**Introduction**

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

**Truth Table**

**K-Map**

**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**

**Applications**

- 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,

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