Octal Conversion

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Octal Conversion

a)   Octal to Binary
Convert each octal digit to a 3-digit binary number.
Example
Convert Octal Number (25)8 to Binary.
  2   |     5   |
       010 |   101 |
 = (010101)2

b)  Octal Fraction to Binary
Convert each octal digit to a 3-digit binary number.
Example
Convert Octal Number (23.25)8 to Binary.
  2   |     3   |  .   |    2      |    5  |
       010 |   011 |  .   |  010    |  101 |
    = (010011.010101)2

c)    Octal to Decimal
1.      Start at the rightmost bit.
2.      Take that bit and multiply by 8n where n is the current position beginning at 0 and increasing by 1 each time. This represents the power of 8.
3.      Sum each of the product terms until all bits have been used.
Example
Convert the Octal number (321)8 to its Decimal equivalent.
2 * 82 + 2 * 81 + 1 * 80
192   +   16    +   1
= (209)10

d)  Octal Fraction to Decimal
Example

Convert (23.25)8 to decimal
= (2 x 81) + (3 x 80) + (2 x 8-1) + (5 x 8-2)
=     16     +      3      +    0.25    + 0.07812
= (19.32812)10

e)    Octal to Hexadecimal
To convert Octal to hexadecimal, convert each digit of Octal Number to its binary equivalent and write them in 3 bits. Then, combine each 4 bit binary number and that is converted into hexadecimal.
Example
Convert the Octal number (762)8 to its hexadecimal equivalent.
=   7   |   6    |  2
= 111 |  110 | 010
= (111110010)2
= 0001 | 1111 | 0010
=    1    |    F       |    2
= (1F2)16

f)   Octal Fraction to Hexadecimal
Example
Convert the Octal Fraction to (23.25)8 to Hexadecimal
=  2   |    3   |  .   |   2    |    5    |
= 010|  011 |  .   | 010  |  101  |
=  (010011.010101)2
=  0001  |  0011  | .  |  0101  |  0100  |
=     1     |     3     | .  |    5      |    4      |

= (13.54)16






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