CONVERSIÓN DE UNIDADES

1. 1.   ¿Cómo se convierte de decimal a cualquier otra base?

Por medio de divisiones sucesivas por el número que se desea convertir; y el residuo, ya sea cero o 1 es el que se coloca. Ejm:
Convertir el #50 (10) a base 2
50/2 = 25, (Como es exacta la división, se coloca el residuo 0)
Luego 25/2= 12 (Como la división no es exacta, se coloca el residuo 1)
Luego 12/2= 6 (Como es exacta la división, se coloca el residuo 0)
Luego 6/2= 3 (Como es exacta la división, se coloca el residuo 0)
Luego 3/2= 1 (Como la división no es exacta, se coloca el residuo 1)
Además, hay que tener en cuenta el último número 1, no es divisible por 2, por lo tanto hasta allí se realizan las divisiones sucesivas.
Después de tener todas las divisiones, se empieza por el último número (el divisor) en este caso 1, y luego se colocan los residuos o cocientes de abajo hacia arriba, tal y como lo indica la flecha.
Por lo tanto, el número convertido en binario es: 10010

1. 2.   ¿Cómo se convierte de cualquier otra base a decimal?

Para pasar cualquier número de cualquier base a base 10. Para ello, se tiene que hacer uso del Teorema Fundamental de la Numeración.
Ejemplos:
El número está formado por un solo símbolo repetido tres veces. No obstante, cada uno de esos símbolos tiene un valor diferente, que depende de la posición que ocupa en el número. Así, el primer 1 (empezando por la izquierda) representa un valor de , el segundo de y el tercero de , dando como resultado el valor del número:

1. 3.   ¿Cómo se convierte decimales (después del punto) en base 10 a cualquier otra base?

Para convertir una fracción decimal a binario, el sistema que se sigue es similar al que utilizamos para los enteros, sin embargo, se usa la multiplicación en lugar de la división, y los enteros se acumulan en lugar de los residuos.
Ejemplo: Convertir (0.6875)10 a base 2
Entero      Fracción             Coeficiente

  0.6875      *2 1 0.3750 a-1       =  1

  0.3750      *2 0 0.75a-2          =  0

  0.75        *2 1 0.5a-3           =  1

  0.5         *2 1 0.0a-4           =  1

(0.6875)10=(0.1011)2

1. 4.   Como se convierte después del punto decimal a binario (y además en cualquier otra base)

Cuando deseamos hacer la conversión de un número decimal de una parte entera y una parte fraccionaria la conversión se hace por separado y posteriormente se combinan las dos respuestas, es decir, antes del punto se hacen divisiones consecutivas y después del punto multiplicaciones consecutivas.
Ejemplo:
  (41.6875)10 → (101001.1011)2

1. 5.   Ejercicios

a) Convertir a binario octal y hexadecimal
• 119(10)  
Binario = 1110111
Octal = 167
Hexadecimal = 77
• ABEF2 (16)
Binario = 10101011111011110010
Octal = 25373662
• 0111011(2)
Octal = 73
Hexadecimal= 3B                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
• 545(6)
Decimal = 209
Binario = 11010001
Octal = 321
Hexadecimal = D1
• 345,2 (8)
Decimal = 229,125
Binario = 11100101,001
Hexadecimal = E5,2
b)  Convertir el numero decimal en: Binario, octal y hexadecimal
• 234
Binario = 11101010
Octal = 352
Hexadecimal = EA
• 100
Binario =1100100
Octal = 144
Hexadecimal = 64

• 12.5
Binario = 1100,1000
Octal = 14,4
Hexadecimal = 8
c) Los siguientes binarios convertirlos a la base pedida:
• 10111010101 a base 10 =1493
• 1001011.011 a base 10 y 16
Base 10= 75.375
Base 16= 46
• 1111111000111 a base 8 y 16
Base 8= 17707
Base 16= 1FC7