# Full adder truth table, circuit, k map & its implementation

In this article we will going to learn about full adder truth table and then drive its k map to form its equation. After this we will reduce the equation, so that we can implement full adder using XOR gate. We will also see how to make full adder using half adder.

A Full adder is a combinational ciruit that performs the sum of three bits. It includes two significant bits and one carry bits.

• When both inputs are low then sum and carry outputs will be logic low or 0.
• If any one input is high then sum will be logic high (1) and carry out will be logic low (0).
• When two inputs are high then sum becomes logic low (0) and carry out will be logic high (1).
• And if all inputs are high(1) then the output sum and carry will be logic high (1).

#### Full Adder equation & its reduction to XOR logic form

Sum = X’ Y Z’ + X Y’ Z’ + X’ Y’ Z + X Y Z

= Z’ ( X’ Y + X Y’ ) + Z( X’ Y’ + X Y )

= X xor Y xor Z

Carry = X Z + X Y + Y Z

or Carry = Z ( X Y’ + X’ Y) + X Y

= Z X Y’ + Z X’ Y + X Y ( note: we can verify these equation by using truth table)

```library IEEE;
use IEEE.std_logic_1164.all;

port (x : in std_logic;
y : in std_logic;
cin : in std_logic;
sum : out std_logic;
cout :out std_logic);