half adder and full adder | Circuit & K-Map

Half adder and full adder is a part of combinational circuits. Combinational circuits are those whose output characteristics depends on their input levels at a particular time. Some examples of combinational circuits are – multiplexer ( MUX ), demultiplexer ( DEMUX ), encoder, decoder, half adder and full adder half subtractor and full subtractor. These type of circuit does not include any memory, so the previous state of input and output doesn’t influence the current or further state.

In this article we are going to discuss about half adder and full adder in detail.

What is Adder ?

The digital logic circuit in electronics that is extensively used for addition of numbers is known as adder. Adders are used in processors that calculates addresses and similar activities. Adders are used in numerical representations like Binary Coded Decimal ( BCD ).

Adders are classified into two types –

1. Half adder
2. Full adder

What is Half Adder ?

A half adder is a combinational logic circuit. It has two inputs ( one bit each ) termed as A and B that generates sum ( S ) and carry ( C ) as output. Half adder is designed using two logic gates that is AND gate and XOR gate. The output of sum is obtained from XOR gate and the output of carry is obtained from AND gate.

Truth Table for Half Adder

The truth table of half adder is written by the concept of binary addition. The binary addition is done as shown below –

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0, carry = 1.

Expression is written only when logic 1 is obtained in output. Expression is written in SOP form where A = 1 and A’ = 0 also B = 1 and B’ = 0

A	B	Sum	Carry	Sum	Carry
0	0	0	0	–	–
0	1	1	0	A’B	–
1	0	1	0	AB’	–
1	1	0	1	–	AB

 

K Map for Half Adder

Expression for Half Adder

The logic expression for half adder is given as

Sum ( S ) = A’B + AB’ = A ⊕ B

Carry ( C ) = A . B

Half Adder Circuit

What is Full Adder ?

A full adder is a combinational logic circuit. It has three inputs ( one bit each ) termed as A, B and C_in that generates sum ( S ) and carry ( C )as output. Full adder is designed using two XOR gate, two AND gate, and one OR gate. The output of sum is obtained from XOR gate and the output of carry is obtained from OR gate. Shown in circuit below.

Truth Table for Full Adder

The truth table of full adder is also written by the concept of binary addition.

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 0, carry = 1.

Also, Expression is written only when logic 1 is obtained in output. Expression is written in SOP form where A = 1 and A’ = 0 also B = 1 and B’ = 0. Similarly, C = 1 and C’ = 0.

A	B	Cin	Sum	Carry	Sum	Carry
0	0	0	0	0	–	–
0	0	1	1	0	A’B’Cin	–
0	1	0	1	0	A’BC’	–
0	1	1	0	1	–	A’BC
1	0	0	1	0	AB’C’in	–
1	0	1	0	1	–	AB’C
1	1	0	0	1	–	ABC’in
1	1	1	1	1	ABC	ABC

K Map for Full Adder

Expression for Full Adder

The logic expression for full adder is given as

Sum = (A ⊕ B) ⊕ C_in

Carry = AB + BC_in + AC_in

Full Adder Circuit

Difference Between Half Adder and Full Adder

Half Adder	Full Adder
It is a type of combinational logic circuit that adds two binary digit of one bit each and provides output in the form of sum and carry.	It is a type of combinational logic circuit that adds three binary digits of one bit each and provides output on the form of sum and carry.
Half adder does not add the carry obtained from previous addition to the next addition.	Full adder adds the carry obtained from A, B to Cin.
A half adder circuit is designed using only one AND gate and XOR gate.	A full adder circuit is designed using two XOR gate, two AND gate and one OR gate.
Half adder has two inputs	Full adder has 3 inputs
Half adder is used in digital measuring devices and calculators, etc.	Full adder is used in digital processors and addition of multiple bits, etc.
The logic expression for half adder is given as Sum ( S ) = A’B + AB’ = A ⊕ B Carry ( C ) = A . B	The logic expression for full adder is given as Sum = (A ⊕ B) ⊕ Cin Carry = AB + BCin + ACin

 

Author

Akash Sharma

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