Half adder is a combinational logic circuit perform addition of two single bit number. It is a digital circuit has two input X, Y and two output sum (S), carry (C). Here sum is the least significant bit (LSB) and carry is the most significant bit (MSB). Half adder circuit is used in computer ALU (Arithmetic and Logic Unit ) to perform arithmetic operation.

## Truth Table of Half Adder

The half adder circuit perform OR (addition) operation between two single bit binary number. Two input X and Y having four input combination. After addition of two single bit binary number this circuit produces two outputs Sum (S) and carry (C).

Truth table explain the relationship between inputs and outputs.

In the above table,

- X and Y are the two inputs and two input having 2
^{2}= 4 Possible combination. - When we perform OR operation between two inputs, it produces two output sum (s) and carry (c).
- Here sum is the least significant bit (LSB) and carry is the most significant bit (MSB).
- Carry output is “1” only when both the inputs are “1”.
- The least significant bit of the sum is defined by the ‘sum’ bit.

Now, we find the Boolean logical expression from truth table for outputs Sum (S) and carry (C) in SOP form.

Now , we draw the circuit diagram using logical expression of Sum (S) and Carry (C)

**Sum = X’Y+XY’ = X xor YCarry = XY**

**Sum** bit is generated with the help of the **Exclusive-OR** or **XOR** Gate

**Sum = X’Y+XY’ = X xor Y**

**Carry** bit is generated with the help of the **AND** Gate

**Carry = XY**

Now, add above sum and Carry circuits to get half adder circuit diagram

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