Binary addition involves adding binary numbers by applying the following rules: 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 with a carry of 1 to the next column. To perform multi-bit addition, a half or full adder table is used to calculate the sum and carry out for each bit while accounting for any carries from the previous column. Examples are provided showing how addition is performed on multiple bits using the adder table and propagating any carries to the next position.

1. 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

2. 1+0=1
0+1=1
1+1=0 , and a carry to the next significant digit
For more in basic digital computing visit :http://basicsofdigitalcomputing.blogspot.com/