Binary Number System: Representations

Unsigned Binary Integer

BITS

High order bit is leftmost, low order (least significant) bit is rightmost. The location of each bit determines its value: 

     33222222222211111111110000000000
     10987654321098765432109876543210
     BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
     |                    |         |
     231 place            210        20

EXAMPLE

What is the 32-bit unsigned binary integer representation for the decimal integer 86420?

SOLUTION

1. Succesively divide by 2 until the result is zero. The remainders of these divisions will be the bits used to construct the solution. 

     86420 ÷ 2 = 43210     rem 0    Low order bit
     43210 ÷ 2 = 21605     rem 0
     21605 ÷ 2 = 10802     rem 1 
     10802 ÷ 2 =  5401     rem 0
      5401 ÷ 2 =  2700     rem 1
      2700 ÷ 2 =  1350     rem 0
      1350 ÷ 2 =   675     rem 0
       675 ÷ 2 =   337     rem 1
       337 ÷ 2 =   168     rem 1
       168 ÷ 2 =    84     rem 0
        84 ÷ 2 =    42     rem 0
        42 ÷ 2 =    21     rem 0
        21 ÷ 2 =    10     rem 1
        10 ÷ 2 =     5     rem 0
         5 ÷ 2 =     2     rem 1
         2 ÷ 2 =     1     rem 0
         1 ÷ 2 =     0     rem 1    High order bit

2. Organize the remainder bits into the binary integer:

10101000110010100
3. Pad the bits to the left with zeroes to bring to a total of 32:
000000000000000 10101000110010100
4. Convert to hex:
0000 0000 0000 0001 0101 0001 1001 0100

00015194



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