# Full 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 full adder (FA) circuit has three inputs: A, B and Cin, which add three 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
0+0+1 = 1
0+1+0 = 1
0+1+1 = 10

1+0+0 = 1
1+0+1 = 10
1+1+0 = 10
1+1+1 = 11

These are the least possible single-bit combinations. But the result for 1+1+1 is 11, the sum result must be re-written as a 2-bit output. Thus, the equations can be written as

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

1+0+0 = 01
1+0+1 = 10
1+1+0 = 10
1+1+1 = 11

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 full adder

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

Logical expression for Sum,

Logical expression for Carry,

Carry = AB + BCin + ACin

The FA works by combining the operations of basic logic gates, with the simplest form using two XOR, one OR & two AND gate.

Note:

1. Minimum number of NAND Gate required implementing FA = 9

2. Minimum number of NOR Gate required implementing FA = 9

3. FA can be implemented by a combination of two half adder and one OR gate.

4. FA can be implemented by a combination of one 3×8 decoder and two OR gate.

## Questions

Q.1 Which of the following circuits come under the class of combinational logic circuits?

2. Full subtracter
4. J-K flip-flop
5. Counter

Select the correct answer from the codes given below:

1. 1 only
2. 3 and 4
3. 4 and 5
4. 1, 2, and 3

Ans. option d is correct