Hexadecimal Conversion

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       Hexadecimal Conversion

a)   Hexadecimal to Binary
Convert each digit of Hexadecimal Number to its binary equivalent and write them in 4 bits. Then, combine each 4 bit binary number and that is the resulting answer.
Example
Convert the Hexadecimal number (10AF)16 to its Binary equivalent.
=   1     |     0   |    A   |    F |
= 0001 | 0000 | 1010 | 1111
= (0001000010101111)2
= (1000010101111)2

b)  Hexadecimal Fraction to Binary
Example
Convert the Hexadecimal number (13.54)16 to its Binary equivalent.
=   1     |   3     |  .   |  5      |   4     |
= 0001 | 0011 |  .   | 0101 | 0100 |
= (00010011.01010100)2
= (10011.010101)2

c)    Hexadecimal to Octal
To convert Hexadecimal to Octal, Convert each digit of Hexadecimal Number to its binary equivalent and write them in 4 bits. Then, combine each 3 bit binary number and that is converted into octal.
Example
Convert the Hexadecimal number (A42)16 to its Octal equivalent.
=   A    |    4    |   2
= 1010 | 0100 | 0010
= (101001000010)2
= 101 | 001 | 000 | 010
=   5   |   1   |   0   |   2
= (5102)8

d)  Hexadecimal Fraction to Octal
Example
Convert the Hexadecimal fraction (15.34)16 to its Octal equivalent.
=     1     |      5     |  .   |   3     |     4
=  0001  |   0101  |  .   | 0011 | 0100
= (10101.001101)2
=  010  |  101  |  .  |  001 |  101 |
=    2    |    5    |  .  |    1   |    5   |
= (25.15)8

e)   Hexadecimal to Decimal
1. Start at the rightmost bit.
2. Take that bit and multiply by 16n where n is the current position beginning at 0                                                 and increasing by 1 each time. This represents a power of 16.
3. Sum each terms of product until all bits have been used.
Example
Convert the Hexadecimal number (AB)16 to its Decimal equivalent.
=    A * 161   +    B * 160
=    10 * 161  +    11 * 160
=      160       +        11
= (171)10

f)     Hexadecimal fraction to Decimal
Example
Convert (1E.8C)16 to decimal
=      1          |        E          |        8         |        C       |
=  (1 x 161)  +  (14 x 160)  +   (8 x 16-1)  +   (12 x 16-2)
=       16       +         14       +        0.5       +     0.04688
= (30.54688)10




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