{"id":22760,"date":"2014-09-07T20:33:47","date_gmt":"2014-09-07T23:33:47","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=22760"},"modified":"2022-12-24T21:41:07","modified_gmt":"2022-12-25T00:41:07","slug":"principio-fundamental-de-contagem-o-pfc-nas-comunicacoes","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/sala-de-estudos-principio-fundamental-da-contagem\/principio-fundamental-de-contagem-o-pfc-nas-comunicacoes\/","title":{"rendered":"Princ\u00edpio Fundamental da Contagem &#8211; O PFC nas comunica\u00e7\u00f5es"},"content":{"rendered":"<table style=\" height:auto;text-align:justify;margin-left: auto; margin-right: auto;width:428px;\">\n<tr>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:300px;background-color: #CDC673;\" >\u00c9 aqui que estudaremos informa\u00e7\u00f5es computacionais utilizando o PFC?<\/p>\n<\/td>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2014\/04\/carinha12.jpg\" style=\"border: 0px;\"  alt=\"carinha12\" width=\"100\" height=\"90\" class=\"alignleft size-full wp-image-17466\" \/><\/td>\n<\/tr>\n<\/table>\n<table style=\" height:auto;text-align:justify;margin-left: auto; margin-right: auto; width:637\">\n<tr>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:500px;background-color: #CDC673;\" >Isso mesmo!<br \/>\nAntes, por\u00e9m, seria melhor se voc\u00ea assistisse ao <a href=\"http:\/\/clubes.obmep.org.br\/blog\/video-p1\/\" title=\"Clique aqui para assistir.\" target=\"_blank\"><span style=\"color: #ffffff; letter-spacing: 1px;\"><strong><em>V\u00eddeo 1 do PIC,<\/em><\/strong><\/span><\/a> pois \u00e9 interessante que voc\u00ea conhe\u00e7a o sistema bin\u00e1rio para continuar a leitura.<\/p>\n<\/td>\n<\/tr>\n<\/table>\n<table style=\" height:auto;text-align:justify;margin-left: auto; margin-right: auto;width:368px;\">\n<tr>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:250px;background-color: #CDC673;\" >Vamos assistir juntos, pessoal?<\/p>\n<\/td>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2014\/04\/carinha11.jpg\" style=\"border: 0px;\" alt=\"carinha11\" width=\"95\" height=\"90\" class=\"alignleft size-full wp-image-17465\" \/><\/td>\n<\/tr>\n<\/table>\n<table style=\" height:auto;text-align:justify;margin-left: auto; margin-right: auto;width:644px;\">\n<tr>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:520px;background-color: #CDC673;\" >Ent\u00e3o aproveitem e passem, tamb\u00e9m,  por nossa <a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=41147\" title=\"Visitem a Sala!\" target=\"_blank\"><span style=\"color: #ffffff; letter-spacing: 1px;\"><strong>Pequena Galeria de Grandes Matem\u00e1ticos<\/strong><\/span><\/a> para dar uma olhadinha na biografia do genial <strong> Gottfried Wilhelm Leibniz<\/strong>, o matem\u00e1tico alem\u00e3o que, entre muitas outras valiosas contribui\u00e7\u00f5es, nos legou o sistema num\u00e9rico bin\u00e1rio tal como \u00e9 conhecido hoje!<\/p>\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:20px;\">\n<div style=\"border: 8px double #BDB76B; padding: 10px; padding-right:10px; padding-left: 10px; text-align:justify\">\n<p class=\"ti1\" style=\"color: #BDB76B; font-size:33px;line-height:30px;margin:20px\">O PFC nas Comunica\u00e7\u00f5es*<\/p>\n<hr style=\"height:2px;background-color:#BDB76B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px;background-color:#BDB76B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<p style=\"margin:60px;\">\n<div style=\"border: 2px solid #BDB76B; padding: 8px;padding-right: 20px; padding-left:20px;\">\n<p class=\"ti1\" style=\"color: #BDB76B;line-height:30px;margin:20px\">REPRESENTA\u00c7\u00c3O DAS INFORMA\u00c7\u00d5ES<\/p>\n<hr style=\"height:2px;background-color:#BDB76B; border: 0 none\"\/>\n<p style=\"margin:20px;\">\n<div style=\"font-size: 15px; font-family: Calibri, sans-serif; color: #000000; border: 2px solid #000000; padding: 10px; line-height: 20px;text-align:justify\">\n<img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2014\/09\/informa.png\" style=\"border: 0px;\" alt=\"informa\" width=\"380\" height=\"280\" class=\"alignright size-full wp-image-22906\" \/><\/p>\n<p class=\"ti3\"style=\"line-height:25px;margin:5px\">REPRESENTA\u00c7\u00c3O DAS INFORMA\u00c7\u00d5ES<\/p>\n<p>Em um texto, as informa\u00e7\u00f5es apresentadas em forma de caracteres s\u00e3o entendidas pelo leitor porque este conhece o formato e o significado dos s\u00edmbolos que representam os caracteres alfab\u00e9ticos, os num\u00e9ricos (algarismos) e os sinais de pontua\u00e7\u00e3o ou matem\u00e1ticos (+, -, X, \/, &gt;, &lt;, = etc.).<br \/>\nDa mesma forma, toda informa\u00e7\u00e3o introduzida em um computador precisa ser entendida pela m\u00e1quina, para depois ser processada.<br \/>\nPor s\u00f3 entender dois tipos de informa\u00e7\u00e3o &#8211; ligado e desligado, a forma de representa\u00e7\u00e3o interna de uma informa\u00e7\u00e3o nos computadores \u00e9 feita por meio de um sistema bin\u00e1rio, no qual cada d\u00edgito assume os valores <strong>0<\/strong> (desligado) e <strong>1<\/strong> (ligado). Assim, letras, sinais, desenhos, gr\u00e1ficos, gravuras, fotos, imagem em movimento, som, palavras, m\u00fasica, texto, filme, s\u00e3o representados no computador esses dois elementos. \u00c9 isso mesmo, a enorme quantidade de informa\u00e7\u00f5es que circulam pela internet ou pelos computadores em todo o mundo se reduz, em \u00faltima inst\u00e2ncia, a combina\u00e7\u00f5es intermin\u00e1veis de zeros e uns. Cada d\u00edgito bin\u00e1rio \u00e9 conhecido como <strong>bit <\/strong>(contra\u00e7\u00e3o das palavras inglesas binary digit), e por ter somente dois valores, ele pouco representa isoladamente; por essa raz\u00e3o, as informa\u00e7\u00f5es manipuladas por um computador s\u00e3o codificadas em grupos ordenados. O menor grupo ordenado de bits que representa uma informa\u00e7\u00e3o \u00fatil e intelig\u00edvel para o ser humano \u00e9 o <strong>byte <\/strong>(leia-se &#8220;baite&#8221;), formado, em geral, por 8 bits.<br \/>\nAssim, letras, n\u00fameros, sinais de pontua\u00e7\u00e3o, s\u00edmbolos, como o cifr\u00e3o ($), o arroba (@) ou um asterisco (*), s\u00e3o bytes, isto \u00e9, conjuntos  de zeros e uns. <\/p>\n<p style=\"text-align: right;\"><span style=\"font-size: 13px;\"> Informa\u00e7\u00f5es extra\u00eddas de: <a href=\"http:\/\/www.di.ufpb.br\/raimundo\/Generalidades\/RepInfo.html\" target=\"_blank\"><strong><span style=\"color: #B0A84E;\">http:\/\/www.di.ufpb.br\/raimundo\/Generalidades\/RepInfo.html<\/span><\/strong><\/a>. \u00daltimo acesso em: 08\/08\/2018<\/span><\/p>\n<\/div>\n<p style=\"margin:20px;\">\n<table style=\" height:auto;text-align:justify;margin-left: auto; margin-right: auto; width:498px;\">\n<tr>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:370px;background-color: #CDC673;\" >Vamos aprofundar esta discuss\u00e3o um pouco mais&#8230; <\/p>\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:40px;\">\n<div style=\"font-size: 16px; font-family: Calibri, sans-serif; color: #1c1c1c; padding: 10px; line-height: 20px;text-align:justify\">\nObserve que existem quatro informa\u00e7\u00f5es de 2 bits (vide <strong>Tabela 1<\/strong>) e oito informa\u00e7\u00f5es de 3 bits (vide <strong>Tabela 2<\/strong>).<br \/>\n&nbsp;<\/p>\n<div style=\"width: 40%; float: left;\">\n<table style=\" border: 2px solid #000000; width: 30%; height:auto; margin-left: 200px;  text-align:center;\">\n<caption><strong>Tabela 1<\/strong><\/caption>\n<tr>\n<td  style=\"text-align:center; border-bottom: 1px solid #000000\">1&ordm; bit<\/td>\n<td  style=\"text-align:center; border-bottom: 1px solid #000000\">2&ordm; bit<\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<\/table>\n<\/div>\n<div style=\"width: 55%; float: right;  text-align: left;\">\n<table style=\" border: 2px solid #000000; width: 40%; height:auto; margin-left: 20px;  height:auto; text-align:center;\">\n<caption><strong>Tabela 2<\/strong><\/caption>\n<tr>\n<td  style=\"text-align:center;border-bottom: 1px solid #000000\">1&ordm; bit<\/td>\n<td  style=\"text-align:center;border-bottom: 1px solid #000000\">2&ordm; bit<\/td>\n<td  style=\"text-align:center;border-bottom: 1px solid #000000\">3&ordm; bit<\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<\/table>\n<\/div>\n<div style=\"clear: both;\"><\/div>\n<p style=\"margin:30px;\">\n<p>Para uma informa\u00e7\u00e3o de 4 bits temos 16 possibilidades, conforme podemos observar na <strong>Tabela 3<\/strong>. Usando a Tabela 3 podemos, facilmente, obter a quantidade de possibilidades para as informa\u00e7\u00f5es de 5 bits, conforme a <strong>Tabela 4<\/strong>.<br \/>\n<br \/>&nbsp;<\/p>\n<div style=\"width: 40%; float: left;\">\n<table style=\" border: 2px solid #000000; width: 60%; height:auto; margin-left: 120px;  text-align:center;\">\n<caption><strong>Tabela 3<\/strong><\/caption>\n<tr>\n<td  style=\"text-align:center; border-bottom: 1px solid #000000\">1&ordm; bit<\/td>\n<td  style=\"text-align:center; border-bottom: 1px solid #000000\">2&ordm; bit<\/td>\n<td  style=\"text-align:center; border-bottom: 1px solid #000000\">3&ordm; bit<\/td>\n<td  style=\"text-align:center; border-bottom: 1px solid #000000\">4&ordm; bit<\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<\/table>\n<\/div>\n<div style=\"width: 55%; float: right;  \">\n<table style=\" border: 2px solid #000000; width: 60%; height:auto; margin-left: 20px;  text-align:center;\">\n<caption><strong>Tabela 4<\/strong><\/caption>\n<tr>\n<td  style=\"text-align:center; border-bottom: 1px solid #000000\">1&ordm; bit<\/td>\n<td  style=\"text-align:center; border-bottom: 1px solid #000000\">2&ordm; bit<\/td>\n<td  style=\"text-align:center; border-bottom: 1px solid #000000\">3&ordm; bit<\/td>\n<td  style=\"text-align:center; border-bottom: 1px solid #000000\">4&ordm; bit<\/td>\n<td  style=\"text-align:center; border-bottom: 1px solid #000000\">5&ordm; bit<\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>1<\/strong><\/td>\n<\/tr>\n<tr>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<td><strong>0<\/strong><\/td>\n<\/tr>\n<\/table>\n<\/div>\n<div style=\"clear: both;\"><\/div>\n<p style=\"margin:30px;\">\n<p>Utilizando o Princ\u00edpio Fundamental da Contagem, \u00e9 poss\u00edvel calcular, rapidamente, o n\u00famero de informa\u00e7\u00f5es de 6 bits, de 7 bits, de 8 bits, etc.<br \/>\nObserve: <\/p>\n<ul>\n<li> Uma informa\u00e7\u00e3o de 6 bits \u00e9 uma sequ\u00eancia de seis <strong>zeros <\/strong>ou <strong>uns<\/strong>, ou seja:<\/li>\n<\/ul>\n<div style=\"margin-left:40px;\">\n<table style=\" border: 2px solid #000000; width: 30%; height:auto; margin-left: auto; margin-right: auto; height:auto; text-align:center;\">\n<tr>\n<td  style=\"border: 1px solid #000000\">d<sub>1<\/sub><\/td>\n<td  style=\"border: 1px solid #000000\">d<sub>2<\/sub><\/td>\n<td  style=\"border: 1px solid #000000\">d<sub>3<\/sub><\/td>\n<td  style=\"border: 1px solid #000000\">d<sub>4<\/sub><\/td>\n<td  style=\"border: 1px solid #000000\">d<sub>5<\/sub><\/td>\n<td>d<sub>6<\/sub><\/td>\n<\/tr>\n<\/table>\n<p>onde cada d<sub>i<\/sub> \u00e9 um <strong>0<\/strong> ou um <strong>1<\/strong>.<br \/>\nAssim, s\u00e3o duas as possibilidades para d<sub>1<\/sub>: <strong>0<\/strong> ou <strong>1<\/strong>. Para cada uma dessas, sabemos que existem 32 possibilidades para o bloco<\/p>\n<table style=\" border: 2px solid #000000; width: 24%; height:auto; margin-left: auto; margin-right: auto; height:auto; text-align:center;\">\n<tr>\n<td  style=\"border: 1px solid #000000\">d<sub>2<\/sub><\/td>\n<td  style=\"border: 1px solid #000000\">d<sub>3<\/sub><\/td>\n<td  style=\"border: 1px solid #000000\">d<sub>4<\/sub><\/td>\n<td  style=\"border: 1px solid #000000\">d<sub>5<\/sub><\/td>\n<td>d<sub>6<\/sub><\/td>\n<\/tr>\n<\/table>\n<p>que, na verdade, s\u00e3o as possibilidades de informa\u00e7\u00f5es de 5 bits.<br \/>\nLogo, pelo Princ\u00edpio Fundamental da Contagem, temos <strong> 2 x 32=64 informa\u00e7\u00f5es de 6 bits.<\/strong><\/div>\n<p style=\"margin:20px;\">\n<ul>\n<li>Uma informa\u00e7\u00e3o de 7 bits, por sua vez, \u00e9 uma sequ\u00eancia de sete zeros ou uns: <\/li>\n<\/ul>\n<div style=\"margin-left:40px;\">\n<table style=\" border: 2px solid #000000; width: 35%; height: auto; margin-left: auto; margin-right: auto; height:auto; text-align:center;\">\n<tr>\n<td  style=\"border: 1px solid #000000\">e<sub>1<\/sub><\/td>\n<td  style=\"border: 1px solid #000000\">e<sub>2<\/sub><\/td>\n<td  style=\"border: 1px solid #000000\">e<sub>3<\/sub><\/td>\n<td  style=\"border: 1px solid #000000\">e<sub>4<\/sub><\/td>\n<td  style=\"border: 1px solid #000000\">e<sub>5<\/sub><\/td>\n<td  style=\"border: 1px solid #000000\">e<sub>6<\/sub><\/td>\n<td>e<sub>7<\/sub><\/td>\n<\/tr>\n<\/table>\n<p>onde cada e<sub>i<\/sub> \u00e9, tamb\u00e9m, um <strong>0<\/strong> ou um <strong>1<\/strong>.<br \/>\nS\u00e3o duas as possibilidades para e<sub>1<\/sub>: <strong>0<\/strong> ou <strong>1<\/strong>; e, para cada uma dessas, sabemos que existem 64 possibilidades (que s\u00e3o as possibilidades de informa\u00e7\u00f5es de 6 bits).<br \/>\nLogo, pelo Princ\u00edpio Fundamental da Contagem, temos <strong>2 x 64=128 informa\u00e7\u00f5es de 7 bits<\/strong>. <\/div>\n<table style=\" height:auto;text-align:justify;margin-left: auto; margin-right: auto; width:477px;\">\n<tr>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:350px;background-color: #CDC673;\" >Agora \u00e9 com voc\u00eas!<br \/>\n<strong><em>Sendo n um n\u00famero natural n\u00e3o nulo, quantas informa\u00e7\u00f5es com n bits existem ?<\/em><\/strong><\/p>\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:20px;\">\n<\/div>\n<\/div>\n<p style=\"margin:40px\">\n<hr style=\"height:1px; width:50%;background-color:#BDB76B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:60%;background-color:#BDB76B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:3px; width:70%;background-color:#BDB76B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:4px; width:75%;background-color:#BDB76B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:3px; width:70%;background-color:#BDB76B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:60%;background-color:#BDB76B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; width:50%;background-color:#BDB76B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<p style=\"margin:40px\">\n<div style=\"border: 2px solid #BDB76B; padding: 8px;\">\n<p class=\"ti1\" style=\"color: #BDB76B;line-height:30px;margin:20px\"><em>O Sistema Braile<\/em><\/p>\n<hr style=\"height:2px;background-color:#BDB76B; border: 0 none\"\/>\n<table style=\" height:auto;text-align:justify;margin-left: auto; margin-right: auto;width:584px;\">\n<tr>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:450px;background-color: #CDC673;\" >Podemos, tamb\u00e9m, utilizar o PFC para entender um pouco mais de uma interessante forma de comunica\u00e7\u00e3o: o Braile.<br \/>\nVamos l\u00e1?<\/p>\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:40px\">\n<div style=\"font-size: 15px; font-family: Calibri, sans-serif; color: #000000; border: 2px solid #000000; padding: 10px; line-height: 20px;text-align:justify\">\n<p class=\"ti3\" style=\"line-height:25px;margin:10px\"> O Sistema Braile<\/p>\n<p><div id=\"attachment_23036\" style=\"width: 209px\" class=\"wp-caption alignleft\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-23036\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2014\/09\/brile.png\" style=\"border: 0px;\" alt=\"M\u00e1quina para escrever em braile\" width=\"209\" height=\"122\" class=\"size-full wp-image-23036\" \/><p id=\"caption-attachment-23036\" class=\"wp-caption-text\">M\u00e1quina para escrever em braile<\/p><\/div>O braile \u00e9 um sistema de escrita e leitura para portadores de defici\u00eancias visuais, no qual a leitura \u00e9 feita por meio do tato. Nesse sistema, as letras, os n\u00fameros e os outros sinais s\u00e3o representados por caracteres formados por matrizes de seis pontos, dos quais pelo menos um se destaca, em relevo, com rela\u00e7\u00e3o aos outros. O sistema \u00e9 empregado escrevendo-se a palavra letra por letra ou de forma abreviada, adotando-se c\u00f3digos especiais de abreviaturas para cada l\u00edngua ou grupo lingu\u00edstico.<br \/>\nEsse processo de escrita foi inventado pelo franc\u00eas Louis Braille (1809-1852). Braille, aos 3 anos de idade, adquiriu a defici\u00eancia visual ao ferir-se com um instrumento de trabalho do seu pai, que produzia selas. Aos 10 anos iniciou os seus estudos na Escola para cegos de Paris. Aos 15 anos, Louis Braille dedicou-se a encontrar um sistema que possibilitasse ao cego escrever em relevo, surgindo o sistema que hoje conhecemos como braile. \u00c9 curioso constatar que para criar esse sistema ele inspirou-se nos desenhos em relevo que enfeitavam as selas confeccionadas pelo seu pai, feitos pelo pr\u00f3prio instrumento que o cegou.<br \/>\nApesar do sistema braile n\u00e3o ter sido muito aceito naquela \u00e9poca, ele evoluiu ao longo dos anos e foi aperfei\u00e7oado, sendo, nos dia de hoje, amplamente utilizado pelos portadores de defici\u00eancia visual de todo o mundo. Hoje, com o braile, representam-se os alfabetos latino, grego, hebraico, cir\u00edlico e outros, bem como os alfabetos e outros processos de escrita das l\u00ednguas orientais; escreve-se o texto vocabular, tanto no modo integral como no estenogr\u00e1fico, a matem\u00e1tica, a geometria, a qu\u00edmica, a fon\u00e9tica, a inform\u00e1tica, a m\u00fasica, etc.  <img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2014\/09\/braile2.png\" style=\"border: 0px;\" alt=\"braile2\" width=\"704\" height=\"105\" class=\"aligncenter size-full wp-image-23038\" srcset=\"https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2014\/09\/braile2.png 704w, https:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2014\/09\/braile2-300x44.png 300w\" sizes=\"auto, (max-width: 704px) 100vw, 704px\" \/><\/p>\n<p style=\"text-align: right;\"><span style=\"font-size: 13px;\"> Informa\u00e7\u00f5es e figura extra\u00eddas das refer\u00eancias abaixo, acessadas em 08\/08\/ 2018:<br \/>\n <a href=\"http:\/\/www.acessibilidade.net\/\" target=\"_blank\"><strong><span style=\"color: #B0A84E;\">http:\/\/www.acessibilidade.net\/<\/span><\/strong><\/a>;<br \/>\n <a href=\"http:\/\/www.bengalalegal.com\/sbraille\" target=\"_blank\"><strong><span style=\"color: #B0A84E;\"> http:\/\/www.bengalalegal.com\/sbraille <\/span><\/strong><\/a>.<\/span><\/p>\n<\/div>\n<table style=\" height:auto;text-align:justify;margin-left: auto; margin-right: auto;width:625px;\">\n<tr>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:500px;background-color: #CDC673;\" >E a\u00ed, pessoal, qual \u00e9 o n\u00famero m\u00e1ximo de caracteres distintos que podem ser representados no sistema braile?<br \/>\n\u00c9 s\u00f3 utilizar o PFC! Vamos tentar?<br \/>\nPara ajudar, vejam a resposta abaixo.<\/p>\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:40px;\">\n<div style=\"text-align:center;\">\n<input  value=\"Ver a resposta\" style=\"cursor:pointer; padding: 0px; width: 150px; height: 40px; background-color:#BDB76B; font-size: 18px; font-family: Calibri, sans-serif; color: #ffffff;\" onclick=    \"if(this.parentNode.getElementsByTagName('div')[0].style.display != ''){this.parentNode.getElementsByTagName('div')[0].style.display = '';this.value = 'Ocultar a resposta';} else{this.parentNode.getElementsByTagName('div')[0].style.display = 'none'; this.value = 'Ver a resposta';}\"    type=\"button\" \/>    <\/p>\n<div style=\"display: none;\">\n<div style=\"font-size: 20px; font-family: Calibri, sans-serif; color: #1c1c1c; border: 1px dotted #000000;padding: 10px; width:150px; ;margin-left: auto; margin-right: auto; line-height: 20px;text-align:center\">\n<strong>Resposta: 63 <\/strong>\n<\/div>\n<\/div>\n<\/div>\n<p style=\"margin:20px;\">\n<\/div>\n<p style=\"text-align: right;\"><span style=\"color: #BDB76B; font-family:  Verdana, Arial, Helvetica, sans-serif; font-size: 14px;\"><strong>* <em>Texto adaptado do material did\u00e1tico da Forma\u00e7\u00e3o Continuada de Professores da Rede Estadual de Ensino,<br \/>\nministrado no estado do Mato Grosso do Sul em 2003 e escrito pela professora Sonia Regina Di Giacomo.<\/em><\/strong><\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2014\/09\/carinha_legal.jpg\"  style=\"border: 0px;\" alt=\"carinha_legal\" width=\"150\" height=\"100\" class=\"aligncenter size-full wp-image-22758\" \/><\/p>\n<p style=\"text-align: center;padding: 10px; border-style: dotted;border-color :#1C1C1C; border-width :thin; width:270px;background-color: #CDC673;margin-left: auto; margin-right: auto;\"><span style=\"color: #000000; font-family: Calibri, sans-serif; font-size: 16px;\"><strong>P F C<\/strong>: tr\u00eas letrinhas poderosas, hein?<\/span><\/p>\n<p style=\"margin:30px;\">\n<hr style=\"height:1px; background-color:#BDB76B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px; background-color:#BDB76B;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<p style=\"text-align: right; padding-right: 10px;\"><span style=\"color: #BDB76B;\"><strong>&#8211; Francimar de Brito Vieira<\/strong><br \/>\n<strong>&#8211; Noemi Zeraick Monteiro<\/strong><br \/>\n<strong>&#8211; Sonia Regina Di Giacomo<\/strong><br \/>\n&#9670; Equipe COM &#8211; OBMEP<\/span><\/p>\n<\/div>\n<p style=\"text-align: right;\"><a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=22162\" title=\"Voltar\"><span style=\"color: #BDB76B;\"><strong>Voltar para a Sala de Estudos sobre o PFC<\/strong><\/span><\/a><\/p>\n<table style=\" height:auto;text-align:justify;margin-left: auto; margin-right: auto; width:640px;\">\n<tr>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:500px;background-color: #CDC673;\" >Ei! E quanto aos problemas iniciais, sobre a Mega-Sena, as placas de autom\u00f3veis e o fragmento de DNA?!<br \/>\nAgora eu sei resolv\u00ea-los!<\/p>\n<\/td>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/02\/carinha3.jpg\" style=\"border: 0px;\" alt=\"carinha3\" width=\"98\" height=\"86\" class=\"alignleft size-full wp-image-3059\" \/><\/td>\n<\/tr>\n<\/table>\n<table style=\" height:auto;text-align:justify;margin-left: auto; margin-right: auto;width:445px;\">\n<tr>\n<td class=\"bf\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td class=\"bf\">\n<p class=\"fala\" style=\"width:320px;background-color: #CDC673;\" >Calma, n\u00e3o me esqueci deles!<br \/>\nVamos conferi-los na <a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=23047\" title=\"Confiram as respostas\"><span style=\"color: #ffffff; letter-spacing: 1px;\"><strong>pr\u00f3xima Sala<\/strong><\/span><\/a>.<\/p>\n<\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>\u00c9 aqui que estudaremos informa\u00e7\u00f5es computacionais utilizando o PFC? Isso mesmo! Antes, por\u00e9m, seria melhor se voc\u00ea assistisse ao V\u00eddeo 1 do PIC, pois \u00e9 interessante que voc\u00ea conhe\u00e7a o sistema bin\u00e1rio para continuar a leitura. Vamos assistir juntos, pessoal? Ent\u00e3o aproveitem e passem, tamb\u00e9m, por nossa Pequena Galeria de Grandes Matem\u00e1ticos para dar uma &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/sala-de-estudos-principio-fundamental-da-contagem\/principio-fundamental-de-contagem-o-pfc-nas-comunicacoes\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":2970,"parent":22162,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-22760","page","type-page","status-publish","has-post-thumbnail","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/22760","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=22760"}],"version-history":[{"count":213,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/22760\/revisions"}],"predecessor-version":[{"id":55658,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/22760\/revisions\/55658"}],"up":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/22162"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media\/2970"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=22760"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}