by E-Computer Concepts August 8, 2019 at 4:09 pm

Adding two numbers is one of the basic tasks performed by a computer. Addition operation of two binary digits can be represented as follows –

For all values of A and B except 11, the result is a single digit value but for AB = 11, the result is in two digits. The value at higher significant position, i.e., on this case is known as carry and has to be added to the pair of next higher significant bits as is done in real algebra also. Combinational Circuit that performs addition of two bits in known as HALF ADDER whereas the one in which we also take account of carry from lower significant bits is known as FULL ADDER.

For designing a half adder, we will follow steps described follows –

1. As we know that half adder is used to add two bits, from the statement of the problem it is clear that we have to add two bits in binary.
2. As two bits have to be added, number of input variables will be 2. Now, the result when value for AB = 11 consists of two digits out of which higher significant bits is known as carry, we have to use two output variables, one of which is used for sum and another for carry.
3. We give names A, B to input variables and c and s to output as carry and sum respectively.
4. We know the required output value for given set of input values, so the truth table for half adder can be designed as follows –

5. From above truth table, we can obtain Boolean function for both the output variables.

C = AB , S = A’ B + AB’ , =A+B

### Logical Diagram of Half Adder

The main disadvantage of this circuit is that it can only add two inputs and if there is any carry it is neglected.