Half Adder and Full Adder Circuit | Truth Table

Half and full adders are combinational logic circuits, but they are different for input processing. Any combinational circuit does not have a memory unit but comes with logic gates. There is a main difference between a half and a full adder. Hald Adder just added the current input single-bit number and did not focus on previous inputs. While Full Adder has a feature to carry current input to output from previous. Here we will cover the differences between the half-adder and full-adder circuits and their truth table. So let’s get started.

What is a half-adder?

A half-adder is a combinational logic circuit. It can be made by linking one AND gate and one EX-OR gate. The half-adder circuit has two inputs, normally X and Y. These two inputs are added and give output in the form of carry and sum. So it means it has two outputs as well.

The output we get from the EX-OR gate is the addition of both inputs. The output from the AND gate is carried. So it is not possible to send the carry that got in one addition in another addition. Since there is no logic gate for procprocessing, t is called the half-adder circuit. The equation of output from both gates in the form of a logical operation is written and performed by logic gates.

Half Adder Logical Equation

Sum (S) = X + Y

Carry (C) = X . Y

Half Adder Truth Table


X Y Z (Output) S (output)
0 0 0 0
1 0 0 1
0 1 0 1
1 1 1 0

What is Full Adder?

The full adder circuit comes with two AND gates, two EX-OR gates, and one OR gate. The full adder added 3 binary digits. In these three, one is the carry that we get from the previous addition as Z-IN, and the other is the two inputs X and Y. It denoted the input carry as Z-OUT and the normal output as S, which is SUM. Like the half adder, the full adder is a combinational logic circuit; it does not have a storage component. But it comes with extra logic gates. So it added the previous carry to produce the complete output. So it is known as a full adder.

Full adders can also be made with a combination of OR gat and two half adders. The OR gate produces carry what it gets after addition. We get a sum of these digits as output from the second-half adder. The equation for output that we can get through the EX-OR gate is the sum of all binary digits.

Full Adder logical  Equation

CARRY-OUT = XY + YZin + XZin

SUM = (X + Y) + Zin

Full Adder Truth Table

The full Adder Truth table is shown here

Inputs Outputs
X Y Cin S (Sum) Zout (Carry)
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
0 1 1 0 1
1 0 0 1 0
1 0 1 0 1
1 1 0 0 1
1 1 1 1 1


Difference Between Half Adder and Full Adder

Features Half Adder Full Adder
Definition a half-adder combinational logic circuit that added two one-bit binary digits. It produces carry and the sum of inputs. It is combinational logic that adds three one-bit binary digits for addition. It produces the sum of three inputs with a carrying value.
Previous Carry Addition This circuit does not add the carry from the previous addition to the next. This circuit, with its current inputs X and Y, added the previous carry.
Hardware It comes with an AND gate and an EX-OR gate. It has one OR gate and two EX-OR and AND gates.
Inputs It has two inputs, X and Y. It has three inputs, X, X. and Z-in.

It is used for digital calculation in

calculators, computers, etc.

It is used for the addition of different bits and digital processors.
Logical Equation

Z = X * Y

S = X + Y

Zout = (XY) +CinX +CinY

S =X ⊕ Y ⊕ Cin

Half Adder and Full Adder Circuit

Here we can see The Half Adder Circuit

Half Adder circuit


The basic disadvantage of this circuitry is that it adds two inputs and if an answer is carried it will not considered. So it does not have a complete process. For covering this feature full adder is made. That is used for complex addition, where a larger number of bits.

Full adder circuit diagram

The full adder circuit diagram is made here

Full adder circuit diagram

With the use of this circuit, we can add two bits, get them from the next lower order, and send them to the next higher order of magnitude. In a computer for multi-bit operation, every bit should be denoted with a full adder and should be added at the same time. So for the addition of two 8-bit numbers, eight full addresses are required, which can be made by cascading two of the 4-bit blocks.

Advantages of the Half Adder in Digital Logic

  1. The half-adder is easy to make and needs just simple components like XOR and AND. It is not difficult to carry out and can be used in different projects.
  2. Its working speed is high, making it best to use in high-speed computerized circuits.


  • It can add two numbers, generate a total, and convey a bit. It does not do expansion of many numbers that need the use of additionally completed circuits like a full adder.
  • It does not have a function to add a carry bit from the addition of previous results.
  • It is used to add multiple bits.
  • It is not used for cascading multi-bit additions.

Application of the Half Adder in Digital Logic

  1. is used in number crunching circuits for the addition of double numbers. So if different half-adders are connected in the series, they can add multi-bit double numbers.
  2. It is used for handling data, such as computerized signal processing and data encryption.
  3. It is used for addressing and deciphering circuits to generate the location of certain memory areas.
  4. It is used as an encoder and decoder for circuits.
  5. It is also part of multiplexers and demultiplexers.
  1. Advantages and Disadvantages of Full Adder in Digital Logic

    Advantages of Full Adder in Digital Logic

    1. It can add 3 bits to make it flexible, then a half adder. It is used to add many numbers with a combination of different full-adder circuits.
    2. It is used to carry input that helps with the expansion of many bits and the sequence of different adders with each other.
    3. It operates at high speed, making it the best choice for fast computer functions.

    Disadvantages of Full Adder in Digital Logic:

    • its circuit is completed, then half adder since it needed more XOR, AND,
    • It comes with a proliferation delay, which is the time taken from the result to adjust the data. It can result in time problems in computerized circuits, especially in high-speed frameworks.

    Application of Full Adder in Digital Logic:

    1. It is used for math circuits to add two numbers. It can make multiple-bit paired numbers.
    2. Full adders are used in data handling circuits such as advanced signal handling, data encryption, and error rectification.
    3. It is used in the counter for addition or reducing the count by one.
    4. Full adders are used in multiplexers and demultiplexers for choosing and data courses.
    5. Full adders are used in memory addressing circuits to generate the location of certain memory units.
    6. It is part of the ALUs used in chip and computerized signal processors.
    7. It is also used in the GPU (Graphical Processing Unit).

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