Question

Convert the decimal number 183 into an equivalent 32 bit binary number. show all your work.

Answer 1

The bits are determined by repeated division by 2 to yield either 0 or 1.
 
183/2 = 91 rem 1  =>  1  (lowest bit)             2⁰
  91/2 = 45 rem 1  =>  1 (next higher bit)     2¹
  45/2 = 22 rem 1 => 1  (next higher bit)     2²
  22/2 = 11 rem 0  => 0 (next highrt bit)      2³
    11/2 = 5 rem 1    => 1 (next higher bit)     2⁴
     5/2 = 2 rem 1   => 1 (next higher bit)     2⁵
     2/2 = 1 rem 0   => 0 (next higher bit)    2⁶
     1/2 = 0 rem 1   => 1 (next higher bit)      2⁷
The next higher 24 bits have 0 in each bit.

For 32-bit system,
183 = 00000000 00000000 00000000 10110111 (with a space between bytes for readability)

Answer: 00000000000000000000000010110111