<?xml version="1.0" encoding="utf-8"?><!DOCTYPE article  PUBLIC '-//OASIS//DTD DocBook XML V4.4//EN'  'http://www.docbook.org/xml/4.4/docbookx.dtd'><article><articleinfo><title>WebHome/TrabajosPracticos/PracticoBase1</title><revhistory><revision><revnumber>13</revnumber><date>2020-04-02 23:05:29</date><authorinitials>GuillermoSteiner</authorinitials></revision><revision><revnumber>12</revnumber><date>2019-06-15 14:11:42</date><authorinitials>EstefaniaPereyra</authorinitials></revision><revision><revnumber>11</revnumber><date>2019-04-16 18:42:48</date><authorinitials>EstefaniaPereyra</authorinitials></revision><revision><revnumber>10</revnumber><date>2019-04-16 18:31:48</date><authorinitials>EstefaniaPereyra</authorinitials></revision><revision><revnumber>9</revnumber><date>2019-04-16 18:29:05</date><authorinitials>EstefaniaPereyra</authorinitials></revision><revision><revnumber>8</revnumber><date>2019-03-26 18:07:19</date><authorinitials>EstefaniaPereyra</authorinitials></revision><revision><revnumber>7</revnumber><date>2013-05-13 14:35:29</date><authorinitials>GuillermoSteiner</authorinitials></revision><revision><revnumber>6</revnumber><date>2012-08-22 20:02:14</date><authorinitials>GuillermoSteiner</authorinitials></revision><revision><revnumber>5</revnumber><date>2010-09-09 14:02:27</date><authorinitials>GuillermoSteiner</authorinitials><revremark>Se cambia nombre desde &quot;TrabajosPracticos/PracticoBase1&quot;</revremark></revision><revision><revnumber>4</revnumber><date>2010-09-09 13:56:11</date><authorinitials>GuillermoSteiner</authorinitials><revremark>Se cambia nombre desde &quot;PracticoBase1&quot;</revremark></revision><revision><revnumber>3</revnumber><date>2010-09-09 13:55:25</date><authorinitials>GuillermoSteiner</authorinitials></revision><revision><revnumber>2</revnumber><date>2010-06-01 16:07:57</date><authorinitials>TiN</authorinitials></revision></revhistory></articleinfo><section><title>Trabajo Práctico Nro 1 Bases Numéricas</title><para>Este práctico tiene como objetivo el repaso de las bases numéricas y las operaciones aritméticas básicas (suma y resta) realizadas en binario. </para><section><title>Guía de ejercicios</title><para><ulink url="https://ciii.frc.utn.edu.ar/TecnicasDigitalesII/WebHome/TrabajosPracticos/PracticoBase1/TecnicasDigitalesII/WebHome/TrabajosPracticos/PracticoBase1?action=AttachFile&amp;do=get&amp;target=tp1.pdf">Descargar</ulink> subido el 02 de abril de 2020. </para></section><section><title>Ejercicios ejemplos</title><section><title>Ejercicio Nro 1</title><itemizedlist><listitem override="none"><para>Representar 421<subscript>10 </subscript>en base 2  </para></listitem></itemizedlist><para><inlinemediaobject><imageobject><imagedata fileref="https://ciii.frc.utn.edu.ar/TecnicasDigitalesII/WebHome/TrabajosPracticos/PracticoBase1?action=AttachFile&amp;do=get&amp;target=binario1.png" width="30%"/></imageobject><textobject><phrase>&quot;binario1.png&quot;</phrase></textobject></inlinemediaobject>  </para><para>Resultado: 110100101b  </para></section><section><title>Ejercicio Nro 2</title><para>Representar 11010111<subscript>2</subscript> en base 10 </para><informaltable><tgroup cols="3"><colspec colname="col_0"/><colspec colname="col_1"/><colspec colname="col_2"/><tbody><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>0</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para>  1 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>1</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para>  2 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>2</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para>  4 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0 x 2<superscript>3</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para>  0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>4</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para>  16 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0 x 2<superscript>5</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para>  0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>6</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para>  64 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>7</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para>  128 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> Resultado </para></entry><entry align="center" colsep="1" nameend="col_2" namest="col_1" rowsep="1"><para>  215 </para></entry></row></tbody></tgroup></informaltable><para>Resultado: 215 </para></section><section><title>Ejercicio Nro 3</title><para>Representar 1101,101<subscript>2</subscript> en base 10 </para><informaltable><tgroup cols="3"><colspec colname="col_0"/><colspec colname="col_1"/><colspec colname="col_2"/><tbody><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>-3</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0,125 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0 x 2<superscript>-2</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>-1</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0,5 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>0</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 1 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0 x 2<superscript>1</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>2</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 4 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>3</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 8 </para></entry></row></tbody></tgroup></informaltable><para>Resultado: 13,625 </para></section><section><title>Ejercicio Nro 4</title><para>Representar 23,43<subscript>10</subscript> en base 2 con 8 dígitos después de la coma. </para><para><emphasis role="strong">Parte Entera</emphasis>  </para><para><inlinemediaobject><imageobject><imagedata fileref="https://ciii.frc.utn.edu.ar/TecnicasDigitalesII/WebHome/TrabajosPracticos/PracticoBase1?action=AttachFile&amp;do=get&amp;target=binario2.png" width="15%"/></imageobject><textobject><phrase>&quot;binario2.png&quot;</phrase></textobject></inlinemediaobject> </para><para><emphasis role="strong">Parte Decimal</emphasis> </para><informaltable><tgroup cols="4"><colspec colname="col_0"/><colspec colname="col_1"/><colspec colname="col_2"/><colspec colname="col_3"/><tbody><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,43 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0,86 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,86 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 1,72 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 1 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,72 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 1,44 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 1 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,44 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0,88 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,88 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 1,76 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 1 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,76 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 1,52 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 1 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,52 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 1,04 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 1 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,04 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0,08 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 0 </para></entry></row></tbody></tgroup></informaltable><para>Resultado: 10111,01101110 </para></section><section><title>Ejercicio Nro 5</title><para>Representar 10,27<subscript>10</subscript> en base 2 con un error maximo de 0,1% </para><screen><![CDATA[E = 0,1 % 
e = 0,01027
]]><![CDATA[
2^n = 0,01027
]]><![CDATA[
n = ln(0,01027) / ln(2) = -6.605]]></screen><para>tomamos el entero menor  </para><screen><![CDATA[n = -7]]></screen><para>Esto significa que para tener un error menor a 0,1 % deberemos tomar hasta el 7 digito  </para><para>Ahora resolvemos  </para><para><emphasis role="strong">Parte Entera</emphasis>  </para><para>1010 </para><para><emphasis role="strong">Parte Decimal</emphasis> </para><informaltable><tgroup cols="4"><colspec colname="col_0"/><colspec colname="col_1"/><colspec colname="col_2"/><colspec colname="col_3"/><tbody><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,27 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0,54 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,54 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 1,08 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 1 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,08 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0,16 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,16 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0,32 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,32 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0,64 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,64 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 1,28 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 1 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0,28 x 2 </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0,56 </para></entry><entry colsep="1" rowsep="1"><para> Entero = 0 </para></entry></row></tbody></tgroup></informaltable><para>Resultado: 1010,010001 </para><para>Comprobación  </para><informaltable><tgroup cols="3"><colspec colname="col_0"/><colspec colname="col_1"/><colspec colname="col_2"/><tbody><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>-6</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0,015625 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0 x 2<superscript>-5</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0 x 2<superscript>-4</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0 x 2<superscript>-3</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>-2</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0,25 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0 x 2<superscript>-1</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0 x 2<superscript>0</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>1</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 2 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0 x 2<superscript>2</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 0 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 1 x 2<superscript>3</superscript> </para></entry><entry colsep="1" rowsep="1"><para> = </para></entry><entry colsep="1" rowsep="1"><para> 8 </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> <emphasis role="strong">Resultado</emphasis>             </para></entry><entry colsep="1" rowsep="1"><para>* *</para></entry><entry colsep="1" rowsep="1"><para> <emphasis role="strong">10,265625</emphasis> </para></entry></row></tbody></tgroup></informaltable><para>El error es  </para><screen><![CDATA[e = 10,27 - 10,265625 = 0,004375 < 0,01027]]></screen></section><section><title>Ejercicio Nro 6</title><para>Representar los siguientes numeros con signo en formato Signo + Magnitud, Complemento a 1,Complemento a 2, Exceso de 7 </para><informaltable><tgroup cols="6"><colspec colname="col_0"/><colspec colname="col_1"/><colspec colname="col_2"/><colspec colname="col_3"/><colspec colname="col_4"/><colspec colname="col_5"/><tbody><row rowsep="1"><entry colsep="1" rowsep="1"><para><emphasis role="strong">Nro</emphasis></para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">Val Abs</emphasis></para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">Sig+Mag</emphasis></para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">Comp 1</emphasis></para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">Comp 2</emphasis></para></entry><entry colsep="1" rowsep="1"><para><emphasis role="strong">Exc 7</emphasis></para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> -5    </para></entry><entry colsep="1" rowsep="1"><para>  0101    </para></entry><entry colsep="1" rowsep="1"><para>  1101      </para></entry><entry colsep="1" rowsep="1"><para>  1010     </para></entry><entry colsep="1" rowsep="1"><para>  1011     </para></entry><entry colsep="1" rowsep="1"><para>  0010     </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> -8    </para></entry><entry colsep="1" rowsep="1"><para>  1000    </para></entry><entry colsep="1" rowsep="1"><para>   x           </para></entry><entry colsep="1" rowsep="1"><para>  x            </para></entry><entry colsep="1" rowsep="1"><para>  1000     </para></entry><entry colsep="1" rowsep="1"><para>  x           </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> -7    </para></entry><entry colsep="1" rowsep="1"><para>  0111    </para></entry><entry colsep="1" rowsep="1"><para>  1111      </para></entry><entry colsep="1" rowsep="1"><para>   1000     </para></entry><entry colsep="1" rowsep="1"><para>  1001     </para></entry><entry colsep="1" rowsep="1"><para>  0000     </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> -3    </para></entry><entry colsep="1" rowsep="1"><para>  0011    </para></entry><entry colsep="1" rowsep="1"><para>  1011      </para></entry><entry colsep="1" rowsep="1"><para>  1100     </para></entry><entry colsep="1" rowsep="1"><para>  1101      </para></entry><entry colsep="1" rowsep="1"><para>  0100     </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 0     </para></entry><entry colsep="1" rowsep="1"><para>  0000    </para></entry><entry colsep="1" rowsep="1"><para>  0000 y 1000  </para></entry><entry colsep="1" rowsep="1"><para>  0000 y 1111 </para></entry><entry colsep="1" rowsep="1"><para>  0000  </para></entry><entry colsep="1" rowsep="1"><para>  0111   </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 7     </para></entry><entry colsep="1" rowsep="1"><para>  0111    </para></entry><entry colsep="1" rowsep="1"><para>  0111      </para></entry><entry colsep="1" rowsep="1"><para>  0111     </para></entry><entry colsep="1" rowsep="1"><para>  0111     </para></entry><entry colsep="1" rowsep="1"><para>  1110     </para></entry></row><row rowsep="1"><entry colsep="1" rowsep="1"><para> 8     </para></entry><entry colsep="1" rowsep="1"><para>  1000    </para></entry><entry colsep="1" rowsep="1"><para>   x          </para></entry><entry colsep="1" rowsep="1"><para>   x           </para></entry><entry colsep="1" rowsep="1"><para>  x          </para></entry><entry colsep="1" rowsep="1"><para>  1111     </para></entry></row></tbody></tgroup></informaltable></section><section><title>Ejercicio Nro 7</title><itemizedlist><listitem override="none"><para>Realizar las siguientes operaciones aritméticas en base 2 </para></listitem></itemizedlist><para><emphasis role="strong">Sumar (1010 0101 + 1001 0011)</emphasis> </para><screen><![CDATA[          11
   1010 0101
+
   1001 0011
 ------------
  10011 1000]]></screen><para><emphasis role="strong">Restar (1010 0101 - 1001 0011)</emphasis> </para><screen><![CDATA[           1
   1010 0101
-
   1001 0011
  -----------
   0001 0010]]></screen><para> Otro método es: </para><para>Sacar el complemento a dos del sustraendo  </para><screen><![CDATA[      1001 0011
 C1 = 0110 1100
    +    1. 
 C2 = 0110 1101]]></screen><para>Sumar el minuendo al complemento a dos del sustraendo  </para><itemizedlist><listitem override="none"><screen><![CDATA[   1010 0101
+
   0110 1101
 ------------
  10001 0010]]></screen></listitem></itemizedlist><para>El 9 bits no se toma y nos queda el resultado final  Resultado = 00010010 </para></section></section></section><section><title>Ejercicios Resueltos</title><para>Página con las soluciones (<ulink url="https://ciii.frc.utn.edu.ar/TecnicasDigitalesII/WebHome/TrabajosPracticos/PracticoBase1/TecnicasDigitalesII/WebHome/TrabajosPracticos/PracticoBase1/PracticoBase1Soluciones#">SOLUCIONES</ulink>) </para></section></article>