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<p><span style="font-size: medium;">El Sistema de numeración Binario, es un sistema en que los números se representan utilizando solamente dos cifras o bit: cero y uno (0 y 1).</span></p> <p><span style="font-size: medium;">Todo número expresado en Sistema Binario, tiene su equivalente en el Sistema Decimal, pudiéndose realizar la conversión a través de los siguientes pasos:</span></p> <p><span style="font-size: medium;">Paso 1: Numeramos los bits de derecha a izquierda comenzando desde el 0.</span></p> <p><span style="font-size: medium;">Paso 2: A cada bit le hacemos corresponder una potencia de base 2 y exponente igual al número de bit.</span></p> <p><span style="font-size: medium;">Paso 3: Por último, se suman todas las potencias.</span></p> <p><span style="font-size: medium;">Ejemplo: Convertir el número 11001011 a decimal.</span></p> <table style="height: 123px; width: 439px;" border="2" cellspacing="1" cellpadding="1" align="center"> <tbody> <tr> <td style="text-align: center;"><span style="font-size: x-small;">7</span></td> <td style="text-align: center;"><span style="font-size: x-small;">6</span></td> <td style="text-align: center;"><span style="font-size: x-small;">5</span></td> <td style="text-align: center;"><span style="font-size: x-small;">4</span></td> <td style="text-align: center;"><span style="font-size: x-small;">3</span></td> <td style="text-align: center;"><span style="font-size: x-small;">2</span></td> <td style="text-align: center;"><span style="font-size: x-small;">1</span></td> <td style="text-align: center;"><span style="font-size: x-small;">0</span></td> <td style="text-align: center;"><span style="font-size: x-small;">Exponente</span></td> </tr> <tr> <td style="text-align: center;"><span style="font-size: medium;">1</span></td> <td style="text-align: center;"><span style="font-size: medium;">1</span></td> <td style="text-align: center;"><span style="font-size: medium;">0</span></td> <td style="text-align: center;"><span style="font-size: medium;">0</span></td> <td style="text-align: center;"><span style="font-size: medium;">1</span></td> <td style="text-align: center;"><span style="font-size: medium;">0</span></td> <td style="text-align: center;"><span style="font-size: medium;">1</span></td> <td style="text-align: center;"><span style="font-size: medium;">1</span></td> <td style="text-align: center;"><span style="font-size: medium;">Bits</span></td> </tr> <tr> <td style="text-align: center;"><span style="font-size: medium;">1*2<sup>7</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">1*2<sup>6</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">0*2<sup>5</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">0*2<sup>4</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">1*2<sup>3</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">0*2<sup>2</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">1*2<sup>1</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">1*2<sup>0</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">Expresión</span></td> </tr> <tr> <td style="text-align: center;"><span style="font-size: medium;">128</span></td> <td style="text-align: center;"><span style="font-size: medium;">64</span></td> <td style="text-align: center;"><span style="font-size: medium;">0</span></td> <td style="text-align: center;"><span style="font-size: medium;">0</span></td> <td style="text-align: center;"><span style="font-size: medium;">8</span></td> <td style="text-align: center;"><span style="font-size: medium;">0</span></td> <td style="text-align: center;"><span style="font-size: medium;">2</span></td> <td style="text-align: center;"><span style="font-size: medium;">1</span></td> <td style="text-align: center;"><span style="font-size: medium;">Potencia</span></td> </tr> <tr class="1"> <td style="text-align: center;" colspan="8"><span style="font-size: medium;">128 + 64 + 0 + 0 + 8 + 0 + 2 + 1 = 203</span></td> <td style="text-align: center;"><span style="font-size: medium;">Resultado</span></td> </tr> </tbody> </table> <p> </p> <p><span style="font-size: medium;">De acuerdo al procedimiento anterior determina a que número en sistema decimal corresponde el siguiente número binario:</span></p> <p style="text-align: center;"><span style="font-size: large;">#b10#b9#b8#b7#b6#b5#b4#b3#b2#b1</span></p>
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<p><span style="font-size: medium;">Para realizar la conversión de un número expresado en sistema binario a sistema decimal, aplicamos los siguientes pasos:</span></p> <p><span style="font-size: medium;">Paso 1: Numeramos los bits de derecha a izquierda comenzando desde el 0.</span></p> <p><span style="font-size: medium;">Paso 2: A cada bit le hacemos corresponder una potencia de base 2 y exponente igual al número de bit.</span></p> <p><span style="font-size: medium;">Paso 3: Por último, se suman todas las potencias.</span></p> <table border="3"> <tbody> <tr> <td style="text-align: center;"><span style="font-size: xx-small;">9</span></td> <td style="text-align: center;"><span style="font-size: xx-small;">8</span></td> <td style="text-align: center;"><span style="font-size: xx-small;">7</span></td> <td style="text-align: center;"><span style="font-size: xx-small;">6</span></td> <td style="text-align: center;"><span style="font-size: xx-small;">5</span></td> <td style="text-align: center;"><span style="font-size: xx-small;">4</span></td> <td style="text-align: center;"><span style="font-size: xx-small;">3</span></td> <td style="text-align: center;"><span style="font-size: xx-small;">2</span></td> <td style="text-align: center;"><span style="font-size: xx-small;">1</span></td> <td style="text-align: center;"><span style="font-size: xx-small;">0</span></td> <td style="text-align: center;"><span style="font-size: xx-small;">Exponente </span></td> </tr> <tr> <td style="text-align: center;"><span style="font-size: medium;">#b10</span></td> <td style="text-align: center;"><span style="font-size: medium;">#b9</span></td> <td style="text-align: center;"><span style="font-size: medium;">#b8</span></td> <td style="text-align: center;"><span style="font-size: medium;">#b7</span></td> <td style="text-align: center;"><span style="font-size: medium;">#b6</span></td> <td style="text-align: center;"><span style="font-size: medium;">#b5</span></td> <td style="text-align: center;"><span style="font-size: medium;">#b4</span></td> <td style="text-align: center;"><span style="font-size: medium;">#b3</span></td> <td style="text-align: center;"><span style="font-size: medium;">#b2</span></td> <td style="text-align: center;"><span style="font-size: medium;">#b1</span></td> <td style="text-align: center;"><span style="font-size: medium;">Bit</span></td> </tr> <tr> <td style="text-align: center;"><span style="font-size: medium;">#b10*2<sup>9</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">#b9*2<sup>8</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">#b8*2<sup>7</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">#b7*2<sup>6</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">#b6*2<sup>5</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">#b5*2<sup>4</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">#b4*2<sup>3</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">#b3*2<sup>2</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">#b2*2<sup>1</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">#b1*2<sup>0</sup></span></td> <td style="text-align: center;"><span style="font-size: medium;">Expresión</span></td> </tr> <tr> <td style="text-align: center;"><span style="font-size: medium;">#j</span></td> <td style="text-align: center;"><span style="font-size: medium;">#i</span></td> <td style="text-align: center;"><span style="font-size: medium;">#h</span></td> <td style="text-align: center;"><span style="font-size: medium;">#g</span></td> <td style="text-align: center;"><span style="font-size: medium;">#f</span></td> <td style="text-align: center;"><span style="font-size: medium;">#e</span></td> <td style="text-align: center;"><span style="font-size: medium;">#d</span></td> <td style="text-align: center;"><span style="font-size: medium;">#c</span></td> <td style="text-align: center;"><span style="font-size: medium;">#b</span></td> <td style="text-align: center;"><span style="font-size: medium;">#a</span></td> <td style="text-align: center;"><span style="font-size: medium;">Potencia</span></td> </tr> <tr> <td style="text-align: center;" colspan="10"><span style="font-size: medium;">#j + #i + #h + #g + #f + #e + #d + #c + #b + #a = #sol1</span></td> <td style="text-align: center;"><span style="font-size: medium;">Resultado </span></td> </tr> </tbody> </table> <p> </p> <p><span style="font-size: medium;">Por lo tanto, el número binario #b10#b9#b8#b7#b6#b5#b4#b3#b2#b1, convertido a sistema decimal equivale a #sol1</span></p>
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