Addition of binary numbers

Binary addition

Counting is the process of adding 1 to the present number to get the next number. In decimal number system counting start from 0 and proceeds like this 0,1,2,3,4,5,6,7,8,9 . After nine we have no more symbols left, so we write 10. This one represent a carry to the tens position.

Like this binary system's count process can also be represented like this 0,1,10,11,100 ….

Based on the above idea we construct a half adder table to represent the addition of binary numbers.

a	b                                              Sum                           Carry
0	0	0	0
0	1	1	0
1	0	1	0
1	1	1	1

Here we have not used carry , but consider the examples below.

11+01=100

Carry	1	1
Augend		1	1
Addend		0	1
Sum	1	0	0

101+001=110

Carry	0	1
Augend	1	0	1
Addend	0	0	1
Sum	1	1	0

These two examples show that addition between two numbers include addition between three bits; the carry bit and the bits of the two numbers to be added. We can construct a addition table having these three values.

a	b                             Carry                     Sum       Carry to next position
0	0	0	0	0
0	0	1	1	0
0	1	0	1	0
0	1	1	0	1
1	0	0	1	0
1	0	1	0	1
1	1	0	0	1
1	1	1	1	1

In short rules for addition are

0+0=0

1+0=1

0+1=1

1+1=0 , and a carry to the next significant digit