Half Adder and Full Adder.

Half Adder

• Two binary inputs and two binary outputs are required for a half-adder circuit. While the output variable generates the total and carry, the input variable displays the augend and addend bits. 
• By creating a truth table, we can comprehend how a half-adder works. A half-adder's truth table is as follows:

Truth table of Half Adder

• 'x' and 'y' are the two inputs, and S (Sum) and C (Carry) are the two outputs.
• The Carry output is '0' unless both the inputs are 1.
• 'S' represents the least significant bit of the sum.

The simplified sum of products (SOP) expressions is:

• S = x'y+xy', C = xy

The logic diagram for a half-adder circuit can be represented as:

Half Adder

Full Adder

• This circuit needs three binary inputs and two binary outputs. The truth table for a full-adder is:

Truth table of Full Adder.

• Two of the input variable 'x' and 'y', represent the two significant bits to be added.
• The third input variable 'z', represents the carry from the previous lower significant position.
• The outputs are designated by the symbol 'S' for sum and 'C' for carry.
• The eight rows under the input variables designate all possible combinations of 0's, and 1's that these variables may have.
• The input-output logical relationship of the full-adder circuit may be expressed in two Boolean functions, one for each output variable.
• Each output Boolean function can be simplified by using a unique map method.

K-Maps for a full-adder:

The logic diagram for a full-adder circuit can be represented as:

 Full Adder.

Difference between the Half adder and full adder:

S.No.	Parameters	Half Adder	Full Adder
1.	Description	Half Adder is a combinational logic circuit that adds two 1-bit digits. The half adder produces a sum of the two inputs.	A full adder is a combinational logic circuit that performs an addition operation on three one-bit binary numbers. The full adder produces a sum of the three inputs and carry value.
2.	Previous carry	The previous carry is not used.	The previous carry is used.
3.	Inputs	In Half adder, there are two input bits ( A, B).	In full adder, there are three input bits (A, B, C-in).
4.	Outputs	The generated output is of two bits-Sum and Carry from the input of 2 bits.	The generated output is of two bits-Sum and Carry from the input of 3 bits.
5.	Used as	A half adder circuit cannot be used in the same way as a full adder circuit.	A full adder circuit can be used in place of a half adder circuit.
6.	Feature	It is simple and easy to implement	The design of a full adder is not as simple as a half adder.
7.	Logical Expression	Logical Expression for half adder is : S=a⊕b ; C=a*b.	Logical Expression for Full adder is : S=a⊕b⊕Cin; Cout=(a*b)+(Cin*(a⊕b)).
8.	Logic gates	It consists of one EX-OR gate and one AND gate.	It consists of two EX-OR, two AND gates, and one OR gate.
9.	Applications	It is used in Calculators, computers, digital measuring devices, etc.	It is used in Multiple bit addition, digital processors, etc.
10.	Alternate name	There is no alternate name for half adder.	Full adder is also known as ripple-carry adder.