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.

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 –

### 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 The logic expression for half adder is given as

Sum ( S ) = A’B + AB’ = A ⊕ B

Carry ( C ) = A . B ### What is Full Adder ?

A full adder is a combinational logic circuit. It has three inputs ( one bit each ) termed as A, B and Cin 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 The logic expression for full adder is given as

Sum = (A ⊕ B) ⊕ Cin

Carry = AB + BCin + ACin 