By BYJU'S Exam Prep

Updated on: September 25th, 2023

The half and full adders are used to add two binary numbers, but the major Difference Between Half Adder and Full Adder is in the aspect of fan input processing. Combinational circuits are devoid of memory storage they only consist of logic gates.

A half adder is used to add two 1 bit binary numbers and is not concerned with the previous inputs/states, while a full adder is concerned with the present and the previous additions. Knowing the primary difference between the half adder and full adder, we can understand each one separately. Let us understand what a full adder and a half adder consist of, along with the detailed full adder vs. half adder comparison.

Major aistinguishing point betwwen half adder and full adder is that a half adder consists of only one AND gate and EX-OR gate. A full adder consists of one OR gate and two EX-OR and AND gates. The difference between the half adder and full adder is based on various metrics and parameters, which are explained below.

Half adder takes 2 inputs and produces 2 outputs (sum and carry). Full adder takes 3 inputs and produces 2 outputs (sum and carry). While a half adder has a simple implementation with just two XOR and one AND gate, a full adder’s implementation is more complex, utilizing additional logic gates and accommodating the carry input. The choice between a half adder and a full adder depends on the specific requirements of the circuit or application, considering factors such as the number of bits being added and the need for carry propagation.

## What is a Half Adder?

It is a combinational logic circuit that uses two logic gates: an AND gate and an EX-OR gate. It consists of two inputs, says A and B; after adding these two inputs, the output is generated in the form of carrying and sum; therefore, there are two output terminals. The sum is generated using the Ex-OR gate, and the carry is generated using the AND gate.

The logical expressions for sum and carry of a half adder are:

Sum (S) = A ⊕ B

Carry (C) = A.B

### Truth Table for Half Adder

When we add 0 to 0, 0 to 1, and 1 to 0, we get the sum 0 and 1, respectively, and both are one-digit binary numbers. Hence, in these cases, there will be no carry during addition, or carry is 0 here. We can summarise this in a truth table for the half adder. The truth table comprising the possible outputs obtained for adding two 1-bit binary numbers using a half adder is as follows.

 Input Output A B CARRY SUM 0 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1

## What is a Full Adder?

A full adder is a combinational circuit used to perform the addition of two n-bit binary numbers. It uses two AND gates, two EX-OR gates, and one OR gate to perform addition. It adds three binary numbers, namely Cin, the carry generated from the previous addition; Cout, the carry generated by the addition of present inputs A and B; and Sum, the addition of the inputs A and B.

A full adder can also be designed using two half adders and an OR gate, where the OR gate is responsible for generating the carry, and Half adders are responsible for generating the sum of the two binary numbers. The logical expression for sum and carry using the full adder is:

CARRY-OUT = AB + BCin + ACin

Sum = (A ⊕ B) ⊕ Cin

### Truth Table for Full Adder

The full adder is a ‘combinational circuit’ that can execute addition on three input bits or two inputs plus the carry-in from the preceding operation. The truth table comprising the possible outputs obtained for adding two binary numbers using a full adder is as follows.

 Input Output A B C SUM CARRYOUT 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 0 1