Page 73 - Computer science 868 Class 12
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2.3 HALF ADDER AND FULL ADDER
In digital systems, combinational circuits are designed to perform various data processing tasks like addition, subtraction,
multiplication, complement, shift, increment, decrement, etc. One such combinational circuit is the adder, which performs
the addition of binary numbers. Adders are of two types: (i) Half Adders and (ii) Full Adders.
2.3.1 Half Adder
The half adder is a combinational circuit that is designed to perform the
addition of two bits and produce the two binary outputs as sum (S) and
carry (C) bits.
Let us revise the rules to binary addition done in class XI to get the truth
table of half adder. A and B denote two inputs, then sum and carry are:
Input Output
A B Sum Carry
0 0 0 0
0 1 1 0
1 0 1 0
1 1 0 1
We can thus derive the Boolean expression of the sum and carry term as:
Sum term = A'.B+A.B' which is the Boolean expression of two variable XOR gate.
Carry term = A.B which can be represented using AND gate.
The logic circuit diagram of the half adder is shown below:
A Sum = A⊕B
B
Carry = A.B
2.3.2 Full Adder
The full adder is a combinational circuit that is designed to perform
the addition of three bits and produce the two binary outputs as sum
(S) and carry (C) bits.
The three bits are two standard input bits and the third one is the
carry from the previous column called the carry bit in input as carry-in
(C ) and the carry bit in output is called carry-out (C ).
in
out
The truth table of a full adder is the same as a binary addition of 3 bits.
Input Output
A B C in Sum C out
0 0 0 0 0
0 0 1 1 0
0 1 0 1 0
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Computer Hardware 71

