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An adder is a digital circuit that performs the arithmetic operation of addition. It takes two binary numbers as input and produces their sum as output. Adders are crucial components in digital systems, widely used in microprocessors, arithmetic logic units (ALUs), and various other digital applications.
There are two common types of adders: half adder and full adder.
1) Half Adder:
A half adder is a basic digital circuit that adds two binary digits (bits) and produces the sum and carry outputs.
It has two input bits, A and B, and two output bits: the sum (S) and the carry (C).
The truth table for a half adder is as follows:
A | B | Sum ( s ) | Carry ( c ) |
0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 |
The sum output (S) is the exclusive OR (XOR) of the input bits (A XOR B).
The carry output (C) is the AND of the input bits (A AND B).
2) Full Adder:
A full adder is a more complex circuit that adds three input bits: A, B, and a carry-in bit (Cin), producing the sum (S) and carry-out (Cout) bits.
It has three inputs (A, B, and Cin) and two outputs (S and Cout).
The truth table for a full adder is as follows:
A | B | D | Sum(S) | Carry (c) |
0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 1 |
1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 1 |
1 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 1 | 1 |
The sum output (S) is the XOR of the input bits and the carry-in (A XOR B XOR Cin).
The carry-out (Cout) is generated by a combination of AND and OR operations.
Implementation of digital logic in combinational circuit :
a) Half Adder Implementation:
A half adder can be implemented using basic logic gates such as AND, XOR, and NOT gates. In the half adder implementation: -
Connect single-bit inputs A and B.
Use an XOR gate to obtain the Sum output: S=A⊕B
Use an AND gate to obtain the Carry output: C=A⋅B
Inputs A and B are connected to both gates to generate the respective outputs.
b) Full Adder Implementation:
A full adder can be implemented using two half adders and an OR gate.
Here's the schematic representation of a full adder:
In the full adder implementation:
The first half adder adds A and B inputs to produce a partial sum and carry-out.
The second half adder adds the partial sum from the first half adder with the Cin input to produce the final sum and carry-out.
The OR gate combines the carry-out from the first half adder and the carry-out from the second half adder to produce the overall carry-out.
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