A combinational logic circuit that can add two binary digits (bits) and a carry bit, and produces a sum bit and a carry bit as output is known as a full-adder.
In other words, a combinational circuit which is designed to add three binary digits and produces two outputs (sum and carry) is known as a full adder. Thus, a full adder circuit adds three binary digits, where two are the inputs and one is the carry forwarded from the previous addition. The block diagram and circuit diagram of the full adder are shown in Figure-1.
Hence, the circuit of the full adder consists of one EX-OR gate, three AND gates and one OR gate, which are connected together as shown in the full adder circuit in Figure-1.
Full adder takes three inputs namely A, B, and Cin. Where, A and B are the two binary digits, and Cin is the carry bit from the previous stage of binary addition. The sum output of the full adder is obtained by XORing the bits A, B, and Cin. While the carry output bit (Cout) is obtained using AND and OR operations.
Truth table is one that indicates the relationship between input and output variables of a logic circuit and explains the operation of the logic circuit. The following is the truth table of the full-adder circuit −
| Inputs | Outputs | |||
|---|---|---|---|---|
| A | B | Cin | S (Sum) | Cout (Carry) |
| 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 |
Hence, from the truth table, it is clear that the sum output of the full adder is equal to 1 when only 1 input is equal to 1 or when all the inputs are equal to 1. While the carry output has a carry of 1 if two or three inputs are equal to 1.
K-Map (Karnaugh Map) is a tool for simplifying binary complex Boolean algebraic expressions. The K-Map for full adder is shown in Figure-2.
The characteristic equations of the full adder, i.e. equations of sum (S) and carry output (Cout) are obtained according to the rules of binary addition. These equations are given below −
The sum (S) of the full-adder is the XOR of A, B, and Cin. Therefore,
The carry (C) of the half-adder is the AND of A and B. Therefore,
The following are the important advantages of full adder over half adder −
The following are the important applications of full adder −
In this tutorial, we discussed all the key concepts related to full adders in digital electronics. Full adders play an important role in many digital electronic circuits because a full adder can be used realize several other critical digital circuits.
