# Half Adder – Truth table & Logic Diagram

An Adder is a digital logic circuit in electronics that performs the operation of additions of two number. Adders are classified into two types: half adder and full adder. The half adder (HA) circuit has two inputs: A and B, which add two input binary digits and generate two binary outputs i.e. carry and sum.

Contents

Let’s see an addition of single bits.

0+0 = 0
0+1 = 1
1+0 = 1
1+1 = 10

These are the least possible single-bit combinations. But the result for 1+1 is 10, the sum result must be re-written as a 2-bit output. Thus, the equations can be written as

0+0 = 00
0+1 = 01
1+0 = 01
1+1 = 10

The bold digit is the sum output. The output ‘1’of ‘10’ is carry output. ‘SUM’ is the normal output and ‘CARRY’ is the carry output.

### Truth table of half adder

The truth table of the Half Adder Circuit is shown in figure 2.

### Implementation of half adder

Logical expression for Sum,

Logical expression for Carry,

Carry = AB

The HA works by combining the operations of basic logic gates, with the simplest form using only an XOR and an AND gate.

Note:

1. Minimum number of NAND Gate required implementing HA = 5

2. Minimum number of NOR Gate required implementing HA = 5

3. Number of Multiplexers required implementing HA = 3

4. HA can be implemented by a combination of one 2×4 decoder and one OR gate.

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