Full adder is a combinational circuit that performs arithmetic addition of three bits. Full adder takes 3 input and produces 2 outputs. Let x, y, z be the inputs and S ( sum ), C ( carry ) be the outputs.
Why we need only 2 outputs?
The maximum value that can be obtained by adding three bits is 3 ( when all three bits equals 1 ), which is a 2-bit number. S represents the least significant bit and C represents the most significant bit of the output.
- 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
Implementation of Full Adder
Full Adder using AND, OR, NOT gates
Full adder using NAND gates
Minimum number of NAND gates required to implement full adder is 9.
Full adder using NOR gates
Minimum number of NOR gates required to implement full adder is 9.
Full adder using two half adder and one OR gate
Full adder using 4×1 Multiplexer
Full adder using 3×8 decoder
- Full adders can be cascaded to implement an n-bit adder. For example, Carry Ripple Adder.
- A full adder can be used as a subtractor using 2’s complement method,