Difference Between Half Adder and Full Adder

By Mona Kumari|Updated : April 13th, 2022

In this article, we will be discussing the difference between half adder and full adder. Before jumping onto the differences let us first understand the meaning of the two combinational circuits and their functionalities. Both the half and full adders are used to add two binary numbers but differ in the aspect of fan in or 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 does not concern with the previous inputs/states while a full adder is concerned with the present as well as the previous additions. Knowing the primary difference between half adder and full adder we can understand each one separately.

What is a Half Adder?

It is a combinational logic circuit that uses two logic gates that is an AND gate and an EX-OR gate. It consists of two inputs say A and B, after performing the addition of 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 of them 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 to generate the carry and Half adders are responsible to generate 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

Difference Between Half Adder and Full Adder

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. Further, we have discussed the difference between half adder and full adder based on various metrics and parameters:

 Metrics Half Adder Full Adder Primary The Half Adder is a type of combinational logic circuit that adds two  1-bit binary digits. It generates carry and sum for the inputs. The Full Adder is a type of combinational logic that adds binary digits. It generates the sum of all three inputs along with a carry value. Addition of the  Previous Carry The Half Adder does not add the carry obtained from the previous addition. The Full Adder, with its current inputs A and B, also adds the previous carry. Hardware Structure A Half Adder consists of only one AND gate and an  EX-OR gate. A Full Adder consists of an OR gate and two EX-OR and AND gates. Inputs There are two inputs in a Half Adder- A and B. There are a total of three inputs in a Full Adder- A, B, and  C-in. Features The Half Adder is good for digital measuring devices, computers, calculators, etc. The Full Adder comes into play in various digital processors, the addition of multiple bits, etc.

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FAQs

• There are various difference between half adder and full adder, half adder consists of two inputs while a full adder consists of three inputs that is the number to be added, carry in and carry out.

• Half adder uses two gates, AND gate and EX-OR gate while full adder uses two AND gates, two EX-OR gates and one OR gate. However, both of these combinational circuits perform the same task.

• Yes, two half adders can be used to implement one full adder at the LSB along with OR gates. A full adder can also be implemented using other combinational circuits like multiplexer.

• Half adder is fast in comparison to full adder as it uses less number of logic gates, which increases the speed of the calculation as the number of gates used are fewer than the number of gates used in the full adder.

• A full adder is a combinational device that has various applications in the field of electronic communications. It is used in the ALU of the CPU for various calculations, it is also used in the graphic processing unit.

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