Difference Between Half Adder and Full Adder

Half Adder Vs. Full Adder: What is the Difference Between Half Adder and Full Adder?

Both Half and Full adders are combinational logic circuits, and they both differ from each other in the aspect of input processing. Any combinational circuit is devoid of memory elements- they only comprise the logic gates. There is a primary difference between half adder and full adder. Half adder only adds the current inputs as 1-bit numbers and does not focus on the previous inputs. On the other hand, Full Adder can easily carry the current inputs as well as the output from the previous additions. 

Before we let us look into more difference between half adder and full adder, let us know a bit more about them individually.

What is a Half Adder?

It is a combinational logic circuit. You can design it by connecting one AND gate and one EX-OR gate. A half-adder circuit consists of two input terminals- namely A and B. Both of these add two input digits (one-bit numbers) and generate the output in the form of a carry and a sum. Thus, there are two output terminals.

The output that one obtains from the EX-OR gate is the sum of both the one-bit numbers. The output obtained from the AND gate is called the carry. But you cannot forward the carry that you obtain in one addition into another addition. It is because of the absence of any logic gate to process it. Thus, it’s called the Half Adder circuit.

We can write the equation of output for both the gates in the form of a logical operation that the logic gates perform. Here, we write the carry equation in the form of AND operation and the sum equation in the form of EX-OR operation.

Logical Expression of Half Adder

Sum (S) = A ⊕ B

Carry (C) = A . B

Truth Table

Here is a truth table representing the possible outputs obtained from the possible inputs in a Half Adder:

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

What is Full Adder?

A full adder is a circuit that has two AND gates, two EX-OR gates, and one OR gate. The full adder adds three binary digits. Among all the three, one is the carry that we obtain from the previous addition as C-IN, and the two are inputs A and B. It designates the input carry as the C-OUT and the normal output as S (or SUM).

Just like the Half Adder, the Full Ladder is a combinational type of logic circuit- meaning, it has no storage element. But it has additional logic gates. Thus, it adds the previous carry to generate the complete output. Thus, it is called the Full Adder.

One can also designate a Full Adder using one OR gate and two Half Adders. The OR gate here generates a carry that it obtains after the addition. We obtain the sum of these digits in the form of output from the second Half Adder.

The equation for the output that you can obtain by the EX-OR gate is the sum of all the binary digits. Here, the output that you obtain from the AND gate is the carry that you obtain by addition. This equation is in the form of a logical operation.

Logical Expression of Full Adder

CARRY-OUT = AB + BCin + ACin

SUM = (A ⊕ B) ⊕ Cin

Truth Table

A truth table represents the possible outputs obtained from the possible inputs. A truth table for the Full Adder is as follows:

Input Output
A B C SUM CARRY OUT
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

Parameter Half Adder Full Adder
Basics The Half Adder is a type of combinational logic circuit that adds two of the 1-bit binary digits. It generates carry and sum of both the inputs. The Full Adder is also a type of combinational logic that adds three of the 1-bit binary digits for performing an addition operation. It generates a sum of all three inputs along with a carry value.
Adding the Previous Carry The Half Adder does not add the carry obtained from the previous addition to the next one. The Full Adder, along with its current inputs A and B, also adds the previous carry.
Hardware Architecture 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.
Total 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. C-in.
Usage The Half Adder is good for digital measuring devices, computers, calculators, and many more. The Full Adder comes into play in various digital processors, the addition of multiple bits, and many more.
Logical Expression Here is the logical expression of Half Adder:

C = A * B

S = A ⊕ B

Here is the logical expression of Full Adder:

Cout = (AB) + CinA ⊕ CinB

S =A ⊕ B ⊕ Cin

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