Implementation of Full Adder Using Half Adders

Below is the logic diagram to implement full adder using half adders

Steps to Implement Full Adder from Half Adders

Steps to implement full adder from half adders in above logic diagram :

• First connect first two input with first XOR gate and first AND gate which outputs A ⊕ B and AB respectively.
• Then, connect the third input and output of first XOR gate [i.e., A ⊕ B]as input to second XOR gate which results in the sum of full adder [i.e., A ⊕ B ⊕ C].
• Then, connect the output of first XOR gate [i.e., A ⊕ B] and third input C as the input to second AND gate [i.e., (A ⊕ B)C].
• After that connect the output of first AND gate [i.e., AB] and output of second AND gate [i.e., (A ⊕ B)C] as the input to OR gate which results in the carry of full adder i.e., AB + AC + BC.
• Since, we require 1 XOR and 1 AND gate to implement half adder and in above diagram we used 2 XOR gate, 2 AND gate and 1 OR gate.
• From above point we get that to implement full adder using half adders we require 2 half adders and 1 OR gate.

Below is the block diagram to implement full adder using half adders.

Steps to implement full adder from half adders in above block diagram :

• Connect first two inputs as the input of first half adder which results in two outputs sum and carry.
• Then, connect sum output of first half adder and third input as input to second half adder.
• Then, connect carry output of the first half adder and carry output of second half adder to OR gate.
• The sum output of second half adder gives us the sum of full adder.
• The output of the OR gate gives us the carry of full adder.
• Hence, to implement full adder using half adders, two half adders and one OR gate is required.

Implementation of full adder from half adders is possible because the half adders add two 1-bit inputs in full adder we add three 1-bit inputs. To obtain a full adder from a half adder we take the first two inputs and add them and use the sum and carry outputs and the third input to get the final sum and carry output of the full adder. In this article, we will explore half adders, and full adders and implement full adders using half adders.