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Difference between Half Adder and Full Adder

Difference between Half Adder and Full Adder

An adder is a circuit in digital electronics that performs addition on two binary digits, usually called bits. In many cases, an adder can also be used to subtract two numbers by inverting the second operand before addition. Digital circuits that perform addition are called adders, while those that perform subtraction are called subtractors. There are various types of adders like Half Adders and Full Adders which have different circuitry and working principles. In this blog post, we will discuss the difference between Half Adders and Full Adders. Stay tuned!

What is Half Adder?

  • Half Adder is a digital circuit that performs addition of two single bit binary numbers. The Boolean expression for Half Adder is given by: Half Adder Output = A XOR B. Where A and B are the input binary bits.
  • The Half Adder circuit diagram is shown below. It has two inputs ‘a’ and ‘b’ and two outputs, sum (S) and carry (C). C is generated when both the inputs are 1. The truth table for the half adder is also shown below.
  • As can be seen from the truth table, when A=B=0, Half Adder output is 0. When A=B=1, Half Adder output is 1. When A=0 and B=1 or A=1 and B=0, Half Adder output is 1. So we can say that Half Adder performs addition of two binary bits just like we perform addition of two decimal numbers.”

What is Full Adder?

  • Full Adder is a logic circuit that performs an addition operation on three input bits. The inputs are two operands and a carry bit, and the output is the sum of the three inputs.
  • Full adders are used in processors, memories, and other digital circuits where addition is required. Full adders are typically implemented using logic gates, but they can also be implemented using other electronic components such as flip-flops.
  • Full adders can be cascaded to form ripple-carry adders, which can be used to add large numbers. Full adders are also used in carry-lookahead adders, which are faster but more complex.

Difference between Half Adder and Full Adder

Half Adder and Full Adder are two important terms associated with digital logic.

  • Half adder is a combinational circuit that performs the addition of two binary digits. Unlike a full adder, it cannot handle carry-over addition.
  • On the other hand, a full adder is a combinational circuit that takes three input bits and produces two output bits, namely sum and carry.
  • A full adder can perform the addition of three binary digits. The main difference between a half adder and a full adder is that a half adder cannot handle carry-over addition whereas a full adder can handle carry-over addition.

Half adders are generally used to create larger digital circuits such as full adders. Other than that, both half and full-adders are used to perform arithmetic operations in digital systems.


The half adder is the simpler of the two circuits, and can be used to add any two one-bit binary numbers together. For example, if you have a three-bit number (binary), the half adder circuit can produce the sum of all those bits by adding the first two bits and then adding the second two bits. The full adder is more complex, but it can be used to add any two n-bit binary numbers together where n is an integer greater than 2. It takes advantage of carryover logic to reduce the number of gates needed in order to produce the sum of all those bits. So which one should you use? If you only need to add a few small numbers together, then go with the half adder. But if you need to perform calculations on larger binary numbers, then you’ll want to use the full adder circuit instead.

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