Converting between Decimal & Binary.

Decimal to binary.

This can require many steps. At each step we simply divide the number by 2, until this finally results in a value of 0.
The remainder produced in each step (including any final remainder), give the digits of the binary conversion from l.s.b. to m.s.b.

e.g. converting 287 to binary;

(l.s.b) 287/2 = 143 remainder 1.
143/2 = 71 remainder 1.
71/2 = 35 remainder 1.
35/2 = 17 remainder 1.
17/2 = 8 remainder 1.
8/2 = 4 remainder 0.
4/2 = 2 remainder 0.
2/2 = 1 remainder 0.
(m.s.b.) 1/2 = 0 remainder 1.

Therefore 287 decimal, = 100011111 binary.

Example converting 65 to binary;

(l.s.b) 65/2 = 32 remainder 1.
32/2 = 16 remainder 0.
16/2 = 8 remainder 0.
8/2 = 4 remainder 0.
4/2 = 2 remainder 0.
2/2 = 1 remainder 0.
(m.s.b.) 1/2 = 0 remainder 1.

Therefore 65 decimal = 1000001 binary.

Binary to decimal.

To convert a binary number to decimal, then for each bit in the number that is 1, we simply add the digit weightings together.

e.g. 1100 1011.

Therefore 1100 1011 binary, = 203 decimal.