Difference Between Half Adder and Full Adder?

Full Adders and Half Adders work on the same basic principle, a half adder is a method of adding two binary numbers using only the left-most bits. Half adders are fast and efficient, but they only work for binary numbers. If you want to add a decimal number, you will need a full adder. A full adder can add decimal numbers just like binary numbers, but it can also add decimal numbers in the middle bits, too

Half Adder

Half Adder is a combinational logic circuit and it is obtained by connecting one EX-OR gate and another is AND gate. The half adder circuit has two inputs which are A and B and two outputs that are Sum and Carry. The output of the EX-OR gate is the Sum that is obtained from the sum of both the one-bit numbers. that is called the Half Adder circuit.

Half Adder Circuit

Half adder Circuit


Half-Adder Circuit Diagram

Truth Table Of Half Adder

Half Adder Truth Table

Logical Expression of Half Adder

Sum (S) = A ⊕ B

Carry (C) = A . B

Full Adder

Full Adder also combinational logic circuits like half adder and it consists of two EX-OR gates, two AND gates, and one OR gate. Full Adder can adds three inputs and gives two outputs from EX-OR, AND, and OR gates. The first two inputs are A and B among three inputs and third input is carry as C-IN. According to circuit diagram the output is designed as C- Out and the normal output is designed as S that is SUM.

Full Adder Circuit


Full Adder circuit

Full Adder Circuit Diagram

Truth Table Of Full Adder


full adder truth table


Logical Expression of Full Adder

CARRY-OUT = AB + BCin + ACin

SUM = (A ⊕ B) ⊕ Cin

Difference Between Half Adder and Full Adder

Half Adder

Full Adder

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.
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.
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.
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.
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.
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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