número máximo de conexões Retorna este PoolingOptions Lança IllegalArgumentException - se a distância ou se o núcleo max. Returns o tempo limite antes de um N conexão remota é removida. Sets o tempo limite antes de uma conexão ociosa é removido. A ordem de magnitude deve ser alguns minutos o padrão é 120 segundos O tempo limite que aciona a remoção tem uma granularidade de 10 secondss. Parameters idleTimeoutSeconds - o novo tempo limite em Seconds Retorna este PoolingOptions Throws IllegalArgumentException - se o tempo limite for negativo. Returna o tempo limite ao tentar adquirir uma conexão do pool de um host. Sets o tempo limite ao tentar adquirir uma conexão do pool de um host s. Se nenhuma conexão está disponível dentro desse O driver irá tentar o próximo host a partir do plano de consulta. Se esta opção for definida como zero, o driver não vai esperar em all. Parameters poolTimeoutMillis - o novo valor em milissegundos Retorna este PoolingOptions lança IllegalArgumentException - se o tempo limite for negativo. Retorna o intervalo de batimento cardíaco, após o qual uma mensagem é enviada em uma conexão ociosa para se certificar de que ainda está viva. Define o intervalo de batimentos cardíacos, após o que uma mensagem É enviado em uma conexão ociosa para se certificar de que ele ainda está vivo. Este é um nível de aplicativo keep-alive, fornecido por conveniência, uma vez que ajustar o TCP keep-alive pode não ser prático em todos os ambientes. O valor padrão para esta opção é 30 Secondss. Parameters heartbeatIntervalSeconds - o novo valor em segundos Se for definido como 0, ele desativará o recurso Retorna este PoolingOptions Throws IllegalArgumentException - se o intervalo for negativo. Retorna o executor a ser usado para a inicialização da conexão. Configura o executor a ser usado para a inicialização da conexão. As conexões estão abertas de uma maneira completamente assíncrona. Uma vez que a inicialização do transporte requer consultas CQL separadas, os futuros representando a conclusão dessas consultas são transformados e encadeados. Este executor é onde essas transformações acontecem. Esta é uma opção avançada, que raramente é necessária na prática Ele padrão para Guava s que resulta em executar as transformações na rede IO threads isso é bom se t Ele transformações são rápidas e não IO vinculado que é o caso por padrão Uma razão pela qual você pode querer fornecer um executor personalizado é se você usar a autenticação com uma implementação personalizada Authenticator que executa bloqueio calls. Parameters initializationExecutor - o executor para usar Retorna este PoolingOptions Lança NullPointerException - se o executor é null. Requests o driver para reavaliar o HostDistance através do configurado para todos os hosts conhecidos e soltar adicionar conexões para cada hosts de acordo com a distância calculada. Note que, devido a problemas de compatibilidade com versões anteriores, este método Não é interrompível Se o thread chamador for interrompido, o método será concluído e só então re-interromper o thread que você pode verificar com. Solicita ao driver para reavaliar o HostDistance para um dado node. Option123 LLC é um provedor líder de empregado Administração de opções de ações, software de avaliação e serviços de avaliação nos Estados Unidos Nosso software tem sido usado por 400 c Ustomers em todo o mundo, incluindo empresas Fortune 500, grandes empresas de CPA, como grandes 4, bem como muitas pequenas e médias empresas desde que foi encontrado em 1999. Com a nossa excelência em Microsoft Excel VBA e macros, também fornecemos o estado do Art soluções para opções relacionadas com questões que podem ser considerar desafiador no Microsoft Excel R para contadores, profissionais financeiros e gerentes de negócios. Software for Employee Stock Option s. Simple soluções para profissionais financeiros em avaliações de opções complicadas e beyond. Administration, Valuation, Reporting of. Digite informações básicas. Selecione o modelo adequadoPer FAS123 R. Per ASC 718 FAS123R. Intervalo Variável do Modelo Blomial. Black-Scholes Opção Calculator. Binomial Model Calculator Simulation. Calculator de modelos de preços de opções. Termos estão sujeitos a alterações sem prévia notificações por escrito Contacte-nos através de e-mail. Option123 Excel v 6 0, versão padrão, e OptionX, versão on-line, a seguir, Option123 ou o Programa é projetado para auxiliar empresas em trac Bem como calcular o lucro por ação e preparar o relatório intermediário, Formulário 10 Q e o relatório anual, Formulário 10 K, seguindo a Declaração de Normas Contábeis Financeiras No 123 Revised 2004, Share - Pagamento Baseado em Pagamento FAS 123 R, substituído por FASB ASC Tópico 718 - Compensação de Ações, Normas Contábeis Financeiras 128, Lucro por Ação FAS 128, Normas Contábeis Financeiras No 148, Contabilização de Transações e Divulgação de Compensação Baseada em Ações, No 123 FAS 148, bem como o Securities Exchange Act de 1934. Além de ajudar as empresas a acompanhar seus planos de ações, Option123 automatesputations de valor justo de opção de ações usando o modelo de preço de opção, incluindo Binomial Modelo e Black-Scholes Option Pricing Model calcula o valor justo Das opções ou prêmios similares com base nas suposições de entrada de sua empresa Os valores justos de cada concessão são calculados usando o Modelo Binomial e o Bl Ack-Scholes Modelo de Preços de Opção ao mesmo tempo, se todas as entradas necessárias forem inseridas A simulação de árvore binomial pode ser feita para cada concessão única, com entradas constantes usadas ao longo de todo o termo ou entradas de variáveis ​​inseridas separadamente em cada nó A volatilidade histórica também é calculada em Ao mesmo tempo, se selecionado. Os cálculos do EPS calculam as ações incrementais eo EPS seguindo ASC 718 ou FAS 123 R e FAS 128. As informações de divulgação e de concessão de opções fornecem informações mínimas de divulgação e informações de concessão de opções, conforme exigido pelo ASC718 ou FAS 123 R , SEC, para arquivar o Formulário 10K, Relatório Anual Inclui informações resumidas sobre as opções em exercícios pendentes, informações sobre a média ponderada, as informações sobre a concessão de opções agregadas conforme exigido no Formulário 10 K, Parte II, Item 5, bem como as informações relativas ao executivo Compensações exigidas no Formulário 10K, Item 11 Para empresas que utilizam ano civil como ano fiscal, elas são obrigadas a adotar o FAS 123 R ou ASC 718 no início Do período intercalar que começa após 15 de dezembro de 2005 Antes disso, a divulgação pró-forma ainda é necessária para aqueles que não adotaram o FAS 123 R ou ASC 718.A análise de sensibilidade fornece para cada concessão individual com análise de sensibilidade assumindo essas mudanças de estoque O preço dos activos subjacentes, a volatilidade, a vida útil estimada ea taxa livre de risco, calculando os seguintes 5 Greeks Delta, Gamma, Vega, Theta e Rho, ao mesmo tempo em que o justo valor é calculado para cada concessão Explicações detalhadas destes gregos São detalhadas no capítulo seguinte. A Alocação de Exportação aloca a despesa total associada a um prêmio individual aos períodos contábeis corretos e adiciona alocações individuais por grupo para auxiliar as empresas no desenvolvimento de divulgações de renda líquida ASC 718 ou FAS 123 R. Informação média ponderada e outra divulgação exigida pelo ASC 718 ou FAS 123 R e FAS 148. Transferência automática de preços históricos de ações e Dividendos a O histórico de preços de ações e os dados de dividendos são baixados automaticamente da Internet. Visão geral da opção de ações para empregados e Opção123.Opção123 fornece às empresas um pacote simplificado para gerenciar seus planos de capital. Mantém todas as informações necessárias para registrar todas as atividades relacionadas a opções, warrants ou Incluindo as subvenções, anulações, anulações, exercícios, expirações, avaliações, cálculos de EPS diluídos, divulgação e relato de todas as opções relacionadas com as compensações. EPS Calculation. The Financial Accounting Standards Board emitiu Declaração de Normas de Contabilidade Financeira No. 128, Earnings per Share, que Simplifica as normas para os cálculos Requer a dupla apresentação do BPA básico e diluído na face da demonstração de resultados e requer uma conciliação do numerador e do denominador do cálculo do EPS básico com o numerador do cálculo do EPS diluído As Normas de Contabilidade Financeira no 148 , Contabilização de Compensações Baseadas em Ações Uma alteração da Declaração FASB n º 123, também altera os requisitos de divulgação do FAS 123 para exigir divulgações proeminentes em ambas as demonstrações financeiras anuais e interinas sobre o método de contabilização da remuneração dos empregados em ações eo efeito do método baseado em Além disso, a Demonstração das Normas de Contabilidade Financeira No 123 Revisada 2004, Pagamento Baseado em Ações FAS 123 R, emenda os cálculos do FAS 123, FAS 128 e FAS 148 FAS 123 R foi substituída pelo FASB ASC Tópico 718 - Compensação de Ações. O lucro básico é calculado dividindo o lucro disponível para os acionistas comuns pelo número médio ponderado de ações ordinárias em circulação para o período O EPS diluído reflete a conversão assumida de todos os títulos dilutivos, incluindo opções de ações, warrants, Ofertas dilutivas e não se refere a dívidas conversíveis e ações preferenciais conversíveis Devido à sua natureza específica Também por causa de seu método de cálculo relativamente simples, Option123 não lida com os cálculos do número médio básico de ações ordinárias em circulação e EPS básico diluído mede o desempenho de uma entidade durante o período de relato ao dar efeitos a todos Potenciais ações ordinárias que foram dilutivas e em circulação durante o período O denominador inclui o número de ações ordinárias adicionais que estariam pendentes se as potenciais ações ordinárias que foram dilutivas foram emitidas. Opções de ações afetam EPS diluído é dependente das disposições de aquisição Planos que Estão sujeitas a provisões de aquisição com base no desempenho ou quaisquer critérios de aquisição adicionais, exceto o serviço continuado ou a aquisição de ações relacionadas ao tempo, são tratadas como ações contingentemente emissíveis As concessões que estão sujeitas apenas à aquisição de ações relacionadas ao tempo são tratadas No entanto, o cálculo é diferente dependendo da conta Método utilizado pela empresa para contabilizar os prêmios concedidos aos empregados. A orientação do EPS aplicável ao FAS 128 deve ser aplicada no cálculo do BPA para a apresentação na face das demonstrações de resultados exigidas pelo ASC 718 ou FAS 123 R. O efeito dilutivo das opções em aberto E warrants emitidos por uma entidade geralmente devem ser relatados em EPS diluído por aplicação do método de tesouraria Opções e warrants terão um efeito dilutivo segundo o método das ações em tesouraria somente quando o preço médio das ações ordinárias exceder o preço de exercício da ação Opções ou warrants in-the-money Se em um trimestre os aumentos de preços médios acima do preço de exercício da opção, os dados EPS previamente relatados não devem ser ajustados retroativamente como resultado de mudanças nos preços de mercado de ações ordinárias. Emitidos durante o período de relato ou que expiram ou são anulados ou exercidos durante o período de reporte são incluídos no denominador de d De acordo com o método de tesouraria, todas as opções ou warrants no dinheiro são assumidos como sendo exercidos no início do período de relato ou no momento da emissão, se mais tarde. Se que a diferença entre o número de ações assumidas emitidas eo número de ações assumidas adquiridas, denominadas ações incrementais, deve ser incluída no denominador dos cálculos de EPS diluídos. De acordo com a Opção 123, o preço médio de mercado é o preço médio simples do preço diário das ações, que pode ser o preço médio de abertura, fechamento, mais alto, mais baixo, Apenas automatiza os prêmios em que a aquisição é baseada na passagem do tempo Para o cálculo de ações não adquiridas, ações contingentemente emissíveis ou prêmios que podem ser liquidados em ações ou em dinheiro Se necessário um cálculo separado Cf. SFAS 128. O EBP diluído no trimestre é calculado com base no preço médio das ações durante os três meses do período de relatório Se houver perda em um trimestre de relatório, nenhuma ação incremental deve ser incluída nos cálculos de EPS diluídos Porque o efeito seria anti-dilutivo. Para os cálculos acumulados até o ano e anuais, quando cada trimestre é rentável, as ações incrementais incluídas no denominador são o número médio simples de ações incrementais em cada trimestre no acumulado do ano ou anual No entanto, se um ou mais trimestres tiverem uma perda, o resultado anual ou anual das operações contínuas deve ser utilizado para determinar se as operações em dinheiro ou os warrants estão incluídos no denominador. As opções ou os warrants foram excluídos de um ou mais trimestres para calcular o EBP diluído trimestral devido ao efeito da anti-diluição, essas opções de ações ou warrants devem ser i Desde que o efeito seja dilutivo. Opção123 fornece dois métodos para calcular o EPS a um ano, utilizando a média simples dos trimestres de períodos intermediários e o outro, utilizando o ano para A média ponderada da data com a data de começo começa sempre no primeiro dia do ano fiscal. Modelos do preço de operação. Há dois modelos do preço da opção disponíveis neste modelo de preço binário da opção do programa e modelo do preço da opção de Black-Scholes por ASC 718 ou FAS 123 R, Ambos os modelos são aceitáveis, embora o mais recente Esboço de Exposição do Pagamento Baseado em Ações e uma Emenda das Declarações FASB nºs 123 e 95 mencionassem a preferência do FASB para o Modelo Binomial de Preço Opcional, pois oferece maior flexibilidade para refletir as características únicas das opções de ações dos empregados No entanto, o FASB entende que as entidades podem não ter disponível em um formato utilizável informações sobre os padrões de exercício dos funcionários e talvez outros Fatores necessários para fornecer a entrada apropriada a esses modelos O programa usa o modelo binomial da fixação do preço da opção por defeito, mas você pode escolher usar o modelo da fixação do preço da opção de Black-Scholes. Introduzido por Cox, Ross e Rubinstein para preço de opções de ações americanas em 1979 O modelo divide o tempo para a expiração de uma opção em um grande número de intervalos, ou etapas Em cada passo calcula que o preço das ações vai mover para cima ou para baixo com Uma certa probabilidade Este modelo também leva em consideração a volatilidade do estoque subjacente, o tempo até a expiração, a taxa de juros livre de risco eo rendimento do montante de dividendos. A principal diferença entre opções americanas e opções européias é a característica do exercício precoce a qualquer momento durante No entanto, este recurso traz uma complexidade substancial para efeitos de avaliação. Ao contrário do Modelo de Preços Opcionais Black-Scholes, um modelo de preços fechado para Para as opções europeias ou prêmios similares, o modelo binomial utilizado no Programa é a forma básica usando as seis variáveis ​​requeridas pelo ASC 718 ou pelo FAS 123 R. Preço do estoque. Termos esperados, um resultado calculado com termo do contrato como entrada no modelo Binomial. Volatilidade esperada do estoque subjacente ao longo do termo do contrato. Taxa de juros livre de risco ao longo do prazo do contrato, e. O retorno esperado do dividendo sobre o contrato. O modelo binomial, a vida esperada é uma saída calculada de um modelo de forma fechada, ou seja, Black-Scholes modelo em que o termo esperado é um input. An exemplo de um método aceitável para fins de divulgação de demonstrações financeiras de estimar o esperado Termo baseado nos resultados de um modelo de rede é usar o valor justo estimado do modelo de rede de uma opção de ação como entrada para um modelo de forma fechada e, em seguida, resolver o modelo de forma fechada para o esperado Termo Outros métodos também estão disponíveis para estimar o prazo esperado. No modo binomial, outra decisão que deve ser tomada é quantas etapas de tempo para usar na avaliação ou seja, quanto tempo passa entre nós O número de passos pode ser ilimitado teoricamente desde o preço das ações Os movimentos podem ser infinitos para um período futuro Geralmente, quanto maior o número de passos de tempo, mais preciso será o valor final No entanto, à medida que mais passos de tempo são adicionados, o aumento incremental na precisão diminui O número de passos de tempo assume mais importância em um Robusto, em que mais etapas de tempo podem ser necessárias para modelar adequadamente as estruturas de prazo de volatilidades e taxas de juros, bem como comportamento de exercício de funcionário. Para opções americanas ou prêmios similares, podem ser inseridos mais dois inputs. Suboptimal factor and. Post Por exemplo, um fator de exercício suboptimal de 2 significa que o exercício é geralmente esperado para ocorrer quando o preço da ação é duas vezes a ação acionária. Ns preço de exercício A teoria de preço de opções geralmente sustenta que o tempo otimizado ou que maximiza o lucro para exercer uma opção está no final do prazo da opção, portanto, se uma opção for exercida antes do fim de seu prazo, esse exercício é referido Como suboptimal Exercício Suboptimal também é referido como exercício inicial Suboptimal ou exercício precoce afeta o prazo esperado de uma opção. Independentemente da técnica de avaliação ou modelo selecionado, uma entidade deve desenvolver estimativas razoáveis ​​e suportáveis ​​para cada hipótese utilizada no modelo, incluindo a Opção de ações de empregado ou instrumento similar prazo esperado, levando em conta tanto o prazo contratual da opção e os efeitos do exercício esperado empregados e post-vesting comportamento de terminação de emprego. Option123 fornece duas opções para inserir todas as entradas sob o modelo binomial constante entradas Sobre o prazo do contrato e os inputs variáveis ​​a serem introduzidos em cada nó durante o prazo do contrato. Se os inputs constantes são selecionados Se o pressuposto de entradas variáveis ​​for selecionado neste Programa, exceto o Preço de Exercício e o Preço de Ações dos ativos subjacentes, todos os outros insumos podem ser inseridos diferentemente em cada nó ao longo do período Como indicado no diagrama abaixo, a entrada para taxa livre de risco, rendimento de dividendos, volatilidade esperada ea taxa de terminação são registradas em cada nó. Modelo de precificação de opções de Black-Scholes. No início dos anos 1970, Fischer Black e Myron Scholes fizeram um Grande descoberta derivando uma equação diferencial que deve ser pelo preço de qualquer derivado dependente de uma ação sem pagamento de dividendos Eles usaram a equação para calcular os valores para a opção de compra e venda européia sobre o estoque Em 1997, eles foram premiados Noble. Para calcular o valor das opções de ações usando Black-Scholes Option Pricing Model, cinco entradas são necessárias preço das ações, preço de exercício, taxa livre de risco, tempo até a data de vencimento e volatilidade Black-Scholes Ge O modelo neralizado tem mais uma hipótese de dividend yield esperado - uma empresa pagando um dividendo contínuo durante a vida da opção De acordo com ASC 718, FAS 123 R ou FAS123, seis entradas são necessárias para calcular o valor justo das opções Black-Scholes Generalized Model is Usado na Opção 123 para calcular o valor justo da opção para empresas públicas eo valor mínimo de opções para empresas não públicas. Modelo de Preços Opcionais de Black-Scholes é o modelo teórico mais freqüentemente mencionado para avaliação de opções no mundo dos negócios O padrão Black - Scholes Modelo de precificação de opções foi projetado para estimar o valor de opções de ações transferíveis Embora o modelo tenha sido utilizado por investidores e profissionais de remuneração, também ganhou maior destaque por sua aceitabilidade como um modelo de avaliação pelo FASB e nas regras de proxy SEC Este modelo Foi originalmente desenvolvido para valorizar os tipos de opções negociáveis, mas o FASB também acredita que seu uso é apropriado para Se o preço de mercado observável não estiver disponível para uma opção de compra de ações ou instrumento similar com os mesmos termos ou condições, a entidade deve estimar o valor justo desse instrumento usando Uma técnica ou modelo de avaliação que atenda aos requisitos e leve em consideração, no mínimo. O preço de exercício da opção. O prazo esperado da opção, levando em consideração tanto a duração contratual da opção quanto os efeitos esperados dos exercícios e Comportamento de terminação de emprego pós-vesting Em um modelo de forma fechada, o termo esperado é uma suposição utilizada ou entrada para o modelo, enquanto que em um modelo de rede, o termo esperado é uma saída do modelo. O preço atual da ação subjacente. A volatilidade esperada do preço da ação subjacente para o prazo esperado da opção. Os dividendos esperados sobre a ação subjacente para o prazo esperado da opção. A taxa de juros sem risco s para o esperado t A opção 123 determina o valor justo das opções com base em ações, usando o modelo de precificação de opções da Black-Scholes ou o modelo binomial que leva em conta o preço da ação na data da outorga, o preço de exercício, a expectativa de vida da opção , A volatilidade do estoque subjacente e os dividendos esperados nela e a taxa de juros livre de risco ao longo da vida esperada da opção Se for utilizado o modelo binomial, o fator suboptimal, a taxa de rescisão pós-aquisição e o número de etapas podem ser inseridos como No entanto, nenhum valor justo pode ser calculado até que todas as suposições tenham sido feitas na Página Frontal, todas as entradas mínimas são inseridas na folha de Valor ou Árvore, e todos os dados de preços têm Foram baixados em planilhas de preços. Dois dos seis insumos necessários designados pelo FASB são relativamente diretos e são aplicados de forma consistente para todas as empresas. O preço das ações na data de gra Nt e preço de exercício geral são óbvias preço de exercício também pode ser nomeado como preço de exercício ou preço de subsídio são todos intercambiáveis ​​no Manual. Volatility Calculation. Per ASC 718 ou FAS 123 R, uma entrada de volatilidade é sempre necessário para a avaliação de um baseado em ações Prêmio com Modelo Binomial ou Black-Scholes Opção Modelo de Preços Out das seis entradas exigidas por estes dois modelos de preços de opções, a volatilidade é o mais difícil de estimar. Volatilidade é uma medida do montante pelo qual um preço das ações tem flutuado ou é esperado A flutuar durante um determinado período de tempo Como é geralmente o caso, a materialidade deve ser considerada ao estabelecer o grau de precisão necessária para esta estimativa A volatilidade não é um fator beta de ações O fator beta mede a flutuação de preço de uma ação em relação à média do mercado Flutuação, enquanto que a volatilidade é uma medida da variação de preço de uma ação própria em relação a um período anterior. A oação123 calcula automaticamente a volatilidade com base no historiador Se você optar por não usar a volatilidade histórica calculada, também poderá introduzir a volatilidade estimada manualmente na planilha de Valor. O cálculo da volatilidade histórica é incorporado no Programa Depois de inserir os dados de preço na planilha de preços relacionados e estimar a expectativa de vida da opção na planilha Valor, a volatilidade durante o período histórico com o comprimento igual à expectativa de vida da opção será computada e exibida na planilha Valor depois de clicar em Calcular valores O FAS123 recomenda a utilização de pelo menos 20-30 observações de preços e, de preferência, mais, para calcular uma medida estatisticamente válida. Se as observações, definidas com base na expectativa de vida da opção e no intervalo de tempo usado para calcular a volatilidade, forem inferiores a 20 , O Programa lembrá-lo-á. Você pode continuar a calcular a volatilidade do valor justo para um item de subsídio, mesmo as observações são menos de 20, como lo Ng como o cálculo é matematicamente computável ou seja, as observações são maiores ou iguais a 3.O FASB exige que a estimativa do valor justo da premiação seja baseada na volatilidade esperada durante a vida esperada da opção. Portanto, se a volatilidade baseada em flutuações históricas de preços for Não representativos da volatilidade esperada ao longo da vida esperada da opção, os ajustes à volatilidade histórica podem ser necessários As razões por trás de qualquer desvio da volatilidade histórica devem ser documentadas. Para uma entidade cujas ações ordinárias tenham se tornado recentemente negociadas publicamente e em alguns outros casos , sufficient historical data may not be available to calculate volatility In those situations, expected volatility may be based on the average volatility of similar entities at comparable levels in their history. Similarly, an entity whose common stock has been publicly traded for only a few years generally becomes less volatile as more trading experience has been gained and, therefore , might appropriately place more weight on recent experience An entity also might consider the stock price volatility of similar entities. In addition, periods containing nonrecurring events that clearly cause abnormal effects on the calculation of historical volatility such as a failed takeover bid or an isolated major restructuring might be disregarded for that historical calculation. The FASB acknowledges that a range of reasonable volatility expectations may exist If one amount within that range is a better estimate than any other amount, it should be used Otherwise, it is appropriate to use an expected volatility estimate at the low end of that reasonable range. In Option123 , the summary assumptions used for volatility calculation are presented on the top of Price History , Weekly Price , or Monthly Price worksheet, depending on the type of price you selected on Front Page However, you may not manipulate the historical volatility calculations on any of the price worksheets. FASB sugg ests that price observations should be consistent at regular intervals i e daily, weekly, monthly, etc , thus it should not be change it in the future once you select the proper time-interval on Front Page , unless other intervals provide better estimate Therefore, the only alternative to manipulate historical volatility calculation is to change the expected life of option on Value worksheet. Expected Life of Option. The expected life of option is the number of years expected to elapse before the grantees exercise the options, SARs payable in shares, or similar equity awards As is generally the case, materiality should be considered when establishing the degree of precision necessary for this estimate Expected life is less than the contractual term, but is always at least as long as the vesting period. The expected life is based on several factors, including the company s past experience with similar awards, the vesting period of the award, the volatility of the underlying stock, and curr ent expectations Also, when estimating the expected option life, it may be helpful to stratify the grantees if there is likely to be a significant difference in their option exercise behavior. The following factors to consider when estimating the expected term of an option. The vesting period of the award. Employees historical exercise and post-vesting employment termination behavior for similar grants. The expected volatility of the stock. Blackout periods and other coexisting arrangements such as agreements that allow for exercise to automatically occur during blackout periods if certain conditions are satisfied. Employees ages, lengths of service, and home jurisdictions i e domestic or foreign. External data, if it is more appropriate or internal data is not available. Aggregation by homogeneous employee groups. If Binomial model is selected in Option123, the expected term is automatically calculated using Black-Scholes model However, if the expected volatility is too higher, say greater tha n 150 in some case, the calculated expected term may not be reasonable and the Program may replace it with contract term instead. Expected Dividend Yield. This is the expected annual dividend yield over the expected life of the option, expressed as a percentage of the stock price on the date of grant As is generally the case, materiality should be considered when establishing the degree of precision necessary for this estimate. Estimating expected dividends over the expected term of the option requires judgment ASC 718 or FAS 123 R provides the following guidance on estimating expected dividends. Option-pricing models generally call for expected dividend yield as an assumption However, the models may be modified to use an expected dividend amount rather than a yield An entity may use either its expected yield or its expected payments Additionally, an entity s historical pattern of dividend increases or decreases should be considered For example, if an entity has historically increased divi dends by approximately 3 percent per year, its estimated share option value should not be based on a fixed dividend amount throughout the share option s expected term As with other assumptions in an option-pricing model, an entity should use the expected dividends that would likely be reflected in an amount at which the option would be exchanged. If an entity has a past history of increases in dividends that is reasonably expected to continue in the future, the current dividend yield should be modified to reflect that expectation If an entity has not paid dividends in the past but has announced it will begin paying dividends representing a certain yield that should be used as the expected dividend yield. Adjustments to reflect expected changes from a current dividend yield generally should be based on publicly available information However, some latitude is allowed, and if an emerging entity with no history of paying dividends reasonably expects to declare dividends during the expected l ife of the option, it might consider the dividend payments of a comparable peer group in determining its expected dividend assumption, weighted to reflect the period during which dividends are expected to be paid If dividend equivalents are paid to the grantee or are applied to reduce the exercise price, a dividend yield of zero should be used. Expected Dividends under Binomial Model Binomial model can be adapted to use an expected dividend amount rather than a yield and, therefore, can also take into account the impact of anticipated dividend changes In Option123, if variable inputs method is selected, expected dividend may be entered differently at each node over the entire contract term Such approaches might better reflect expected future dividends, as dividends do not always move in lock-step with changes in the company s stock price Expected dividend estimates in a lattice model should be determined based on the general guidance provided above. The FASB acknowledges that a range of reasonable expectations as to dividend yield may exist If one amount within that range is a better estimate than any other amount, it should be used Otherwise, it is appropriate to use an estimate at the high end of that reasonable range for the expected dividend yield which, because of its inverse relationship, would result in the lowest reasonable fair value estimate. In Option123 , the dividend amount entered on Price History , Weekly Price , or Monthly Price worksheet is used for volatility calculation, while the Annual Dividend Yield entered on Value worksheet is used to compute the fair value of stock-based options Variable dividend yields are to be entered on Tree worksheet. Risk Free Rate. For a U S employer, the risk-free interest rate is the rate currently available for zero-coupon U S Government issues with a remaining term equal to the expected life of the options In a cash option, the assumed risk-free interest rate discount rate represents the return on the cash that will no t be paid until exercise. Risk-Free Interest Rate under Binomial Model If variable risk free rates are to be used under Binomial Model in Option123, a U S entity issuing an option on its own shares must use implied yields from the U S Treasury zero-coupon yield curve over the expected term of the option as its risk-free interest rate assumption if it is using a lattice model incorporating the option s contractual term That is, at each node in the lattice, the company would use the forward rate starting on the date of the node, with a term equal to the period until the next node Such inputs need to be entered on Tree worksheet in Option123.For your reference to the risk free rate, the U S Treasury Securities interest rate data is provided on Risk Free Rate worksheet Periodical update is necessary and available on our web-site if you want to use the provided data as risk free rate. Graded Vesting Schedule. For awards that vest on a cliff basis, i e all at once , the expense would be recogni zed on a straight-line basis over the vesting period If different portions of the overall award vest at different dates, this is called graded vesting For options with graded vesting, companies should consider separating the grants into portions based on their vesting terms because in some cases the expected option lives of each portion could differ significantly. Per ASC 718 or FAS 123 R , for an award with ONLY Service condition that has graded vesting schedule, an entity may decide to recognize compensation cost. a on a straight-line basis as if the award was, in-substance, multiple awards or b on a straight-line basis over the requisite service period for the entire award. However, per ASC 718 or FAS 123 R , the amount of compensation cost recognized at any date must at least equal the portion of the grant-date value of the award that is vested at that date. The choice of attribution method is an accounting policy decision that should be applied consistently to all share-based payments subject to graded service vesting However, this choice does not extend to awards that are subject to performance vesting The compensation cost for each vesting tranche in an award subject to performance vesting must be recognized ratably from the service inception date to the vesting date for each tranche. In Option123 , the awards with graded vesting schedules are still recorded as multiple grant items, instead of just on grant item, but you can choose to recognize compensation cost either by a or b. If the first t ranche is vested immediately on the grant date, the above straight-line attribution method can not be applied as it does not meet the requirement of ASC 718 or FAS 123 R , because the amount of compensation cost recognized at the grant date, practically 0 or 0 , does NOT equal the portion of the grant-date value of the award, 25 , that is vested at that date. Accounting and Expense Allocation. Under ASC 718 or FAS 123 R, expense is recognized only for options that ultimately are vested Compensation expense is not recognized for options that are forfeited because grantees fail to fulfill service requirement Therefore, while the fair value per option would not be re measured, the number of options actually vesting may change, and this would require re-measurement of aggregate compensation expense Compensation expense is not reversed for options that expire unexercised, even if the options turn out to be worthless because the stock price declined. In Option123 , the expense allocation calcul ates the aggregate value of the total award and allocates it over the vesting period. Under ASC 718 or FAS 123 R, if options are not ultimately vested, no compensation cost should be recognized all expense recognized previously should be reversed However, Per FAS 123 R , regardless the nature and numbers of conditions that must be satisfied, the existence of a market condition requires recognition of compensation cost if the requisite service is rendered, even if the market condition is never satisfied. Forfeiture Estimation. When recognizing compensation cost under ASC 718, FAS 123 R, or FAS 123, two methods of accounting are allowed for forfeitures related to continuing employment Estimated and Actual An employer could elect to estimate forfeitures or could recognize compensation cost assuming all awards will vest and reverse recognized compensation cost for forfeited awards when the awards are actually forfeited However, FAS 123 R eliminates the latter accounting alternative and requir es that employers estimate forfeitures resulting from the failure to satisfy service or performance conditions when recognizing compensation cost. Those estimates must be evaluated each reporting period and adjusted, if necessary, by recognizing the cumulative effect of the change in estimate on compensation cost recognized in prior periods to adjust the compensation cost recognized to date to the amount that would have been recognized if the new estimate of forfeitures had been used since the grant date. An employer s estimate of forfeitures should be adjusted as actual forfeitures differ from its estimates, resulting in the recognition of compensation cost only for those awards that actually vest. In Option123 , the initial forfeiture is entered on Basic Info worksheet, and the compensation cost then is recognized over the requisite service period, net of initial estimated forfeiture Estimation adjustment and Actual forfeiture cancellation are entered differently in Option123.All adjust ments to initial estimation or prior estimation can be done Exp Sum worksheet All actual forfeiture needs to be entered on Basic Info in order to report actual forfeiture properly. However, you may always enter both estimation adjustment and actual forfeiture cancellation on Basic Info worksheet All forfeitures, including initial estimation, estimation adjustment, and actual forfeiture, are either entered or transferred onto Exp Sum worksheet. When performance targets also exist, companies must make a best estimate of the number of awards expected to be earned based on attainment of the target If the company elects the estimated forfeitures method for continued employment, a further estimate must be made for awards that will be forfeited based on continued employment. Similar to the requirements of ASC 718, FAS 123, or FAS 123 R requires that the income tax effects of share-based payments be recognized for financial reporting purposes only if such awards would result in deductions on the company s income tax return Generally, the amount of income tax benefit recognized in any period is equal to the amount of compensation cost recognized multiplied by the employer s statutory tax rate An offsetting deferred tax asset also is recognized. If the tax deduction reflected on the company s income tax return for an award generally at option exercise or share vesting exceeds the cumulative amount of compensation cost recognized in the financial statements for that award, the excess tax benefit is recognized as an increase to additional paid-in capital. Alternatively, the tax deduction reported in the tax return may be less than the cumulative compensation cost recognized for financial reporting purposes The deferred tax asset in excess of the benefit of the tax deduction needs to be written-off.1 In equity to the extent that additional paid-in capital has been recognized APIC credits for excess tax deductions from previous employee share-based payments accounted for under ASC 718 or FAS 123 regardless of whether or not an entity elected to recognize compensation cost in the financial statements or only in pro forma disclosures or under ASC 718 OR FAS 123 R , and.2 In operations income tax expense , to the extent the write-off exceeds previous excess tax benefits recognized in equity. Option123 tax-effects compensation expense over the vesting period Unlike other programs, this Program has the ability to adjust deferred tax accounts for any tax rate changes that arise during the vesting period Accounting for income taxes related to share-based compensation can be complicated, consulting to your tax advisor may be necessary Tax rates are entered in the Forfeiture Estimate part on Exp Sum worksheet. Presentation and Disclosure. ASC 718 or FAS 123 R s requirement that the compensation cost associated with share-based payments be recognized in the financial statements eliminating the pro forma disclosure alternative is a significant change in accounting for many compa nies that, in some cases, will be recognizing that compensation cost in their financial statements for the first time. ASC 718 or FAS 123 R require entities to provide disclosures with respect to share-based payments to employees and non - employees that satisfy the following objectives. An entity with one or more share-based payment arrangements shall disclose information that enables users of the financial statements to understand. The nature and terms of such arrangements that existed during the period and the potential effects of those arrangements on shareholders. The effect of compensation cost arising from share-based payment arrangements on the income statement. The method of estimating the fair value of the goods or services received, or the fair value of the equity instruments granted or offered to grant , during the period. The cash flow effects resulting from share-based payment arrangements. ASC 718 or FAS 123 R indicates the minimum information needed to achieve those objectives and illustrate how the disclosure requirements might be satisfied In some circumstances, an entity may need to disclose information beyond that required by ASC 718 or FAS 123 R to achieve the disclosure objectives. An entity that acquires goods or services other than employee services in share-based payment transactions shall provide disclosures similar to those required by ASC 718 or FAS 123R to the extent that those disclosures are important to an understanding of the effects of those transactions on the financial statements In addition, an entity that has multiple share-based payment arrangements with employees shall disclose information separately for different types of awards under those arrangements to the extent that differences in the characteristics of the awards make separate disclosure important to an understanding of the entity s use of share-based compensation. In Option123 , the following disclosures are provided in both interim and annual report For current fiscal period, the number of shares, weighted average exercise price, weighted remaining contract term, and aggregate intrinsic value for. Those outstanding at the end of the year. Those exercisable or convertible at the end of year. Exercised or converted. Forfeited, and. For current fiscal period, the number and weighted grant-date fair value intrinsic value for. Those non-vested at the beginning of the year. Those non-vested at the end of the year. Those granted. For current fiscal period, the summary information of the following assumptions. Expected volatility. Weighted-average volatility. Expected dividend. Expected term. Risk-free rate. Download a Free Demo with limited functions. Daily Foreign Exchange Rate In Namibia. Market participants all over the world will scrutinise this report, as it holds the clue to the timing of the next Federal Reserve Fed interest rate increase In addition to this, the US average hourly earnings and unemployment rate data will also be keenly followed by investors Daily Foreign Ex change Rate In Namibia Zurn Zs880 Grate Options Strategies TorFX is a leading provider of foreign exchange services, offering ultra competitive exchange rates Our customers benefit from an unrivalled personal service and In the UK, the just released data showed that the nation s manufacturing production rose less than expected in August, but industrial production declined Until 31 December 2008 the exchange rates were quoted directly against the Slovak koruna, i e After the daily exchange rates published by the ECB started to be posted on the NBS website, exchanges rates included among those rates were omitted from NBS s Exchange Rates of Selected Foreign Currencies. Questioning To Earn Money Online In Finland. Since 1 January 2009 exchange rates have been quoted indirectly against the euro, i e they show the relative value of the foreign currencies against one euro Daily Foreign Exchange Rate In Namibia Jse Stock Exchange Market Currency resources on the net Home Home Exchange rates Pre dictions and volatility Summaries Foreign Per Diem Rates by Location You may use the dropdown box below to select a country Entering the first letter of the country name will jump to that portion of fx Daily allows you to obtain a multi-currency table of currency exchange rates in ASCII, HTML or CSV format TorFX is a leading provider of foreign exchange services, offering ultra competitive exchange rates Our customers benefit from an unrivalled personal service and Nonfarm payrolls are expected to have risen during the last month. Investors now await the release of Britian s NIESR GDP estimate for 3 months ended September, due later today Daily Foreign Exchange Rate In Namibia To obtain your rates, select the language, date, your home currency and a list of currencies for which you would like to generate the table Calendar Effects In Oman Stock Market Currency resources on the net Home Home Exchange rates Predictions and volatility Summaries Our customers benefit from an unrivalled pers onal service and substantial savings on currency transactions Option, Um Online Geld Verdienen In Deutschland TorFX is a leading provider of foreign exchange services, offering ultra competitive exchange rates Our customers benefit from an unrivalled personal service and Please complete the form below and a member of our team will respond shortly with your quote. they showed the relative value of the Slovak koruna against a set unit of the foreign currency they show the relative value of the foreign currencies against one euro Daily Foreign Exchange Rate In Namibia To Exchange Currency For Forex Rates Colombia Notes for download the Exchange Rates of Selected Foreign Currencies against the EUR Daily Foreign Exchange Rate In NamibiaMeanwhile in the Eurozone, German, French and Spanish industrial output data for August brought some cheer to the region Our customers benefit from an unrivalled personal service and substantial savings on currency transactions. In January 1996 Nrodn banka Slov enska began publishing Exchange Rates of Selected Foreign Currencies on a monthly basis Daily Foreign Exchange Rate In Namibia This is the page of United States Dollar USD to Namibian Dollar NAD conversion, below you can find the latest exchange rate between them and is updated every 1 Of Silver On Forex Online Djibouti Tor FX is a leading provider of foreign exchange services, offering ultra competitive exchange rates Work Of The Exchange Forex Today In Cyprus. Read Daily Foreign Exchange Rate In Namibia Next. Precio del DOLAR HOY, Tipo de Cambio, Cotizacin del Dlar, Conversor de Monedas, Cambio de Divisas, Precio del Euro Cotizacion del dolar en chile. The gallery of comics and cartoons on finance, economy, politics and All CFDs stocks, indexes, futures and Forex prices are not provided by. Chart Forum Indicators Excel Formulae for Calculating EMA Nielsen Supply Demand Indicator canam 21 1 My Favourite Indicator. Connect With Us. A Tutorial on Data Representation. Integers, Floating-point N umbers, and Characters. Number Systems. Human beings use decimal base 10 and duodecimal base 12 number systems for counting and measurements probably because we have 10 fingers and two big toes Computers use binary base 2 number system, as they are made from binary digital components known as transistors operating in two states - on and off In computing, we also use hexadecimal base 16 or octal base 8 number systems, as a compact form for represent binary numbers. Decimal Base 10 Number System. Decimal number system has ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, called digit s It uses positional notation That is, the least-significant digit right-most digit is of the order of 10 0 units or ones , the second right-most digit is of the order of 10 1 tens , the third right-most digit is of the order of 10 2 hundreds , and so on For example. We shall denote a decimal number with an optional suffix D if ambiguity arises. Binary Base 2 Number System. Binary number system has two symbols 0 and 1, called bits It is also a positional notation for example. We shall denote a binary number with a suffix B Some programming languages denote binary numbers with prefix 0b e g 0b1001000 , or prefix b with the bits quoted e g b 10001111.A binary digit is called a bit Eight bits is called a byte why 8-bit unit Probably because 8 2 3.Hexadecimal Base 16 Number System. Hexadecimal number system uses 16 symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F, called hex digits It is a positional notation for example. We shall denote a hexadecimal number in short, hex with a suffix H Some programming languages denote hex numbers with prefix 0x e g 0x1A3C5F , or prefix x with hex digit quoted e g x C3A4D98B. Each hexadecimal digit is also called a hex digit Most programming languages accept lowercase a to f as well as uppercase A to Fputers uses binary system in their internal operations, as they are built from binary digital electronic components However, writing or reading a long sequence of binary bits is cumbersome and error-prone Hexadecimal system is used as a compact form or shorthand for binary bits Each hex digit is equivalent to 4 binary bits, i e shorthand for 4 bits, as follows. Replace each hex digit by the 4 equivalent bits, for examples. Conversion from Binary to Hexadecimal. Starting from the right-most bit least-significant bit , replace each group of 4 bits by the equivalent hex digit pad the left-most bits with zero if necessary , for examples. It is important to note that hexadecimal number provides a compact form or shorthand for representing binary bits. Conversion from Base r to Decimal Base 10.Given a n - digit base r number dn-1 dn-2 dn-3 d3 d2 d1 d0 base r , the decimal equivalent is given by. Conversion from Decimal Base 10 to Base r. Use repeated division remainder For example. The above procedure is actually applicable to conversion between any 2 base systems For example. General Conversion between 2 Base Systems with Fractional Part. Separate the integral and the fractional parts. For the integral part, divide by the target radix repeatably, and collect the ramainder in reverse order. For the fractional part, multiply the fractional part by the target radix repeatably, and collect the integral part in the same order. Exercises Number Systems Conversion. Convert the following decimal numbers into binary and hexadecimal numbers. Convert the following binary numbers into hexadecimal and decimal numbers. Convert the following hexadecimal numbers into binary and decimal numbers. Convert the following decimal numbers into binary equivalent. Answers You could use the Windows Calculator to carry out number system conversion, by setting it to the scientific mode Run calc Select View menu Choose Programmer or Scientific mode.1101100B 1001011110000B 10001100101000B 6CH 12F0H 2328H.218H 80H AAAH 536D 128D 2730D.10101011110011011110B 1001000110100B 100000001111B 703710D 4660D 2063Dputer Memory Data Representationputer uses a fixed number of bits to represen t a piece of data, which could be a number, a character, or others A n - bit storage location can represent up to 2 n distinct entities For example, a 3-bit memory location can hold one of these eight binary patterns 000 001 010 011 100 101 110 or 111 Hence, it can represent at most 8 distinct entities You could use them to represent numbers 0 to 7, numbers 8881 to 8888, characters A to H , or up to 8 kinds of fruits like apple, orange, banana or up to 8 kinds of animals like lion, tiger, etc. Integers, for example, can be represented in 8-bit, 16-bit, 32-bit or 64-bit You, as the programmer, choose an appropriate bit-length for your integers Your choice will impose constraint on the range of integers that can be represented Besides the bit-length, an integer can be represented in various representation schemes, e g unsigned vs signed integers An 8-bit unsigned integer has a range of 0 to 255, while an 8-bit signed integer has a range of -128 to 127 - both representing 256 distinct numbe rs. It is important to note that a computer memory location merely stores a binary pattern It is entirely up to you, as the programmer, to decide on how these patterns are to be interpreted For example, the 8-bit binary pattern 0100 0001B can be interpreted as an unsigned integer 65 or an ASCII character A or some secret information known only to you In other words, you have to first decide how to represent a piece of data in a binary pattern before the binary patterns make sense The interpretation of binary pattern is called data representation or encoding Furthermore, it is important that the data representation schemes are agreed-upon by all the parties, i e industrial standards need to be formulated and straightly followed. Once you decided on the data representation scheme, certain constraints, in particular, the precision and range will be imposed Hence, it is important to understand data representation to write correct and high-performance programs. Rosette Stone and the Decipherme nt of Egyptian Hieroglyphs. Egyptian hieroglyphs next-to-left were used by the ancient Egyptians since 4000BC Unfortunately, since 500AD, no one could longer read the ancient Egyptian hieroglyphs, until the re-discovery of the Rosette Stone in 1799 by Napoleon s troop during Napoleon s Egyptian invasion near the town of Rashid Rosetta in the Nile Delta. The Rosetta Stone left is inscribed with a decree in 196BC on behalf of King Ptolemy V The decree appears in three scripts the upper text is Ancient Egyptian hieroglyphs the middle portion Demotic script, and the lowest Ancient Greek Because it presents essentially the same text in all three scripts, and Ancient Greek could still be understood, it provided the key to the decipherment of the Egyptian hieroglyphs. The moral of the story is unless you know the encoding scheme, there is no way that you can decode the data. Reference and images Wikipedia. Integer Representation. Integers are whole numbers or fixed-point numbers with the radix poin t fixed after the least-significant bit They are contrast to real numbers or floating-point numbers where the position of the radix point varies It is important to take note that integers and floating-point numbers are treated differently in computers They have different representation and are processed differently e g floating-point numbers are processed in a so-called floating-point processor Floating-point numbers will be discussed laterputers use a fixed number of bits to represent an integer The commonly-used bit-lengths for integers are 8-bit, 16-bit, 32-bit or 64-bit Besides bit-lengths, there are two representation schemes for integers. Unsigned Integers can represent zero and positive integers. Signed Integers can represent zero, positive and negative integers Three representation schemes had been proposed for signed integers. Sign-Magnitude representation.1 s Complement representation.2 s Complement representation. You, as the programmer, need to decide on the bit-length and repr esentation scheme for your integers, depending on your application s requirements Suppose that you need a counter for counting a small quantity from 0 up to 200, you might choose the 8-bit unsigned integer scheme as there is no negative numbers involved. n - bit Unsigned Integers. Unsigned integers can represent zero and positive integers, but not negative integers The value of an unsigned integer is interpreted as the magnitude of its underlying binary pattern. Example 1 Suppose that n 8 and the binary pattern is 0100 0001B the value of this unsigned integer is 1 2 0 1 2 6 65D. Example 2 Suppose that n 16 and the binary pattern is 0001 0000 0000 1000B the value of this unsigned integer is 1 2 3 1 2 12 4104D. Example 3 Suppose that n 16 and the binary pattern is 0000 0000 0000 0000B the value of this unsigned integer is 0.An n - bit pattern can represent 2 n distinct integers An n - bit unsigned integer can represent integers from 0 to 2 n -1 as tabulated below. Signed Integers. Signed integers can represent zero, positive integers, as well as negative integers Three representation schemes are available for signed integers. Sign-Magnitude representation.1 s Complement representation.2 s Complement representation. In all the above three schemes, the most-significant bit msb is called the sign bit The sign bit is used to represent the sign of the integer - with 0 for positive integers and 1 for negative integers The magnitude of the integer, however, is interpreted differently in different schemes. n - bit Sign Integers in Sign-Magnitude Representation. In sign-magnitude representation. The most-significant bit msb is the sign bit with value of 0 representing positive integer and 1 representing negative integer. The remaining n -1 bits represents the magnitude absolute value of the integer The absolute value of the integer is interpreted as the magnitude of the n -1 - bit binary pattern. Example 1 Suppose that n 8 and the binary representation is 0 100 0001B Sign bit is 0 positive Absol ute value is 100 0001B 65D Hence, the integer is 65D. Example 2 Suppose that n 8 and the binary representation is 1 000 0001B Sign bit is 1 negative Absolute value is 000 0001B 1D Hence, the integer is -1D. Example 3 Suppose that n 8 and the binary representation is 0 000 0000B Sign bit is 0 positive Absolute value is 000 0000B 0D Hence, the integer is 0D. Example 4 Suppose that n 8 and the binary representation is 1 000 0000B Sign bit is 1 negative Absolute value is 000 0000B 0D Hence, the integer is -0D. The drawbacks of sign-magnitude representation are. There are two representations 0000 0000B and 1000 0000B for the number zero, which could lead to inefficiency and confusion. Positive and negative integers need to be processed separately. n - bit Sign Integers in 1 s Complement Representation. In 1 s complement representation. Again, the most significant bit msb is the sign bit with value of 0 representing positive integers and 1 representing negative integers. The remaining n -1 bits represe nts the magnitude of the integer, as follows. for positive integers, the absolute value of the integer is equal to the magnitude of the n -1 - bit binary pattern. for negative integers, the absolute value of the integer is equal to the magnitude of the complement inverse of the n -1 - bit binary pattern hence called 1 s complement. Example 1 Suppose that n 8 and the binary representation 0 100 0001B Sign bit is 0 positive Absolute value is 100 0001B 65D Hence, the integer is 65D. Example 2 Suppose that n 8 and the binary representation 1 000 0001B Sign bit is 1 negative Absolute value is the complement of 000 0001B i e 111 1110B 126D Hence, the integer is -126D. Example 3 Suppose that n 8 and the binary representation 0 000 0000B Sign bit is 0 positive Absolute value is 000 0000B 0D Hence, the integer is 0D. Example 4 Suppose that n 8 and the binary representation 1 111 1111B Sign bit is 1 negative Absolute value is the complement of 111 1111B i e 000 0000B 0D Hence, the integer is -0D. Again, the drawbacks are. There are two representations 0000 0000B and 1111 1111B for zero. The positive integers and negative integers need to be processed separately. n - bit Sign Integers in 2 s Complement Representation. In 2 s complement representation. Again, the most significant bit msb is the sign bit with value of 0 representing positive integers and 1 representing negative integers. The remaining n -1 bits represents the magnitude of the integer, as follows. for positive integers, the absolute value of the integer is equal to the magnitude of the n -1 - bit binary pattern. for negative integers, the absolute value of the integer is equal to the magnitude of the complement of the n -1 - bit binary pattern plus one hence called 2 s complement. Example 1 Suppose that n 8 and the binary representation 0 100 0001B Sign bit is 0 positive Absolute value is 100 0001B 65D Hence, the integer is 65D. Example 2 Suppose that n 8 and the binary representation 1 000 0001B Sign bit is 1 negative Absolute value is the complement of 000 0001B plus 1 i e 111 1110B 1B 127D Hence, the integer is -127D. Example 3 Suppose that n 8 and the binary representation 0 000 0000B Sign bit is 0 positive Absolute value is 000 0000B 0D Hence, the integer is 0D. Example 4 Suppose that n 8 and the binary representation 1 111 1111B Sign bit is 1 negative Absolute value is the complement of 111 1111B plus 1 i e 000 0000B 1B 1D Hence, the integer is -1Dputers use 2 s Complement Representation for Signed Integers. We have discussed three representations for signed integers signed-magnitude, 1 s complement and 2 s complement Computers use 2 s complement in representing signed integers This is because. There is only one representation for the number zero in 2 s complement, instead of two representations in sign-magnitude and 1 s complement. Positive and negative integers can be treated together in addition and subtraction Subtraction can be carried out using the addition logic. Example 1 Addition of Two Positive Integers S uppose that n 8, 65D 5D 70D. Example 2 Subtraction is treated as Addition of a Positive and a Negative Integers Suppose that n 8, 5D - 5D 65D -5D 60D. Example 3 Addition of Two Negative Integers Suppose that n 8, -65D - 5D -65D -5D -70D. Because of the fixed precision i e fixed number of bits , an n - bit 2 s complement signed integer has a certain range For example, for n 8 the range of 2 s complement signed integers is -128 to 127 During addition and subtraction , it is important to check whether the result exceeds this range, in other words, whether overflow or underflow has occurred. Example 4 Overflow Suppose that n 8, 127D 2D 129D overflow - beyond the range. Example 5 Underflow Suppose that n 8, -125D - 5D -130D underflow - below the range. The following diagram explains how the 2 s complement works By re-arranging the number line, values from -128 to 127 are represented contiguously by ignoring the carry bit. Range of n - bit 2 s Complement Signed Integers. An n - bit 2 s complement signe d integer can represent integers from -2 n -1 to 2 n -1 -1 as tabulated Take note that the scheme can represent all the integers within the range, without any gap In other words, there is no missing integers within the supported range. 2 63 -1 9,223,372,036,854,775,807 18 digits. Decoding 2 s Complement Numbers. Check the sign bit denoted as S. If S 0 the number is positive and its absolute value is the binary value of the remaining n -1 bits. If S 1 the number is negative you could invert the n -1 bits and plus 1 to get the absolute value of negative number Alternatively, you could scan the remaining n -1 bits from the right least-significant bit Look for the first occurrence of 1 Flip all the bits to the left of that first occurrence of 1 The flipped pattern gives the absolute value For example. Big Endian vs Little Endian. Modern computers store one byte of data in each memory address or location, i e byte addressable memory An 32-bit integer is, therefore, stored in 4 memory addresses. The term Endian refers to the order of storing bytes in computer memory In Big Endian scheme, the most significant byte is stored first in the lowest memory address or big in first , while Little Endian stores the least significant bytes in the lowest memory address. For example, the 32-bit integer 12345678H 2215053170 10 is stored as 12H 34H 56H 78H in big endian and 78H 56H 34H 12H in little endian An 16-bit integer 00H 01H is interpreted as 0001H in big endian, and 0100H as little endian. Exercise Integer Representation. What are the ranges of 8-bit, 16-bit, 32-bit and 64-bit integer, in unsigned and signed representation. Give the value of 88 0 1 127 and 255 in 8-bit unsigned representation. Give the value of 88 -88 -1 0 1 -128 and 127 in 8-bit 2 s complement signed representation. Give the value of 88 -88 -1 0 1 -127 and 127 in 8-bit sign-magnitude representation. Give the value of 88 -88 -1 0 1 -127 and 127 in 8-bit 1 s complement representation. The range of unsigned n - bit integers is 0, 2 n - 1 The range of n - bit 2 s complement signed integer is -2 n-1 , 2 n-1 -1.88 0101 1000 0 0000 0000 1 0000 0001 127 0111 1111 255 1111 1111. 88 0101 1000 -88 1010 1000 -1 1111 1111 0 0000 0000 1 0000 0001 -128 1000 0000 127 0111 11 11. 88 0101 1000 -88 1101 1000 -1 1000 0001 0 0000 0000 or 1000 0000 1 0000 0001 -127 1111 1111 127 0111 1111. 88 0101 1000 -88 1010 0111 -1 1111 1110 0 0000 0000 or 1111 1111 1 0000 0001 -127 1000 0000 127 0111 1111.Floating-Point Number Representation. A floating-point number or real number can represent a very large 1 23 10 88 or a very small 1 23 10 -88 value It could also represent very large negative number -1 23 10 88 and very small negative number -1 23 10 88 , as well as zero, as illustrated. A floating-point number is typically expressed in the scientific notation, with a fraction F , and an exponent E of a certain radix r , in the form of F r E Decimal numbers use radix of 10 F 10 E while binary numbers use radix of 2 F 2 E. Representation of floating point number is not unique For example, the number 55 66 can be represented as 5 566 10 1 0 5566 10 2 0 05566 10 3 and so on The fractional part can be normalized In the normalized form, there is only a single non-zero digit befo re the radix point For example, decimal number 123 4567 can be normalized as 1 234567 10 2 binary number 1010 1011B can be normalized as 1 0101011B 2 3.It is important to note that floating-point numbers suffer from loss of precision when represented with a fixed number of bits e g 32-bit or 64-bit This is because there are infinite number of real numbers even within a small range of says 0 0 to 0 1 On the other hand, a n - bit binary pattern can represent a finite 2 n distinct numbers Hence, not all the real numbers can be represented The nearest approximation will be used instead, resulted in loss of accuracy. It is also important to note that floating number arithmetic is very much less efficient than integer arithmetic It could be speed up with a so-called dedicated floating-point co-processor Hence, use integers if your application does not require floating-point numbers. In computers, floating-point numbers are represented in scientific notation of fraction F and exponent E with a radix of 2, in the form of F 2 E Both E and F can be positive as well as negative Modern computers adopt IEEE 754 standard for representing floating-point numbers There are two representation schemes 32-bit single-precision and 64-bit double-precision. IEEE-754 32-bit Single-Precision Floating-Point Numbers. In 32-bit single-precision floating-point representation. The most significant bit is the sign bit S , with 0 for positive numbers and 1 for negative numbers. The following 8 bits represent exponent E. The remaining 23 bits represents fraction F. Normalized Form. Let s illustrate with an example, suppose that the 32-bit pattern is 1 1000 0001 011 0000 0000 0000 0000 0000 with. F 011 0000 0000 0000 0000 0000.In the normalized form the actual fraction is normalized with an implicit leading 1 in the form of 1 F In this example, the actual fraction is 1 011 0000 0000 0000 0000 0000 1 1 2 -2 1 2 -3 1 375D. The sign bit represents the sign of the number, with S 0 for positive and S 1 for negative number In this example with S 1 this is a negative number, i e -1 375D. In normalized form, the actual exponent is E-127 so-called excess-127 or bias-127 This is because we need to represent both positive and negative exponent With an 8-bit E, ranging from 0 to 255, the excess-127 scheme could provide actual exponent of -127 to 128 In this example, E-127 129-127 2D. Hence, the number represented is -1 375 2 2 -5 5D. De-Normalized Form. Normalized form has a serious problem, with an implicit leading 1 for the fraction, it cannot represent the number zero Convince yourself on this. De-normalized form was devised to represent zero and other numbers. For E 0 the numbers are in the de-normalized form An implicit leading 0 instead of 1 is used for the fraction and the actual exponent is always -126 Hence, the number zero can be represented with E 0 and F 0 because 0 0 2 -126 0.We can also represent very small positive and negative numbers in de-normalized form with E 0 For example, if S 1 E 0 and F 011 0000 0000 0000 0000 0000 The actual fraction is 0 011 1 2 -2 1 2 -3 0 375D Since S 1 it is a negative number With E 0 the actual exponent is -126 Hence the number is -0 375 2 -126 -4 4 10 -39 which is an extremely small negative number close to zero. In summary, the value N is calculated as follows. For 1 E 254, N -1 S 1 F 2 E-127 These numbers are in the so-called normalized form The sign-bit represents the sign of the number Fractional part 1 F are normalized with an implicit leading 1 The exponent is bias or in excess of 127 so as to represent both positive and negative exponent The range of exponent is -126 to 127.For E 0, N -1 S 0 F 2 -126 These numbers are in the so-called denormalized form The exponent of 2 -126 evaluates to a very small number Denormalized form is needed to represent zero with F 0 and E 0 It can also represents very small positive and negative number close to zero. For E 255 it represents special values, such as INF positive and negative infinity and NaN no t a number This is beyond the scope of this article. Example 1 Suppose that IEEE-754 32-bit floating-point representation pattern is 0 10000000 110 0000 0000 0000 0000 0000.Example 2 Suppose that IEEE-754 32-bit floating-point representation pattern is 1 01111110 100 0000 0000 0000 0000 0000.Example 3 Suppose that IEEE-754 32-bit floating-point representation pattern is 1 01111110 000 0000 0000 0000 0000 0001.Example 4 De-Normalized Form Suppose that IEEE-754 32-bit floating-point representation pattern is 1 00000000 000 0000 0000 0000 0000 0001.Exercises Floating-point Numberspute the largest and smallest positive numbers that can be represented in the 32-bit normalized formpute the largest and smallest negative numbers can be represented in the 32-bit normalized form. Repeat 1 for the 32-bit denormalized form. Repeat 2 for the 32-bit denormalized form. Largest positive number S 0 E 1111 1110 254 F 111 1111 1111 1111 1111 1111 Smallest positive number S 0 E 0000 00001 1 F 000 0000 0000 00 00 0000 0000.Same as above, but S 1.Largest positive number S 0 E 0 F 111 1111 1111 1111 1111 1111 Smallest positive number S 0 E 0 F 000 0000 0000 0000 0000 0001.Same as above, but S 1.Notes For Java Users. You can use JDK methods bits or bits to create a single-precision 32-bit float or double-precision 64-bit double with the specific bit patterns, and print their values For examples. IEEE-754 64-bit Double-Precision Floating-Point Numbers. The representation scheme for 64-bit double-precision is similar to the 32-bit single-precision. The most significant bit is the sign bit S , with 0 for positive numbers and 1 for negative numbers. The following 11 bits represent exponent E. The remaining 52 bits represents fraction F. The value N is calculated as follows. Normalized form For 1 E 2046, N -1 S 1 F 2 E-1023.Denormalized form For E 0, N -1 S 0 F 2 -1022 These are in the denormalized form. For E 2047 N represents special values, such as INF infinity , NaN not a number. More on Floating-Point Re presentation. There are three parts in the floating-point representation. The sign bit S is self-explanatory 0 for positive numbers and 1 for negative numbers. For the exponent E , a so-called bias or excess is applied so as to represent both positive and negative exponent The bias is set at half of the range For single precision with an 8-bit exponent, the bias is 127 or excess-127 For double precision with a 11-bit exponent, the bias is 1023 or excess-1023.The fraction F also called the mantissa or significand is composed of an implicit leading bit before the radix point and the fractional bits after the radix point The leading bit for normalized numbers is 1 while the leading bit for denormalized numbers is 0.Normalized Floating-Point Numbers. In normalized form, the radix point is placed after the first non-zero digit, e, g 9 8765D 10 -23D 1 001011B 2 11B For binary number, the leading bit is always 1, and need not be represented explicitly - this saves 1 bit of storage. In IEEE 754 s no rmalized form. For single-precision, 1 E 254 with excess of 127 Hence, the actual exponent is from -126 to 127 Negative exponents are used to represent small numbers 1 0 while positive exponents are used to represent large numbers 1 0 N -1 S 1 F 2 E-127.For double-precision, 1 E 2046 with excess of 1023 The actual exponent is from -1022 to 1023 and N -1 S 1 F 2 E-1023.Take note that n-bit pattern has a finite number of combinations 2 n , which could represent finite distinct numbers It is not possible to represent the infinite numbers in the real axis even a small range says 0 0 to 1 0 has infinite numbers That is, not all floating-point numbers can be accurately represented Instead, the closest approximation is used, which leads to loss of accuracy. The minimum and maximum normalized floating-point numbers are.0000 0001H 0 00000000 00000000000000000000001B E 0, F 00000000000000000000001B D min 0 0 1 2 -126 1 2 -23 2 -126 2 -149 1 4 10 -45.007F FFFFH 0 00000000 11111111111111111111111B E 0, F 11111111111111111111111B D max 0 1 1 2 -126 1-2 -23 2 -126 1 1754942 10 -38.0000 0000 0000 0001H D min 0 0 1 2 -1022 1 2 -52 2 -1022 2 -1074 4 9 10 -324.001F FFFF FFFF FFFFH D max 0 1 1 2 -1022 1-2 -52 2 -1022 4 4501477170144023 10 -308.Special Values. Zero Zero cannot be represented in the normalized form, and must be represented in denormalized form with E 0 and F 0 There are two representations for zero 0 with S 0 and -0 with S 1.Infinity The value of infinity e g 1 0 and - infinity e g -1 0 are represented with an exponent of all 1 s E 255 for single-precision and E 2047 for double-precision , F 0 and S 0 for INF and S 1 for - INF. Not a Number NaN NaN denotes a value that cannot be represented as real number e g 0 0 NaN is represented with Exponent of all 1 s E 255 for single-precision and E 2047 for double-precision and any non-zero fraction. Character Encoding. In computer memory, character are encoded or represented using a chosen character encoding schemes aka character set , charset , character map , or code page. For example, in ASCII as well as Latin1, Unicode, and many other character sets. code numbers 65D 41H to 90D 5AH represents A to Z respectively. code numbers 97D 61H to 122D 7AH represents a to z respectively. code numbers 48D 30H to 57D 39H represents 0 to 9 respectively. It is important to note that the representation scheme must be known before a binary pattern can be interpreted E g the 8-bit pattern 0100 0010B could represent anything under the sun known only to the person encoded it. The most commonly-used character encoding schemes are 7-bit ASCII ISO IEC 646 and 8-bit Latin-x ISO IEC 8859-x for western european characters, and Unicode ISO IEC 10646 for internationalization i18n. A 7-bit encoding scheme such as ASCII can represent 128 characters and symbols An 8-bit character encoding scheme such as Latin-x can represent 256 characters and symbols whereas a 16-bit encoding scheme such as Unicode UCS-2 can represents 65,536 characters and symbols .7-bit ASCII Code aka US-ASCII, ISO IEC 646, ITU-T T 50.ASCII American Standard Code for Information Interchange is one of the earlier character coding schemes. ASCII is originally a 7-bit code It has been extended to 8-bit to better utilize the 8-bit computer memory organization The 8th-bit was originally used for parity check in the early computers. Code numbers 32D 20H to 126D 7EH are printable displayable characters as tabulated. ISO IEC-8859 has 16 parts Besides the most commonly-used Part 1, Part 2 is meant for Central European Polish, Czech, Hungarian, etc , Part 3 for South European Turkish, etc , Part 4 for North European Estonian, Latvian, etc , Part 5 for Cyrillic, Part 6 for Arabic, Part 7 for Greek, Part 8 for Hebrew, Part 9 for Turkish, Part 10 for Nordic, Part 11 for Thai, Part 12 was abandon, Part 13 for Baltic Rim, Part 14 for Celtic, Part 15 for French, Finnish, etc Part 16 for South-Eastern European. Other 8-bit Extension of US-ASCII ASCII Extensions. Beside the standardi zed ISO-8859-x, there are many 8-bit ASCII extensions, which are not compatible with each others. ANSI American National Standards Institute aka Windows-1252 or Windows Codepage 1252 for Latin alphabets used in the legacy DOS Windows systems It is a superset of ISO-8859-1 with code numbers 128 80H to 159 9FH assigned to displayable characters, such as smart single-quotes and double-quotes A common problem in web browsers is that all the quotes and apostrophes produced by smart quotes in some Microsoft software were replaced with question marks or some strange symbols It it because the document is labeled as ISO-8859-1 instead of Windows-1252 , where these code numbers are undefined Most modern browsers and e-mail clients treat charset ISO-8859-1 as Windows-1252 in order to accommodate such mis-labeling. EBCDIC Extended Binary Coded Decimal Interchange Code Used in the early IBM computers. Unicode aka ISO IEC 10646 Universal Character Set. Before Unicode, no single character encoding scheme could represent characters in all languages For example, western european uses several encoding schemes in the ISO-8859-x family Even a single language like Chinese has a few encoding schemes GB2312 GBK, BIG5 Many encoding schemes are in conflict of each other, i e the same code number is assigned to different characters. Unicode aims to provide a standard character encoding scheme, which is universal, efficient, uniform and unambiguous Unicode standard is maintained by a non-profit organization called the Unicode Consortium Unicode is an ISO IEC standard 10646.Unicode is backward compatible with the 7-bit US-ASCII and 8-bit Latin-1 ISO-8859-1 That is, the first 128 characters are the same as US-ASCII and the first 256 characters are the same as Latin-1.Unicode originally uses 16 bits called UCS-2 or Unicode Character Set - 2 byte , which can represent up to 65,536 characters It has since been expanded to more than 16 bits, currently stands at 21 bits The range of the legal codes in IS O IEC 10646 is now from U 0000H to U 10FFFFH 21 bits or about 2 million characters , covering all current and ancient historical scripts The original 16-bit range of U 0000H to U FFFFH 65536 characters is known as Basic Multilingual Plane BMP , covering all the major languages in use currently The characters outside BMP are called Supplementary Characters which are not frequently-used. Unicode has two encoding schemes. UCS-2 Universal Character Set - 2 Byte Uses 2 bytes 16 bits , covering 65,536 characters in the BMP BMP is sufficient for most of the applications UCS-2 is now obsolete. UCS-4 Universal Character Set - 4 Byte Uses 4 bytes 32 bits , covering BMP and the supplementary characters. UTF-8 Unicode Transformation Format - 8-bit. The 16 32-bit Unicode UCS-2 4 is grossly inefficient if the document contains mainly ASCII characters, because each character occupies two bytes of storage Variable-length encoding schemes, such as UTF-8, which uses 1-4 bytes to represent a character, was de vised to improve the efficiency In UTF-8, the 128 commonly-used US-ASCII characters use only 1 byte, but some less-commonly characters may require up to 4 bytes Overall, the efficiency improved for document containing mainly US-ASCII texts. The transformation between Unicode and UTF-8 is as follows.11110uuu 10uuzzzz 10yyyyyy 10xxxxxx. In UTF-8, Unicode numbers corresponding to the 7-bit ASCII characters are padded with a leading zero thus has the same value as ASCII Hence, UTF-8 can be used with all software using ASCII Unicode numbers of 128 and above, which are less frequently used, are encoded using more bytes 2-4 bytes UTF-8 generally requires less storage and is compatible with ASCII The drawback of UTF-8 is more processing power needed to unpack the code due to its variable length UTF-8 is the most popular format for Unicode. UTF-8 uses 1-3 bytes for the characters in BMP 16-bit , and 4 bytes for supplementary characters outside BMP 21-bit. The 128 ASCII characters basic Latin letter s, digits, and punctuation signs use one byte Most European and Middle East characters use a 2-byte sequence, which includes extended Latin letters with tilde, macron, acute, grave and other accents , Greek, Armenian, Hebrew, Arabic, and others Chinese, Japanese and Korean CJK use three-byte sequences. All the bytes, except the 128 ASCII characters, have a leading 1 bit In other words, the ASCII bytes, with a leading 0 bit, can be identified and decoded easily. Example Unicode 60A8H 597DH. UTF-16 Unicode Transformation Format - 16-bit. UTF-16 is a variable-length Unicode character encoding scheme, which uses 2 to 4 bytes UTF-16 is not commonly used The transformation table is as follows. Same as UCS-2 - no encoding.000uuuuu zzzzyyyy yyxxxxxx uuuuu 0.110110ww wwzzzzyy 110111yy yyxxxxxx wwww uuuuu - 1.Take note that for the 65536 characters in BMP, the UTF-16 is the same as UCS-2 2 bytes However, 4 bytes are used for the supplementary characters outside the BMP. For BMP characters, UTF-16 is the same as UCS-2 For supplementary characters, each character requires a pair 16-bit values, the first from the high-surrogates range, uD800- uDBFF , the second from the low-surrogates range uDC00- uDFFF. UTF-32 Unicode Transformation Format - 32-bit. Same as UCS-4, which uses 4 bytes for each character - unencoded. Formats of Multi-Byte e g Unicode Text Files. Endianess or byte-order For a multi-byte character, you need to take care of the order of the bytes in storage In big endian the most significant byte is stored at the memory location with the lowest address big byte first In little endian the most significant byte is stored at the memory location with the highest address little byte first For example, with Unicode number of 60A8H is stored as 60 A8 in big endian and stored as A8 60 in little endian Big endian, which produces a more readable hex dump, is more commonly-used, and is often the default. BOM Byte Order Mark BOM is a special Unicode character having code number of FEFF H which is used to differentiate big-endian and little-endian For big-endian, BOM appears as FE FFH in the storage For little-endian, BOM appears as FF FEH Unicode reserves these two code numbers to prevent it from crashing with another character. Unicode text files could take on these formats. Big Endian UCS-2BE, UTF-16BE, UTF-32BE. Little Endian UCS-2LE, UTF-16LE, UTF-32LE. UTF-16 with BOM The first character of the file is a BOM character, which specifies the endianess For big-endian, BOM appears as FE FFH in the storage For little-endian, BOM appears as FF FEH. UTF-8 file is always stored as big endian BOM plays no part However, in some systems in particular Windows , a BOM is added as the first character in the UTF-8 file as the signature to identity the file as UTF-8 encoded The BOM character FEFFH is encoded in UTF-8 as EF BB BF Adding a BOM as the first character of the file is not recommended, as it may be incorrectly interpreted in other system You can have a UTF-8 file without BO M. Formats of Text Files. Line Delimiter or End-Of-Line EOL Sometimes, when you use the Windows NotePad to open a text file created in Unix or Mac , all the lines are joined together This is because different operating platforms use different character as the so-called line delimiter or end-of-line or EOL Two non-printable control characters are involved 0AH Line-Feed or LF and 0DH Carriage-Return or CR. Windows DOS uses OD0AH CR LF or r n as EOL. Unix and Mac use 0AH LF or n only. End-of-File EOF TODO. Windows CMD Codepage. Character encoding scheme charset in Windows is called codepage In CMD shell, you can issue command chcp to display the current codepage, or chcp codepage-number to change the codepage. The default codepage 437 used in the original DOS is an 8-bit character set called Extended ASCII which is different from Latin-1 for code numbers above 127.Codepage 1252 Windows-1252 , is not exactly the same as Latin-1 It assigns code number 80H to 9FH to letters and punctuation, such as smart single-quotes and double-quotes A common problem in browser that display quotes and apostrophe in question marks or boxes is because the page is supposed to be Windows-1252, but mislabelled as ISO-8859-1.For internationalization and chinese character set codepage 65001 for UTF8, codepage 1201 for UCS-2BE, codepage 1200 for UCS-2LE, codepage 936 for chinese characters in GB2312, codepage 950 for chinese characters in Big5.Chinese Character Sets. Unicode supports all languages, including asian languages like Chinese both simplified and traditional characters , Japanese and Korean collectively called CJK There are more than 20,000 CJK characters in Unicode Unicode characters are often encoded in the UTF-8 scheme, which unfortunately, requires 3 bytes for each CJK character, instead of 2 bytes in the unencoded UCS-2 UTF-16.Worse still, there are also various chinese character sets, which is not compatible with Unicode. GB2312 GBK for simplified chinese characters GB2312 uses 2 bytes fo r each chinese character The most significant bit MSB of both bytes are set to 1 to co-exist with 7-bit ASCII with the MSB of 0 There are about 6700 characters GBK is an extension of GB2312, which include more characters as well as traditional chinese characters. BIG5 for traditional chinese characters BIG5 also uses 2 bytes for each chinese character The most significant bit of both bytes are also set to 1 BIG5 is not compatible with GBK, i e the same code number is assigned to different character. For example, the world is made more interesting with these many standards. Notes for Windows CMD Users To display the chinese character correctly in CMD shell, you need to choose the correct codepage, e g 65001 for UTF8, 936 for GB2312 GBK, 950 for Big5, 1201 for UCS-2BE, 1200 for UCS-2LE, 437 for the original DOS You can use command chcp to display the current code page and command chcp codepagenumber to change the codepage You also have to choose a font that can display the characters e g Co urier New, Consolas or Lucida Console, NOT Raster font. Collating Sequences for Ranking Characters. A string consists of a sequence of characters in upper or lower cases, e g apple BOY Cat In sorting or comparing strings, if we order the characters according to the underlying code numbers e g US-ASCII character-by-character, the order for the example would be BOY apple Cat because uppercase letters have a smaller code number than lowercase letters This does not agree with the so-called dictionary order where the same uppercase and lowercase letters have the same rank Another common problem in ordering strings is 10 ten at times is ordered in front of 1 to 9.Hence, in sorting or comparison of strings, a so-called collating sequence or collation is often defined, which specifies the ranks for letters uppercase, lowercase , numbers, and special symbols There are many collating sequences available It is entirely up to you to choose a collating sequence to meet your application s specific req uirements Some case-insensitive dictionary-order collating sequences have the same rank for same uppercase and lowercase letters, i e A a B b Z z Some case-sensitive dictionary-order collating sequences put the uppercase letter before its lowercase counterpart, i e A B C a b c Typically, space is ranked before digits 0 to 9 followed by the alphabets. Collating sequence is often language dependent, as different languages use different sets of characters e g , , a, with their own orders. For Java Programmers. JDK 1 4 introduced a new package to support encoding decoding of characters from UCS-2 used internally in Java program to any supported charset used by external devices. Example The following program encodes some Unicode texts in various encoding scheme, and display the Hex codes of the encoded byte sequences. For Java Programmers - char and String. The char data type are based on the original 16-bit Unicode standard called UCS-2 The Unicode has since evolved to 21 bits, with code range o f U 0000 to U 10FFFF The set of characters from U 0000 to U FFFF is known as the Basic Multilingual Plane BMP Characters above U FFFF are called supplementary characters A 16-bit Java char cannot hold a supplementary character. Recall that in the UTF-16 encoding scheme, a BMP characters uses 2 bytes It is the same as UCS-2 A supplementary character uses 4 bytes and requires a pair of 16-bit values, the first from the high-surrogates range, uD800- uDBFF , the second from the low-surrogates range uDC00- uDFFF. In Java, a String is a sequences of Unicode characters Java, in fact, uses UTF-16 for String and StringBuffer For BMP characters, they are the same as UCS-2 For supplementary characters, each characters requires a pair of char values. Java methods that accept a 16-bit char value does not support supplementary characters Methods that accept a 32-bit int value support all Unicode characters in the lower 21 bits , including supplementary characters. This is meant to be an academic discuss ion I have yet to encounter the use of supplementary characters. Displaying Hex Values Hex Editors. At times, you may need to display the hex values of a file, especially in dealing with Unicode characters A Hex Editor is a handy tool that a good programmer should possess in his her toolbox There are many freeware shareware Hex Editor available Try google Hex Editor. I used the followings. NotePad with Hex Editor Plug-in Open-source and free You can toggle between Hex view and Normal view by pushing the H button. PSPad Freeware You can toggle to Hex view by choosing View menu and select Hex Edit Mode. TextPad Shareware without expiration period To view the Hex value, you need to open the file by choosing the file format of binary. UltraEdit Shareware, not free, 30-day trial only. Let me know if you have a better choice, which is fast to launch, easy to use, can toggle between Hex and normal view, free. The following Java program can be used to display hex code for Java Primitives integer, chara cter and floating-point. In Eclipse, you can view the hex code for integer primitive Java variables in debug mode as follows In debug perspective, Variable panel Select the menu inverted triangle Java Java Preferences Primitive Display Options Check Display hexadecimal values byte, short, char, int, long. Summary - Why Bother about Data Representation. Integer number 1 floating-point number 1 0 character symbol 1 and string 1 are totally different inside the computer memory You need to know the difference to write good and high-performance programs. In 8-bit signed integer integer number 1 is represented as 00000001B. In 8-bit unsigned integer integer number 1 is represented as 00000001B. In 16-bit signed integer integer number 1 is represented as 00000000 00000001B. In 32-bit signed integer integer number 1 is represented as 00000000 00000000 00000000 00000001B. In 32-bit floating-point representation number 1 0 is represented as 0 01111111 0000000 00000000 00000000B i e S 0 E 127 F 0.In 64-bit floating-point representation number 1 0 is represented as 0 01111111111 0000 00000000 00000000 00000000 00000000 00000000 00000000B i e S 0 E 1023 F 0.In 8-bit Latin-1, the character symbol 1 is represented as 00110001B or 31H. In 16-bit UCS-2, the character symbol 1 is represented as 00000000 00110001B. In UTF-8, the character symbol 1 is represented as 00110001B. If you add a 16-bit signed integer 1 and Latin-1 character 1 or a string 1 , you could get a surprise. Exercises Data Representation. For the following 16-bit codes. Give their values, if they are representing. a 16-bit unsigned integer. a 16-bit signed integer. two 8-bit unsigned integers. two 8-bit signed integers. a 16-bit Unicode characters. two 8-bit ISO-8859-1 characters. Ans 1 42 32810 2 42 -32726 3 0 42 128 42 4 0 42 -128 42 5 6 NUL PAD. REFERENCES RESOURCES. Floating-Point Number Specification IEEE 754 1985 , IEEE Standard for Binary Floating-Point Arithmetic. ASCII Specification ISO IEC 646 1991 or ITU-T T 50-1992 , Information technology - 7-bit coded character set for information interchange. Latin-I Specification ISO IEC 8859-1, Information technology - 8-bit single-byte coded graphic character sets - Part 1 Latin alphabet No 1. Unicode Specification ISO IEC 10646, Information technology - Universal Multiple-Octet Coded Character Set UCS. Unicode Consortium. Last modified January, 2014.Binary Calculator. Use the following calculators to perform the addition, subtraction, multiplication, or division of two binary values, convert from binary value to decimal value or vice versa Please note that due to the limitation of computer precision This calculator can only take up to 32 bit of binary value or up to 10 digit decimal values. Binary Calculation Add, Subtract, Multiply, or Divide. Convert Binary Value to Decimal Value. Convert Decimal Value to Binary Value. The binary system is a numerical system that uses only two symbols, 0 and 1 Due to its ease of implementation in digital electronic circuitry using logic gates, all modern computers use the binary system internally. The followi ng are some typical conversions between binary values and decimal values. decimal 0 0 in binary decimal 1 1 in binary decimal 2 10 in binary decimal 3 2 1 11 in binary decimal 4 2 2 100 in binary decimal 7 2 2 2 1 111 in binary decimal 8 2 3 1000 in binary decimal 10 2 3 2 1010 in binary decimal 16 2 4 10000 in binary decimal 20 2 4 2 2 10100 in binary. Binary Addition The addition of binaries is similar to the decimal system The only different is to carry over when the result is 2.0 0 0 0 1 1 1 0 1 1 1 0, carry 1 10.Binary Subtraction Subtraction works similarly.0 - 0 0 0 - 1 1, borrow 1 -1 1 - 0 1 1 - 1 0.