Binary Math for Everyone

See also my HEX2DEC page for a better understanding of conversion between different base numbers.

This is just a quick primer for those wanting to learn how to convert by hand between binary and decimal.
Binary numbers are composed of only 1 and 0. Every positive decimal interger can be expressed in binary.
By contrast, decinal numbers are composed of 0 through 9.
Here is a binary number:
0001101100
To convert this to a decimal number we need to define the placement of the numbers.

DEC	512	256	128	64	32	16	8	4	2	1
BIN	0	0	0	1	1	0	1	1	0	0

The Ones position is equal to 1.
The Tens position is equal to 2.
The Hundreds position is equal to 4.
The Thousands position is equal to 8.
The Ten Thousands position is equal to 16.
The Hundred Thousands position is equal to 32.
The Millions position is equal to 64.
The Ten Millions position is equal to 128.
The Hundred Millions position is equal to 256.
The Billions position is equal to 512.

Reading from left to right, we have a one in the Millions posistion so we start with 64.
Next, there is a one in the Hundred Thousands posistion so we add 32 to 64 and get 96.
We have a zero in the Ten Thousands position so we do not add 16 and we are left with 96 still.
There is a one in the Thousands posistion so we add 8 to 96 and get 104.
The one in the Hundreds position adds 4 to 104 to get 108.
There are no ones in the Tens or the Ones posistion. Our final is 108.
Binary 1101100 equals Decimal 108.

1 = 1
2 = 10
3 = 11
4 = 100
5 = 101
6 = 110
7 = 111
8 = 1000
9 = 1001
10 = 1010

Here is a decimal number:
234
To convert this to binary, we need to find the highest of the of these numbers 512, 256, 128, 64, 32, 16, 8, 4, 2, or 1 that is less than the number we are looking at.

DEC	512	256	128	64	32	16	8	4	2	1
BIN	0	0	1	1	1	0	1	0	1	0

First we find that 512 and 256 are bigger than 234 but 128 is not. So we place a one in the 128 column.
We subtract 128 from 234 and get 106. We put a one in the 64 column because it is smaller than 106.
We subract 64 from 106 and get 42. We put a one in the 32 column because it is smaller than 42.
We subract 32 from 42 and get 10. We put a zero in the 16 column because it is bigger than 10. We can put a 1 in the 8 column because it is smaller than 10.
We subract 8 from 10 and get 2. We put a zero in the 4 column because it is bigger than 2. We put a one the 2 column because it is equal to 2.
We subtract 2 from 2 and get zero. We put a zero in the 1 column because it is smaller than 0.
Decimal 234 equals Binary 11101010.