KembaraXtra – Computer Science – Full Adders
1. Introduction
Problem: Half adders only work for the least significant bits. Subsequent bits require handling a "carry-in" bit from previous additions.
Solution: A "full adder" circuit.
2. Full Adder: Definition
A full adder handles the addition of a single bit (place value) including a carry-in bit (Cin).
3. Full Adder: Symbol
A full adder has three inputs: A, B, and Cin.
A full adder has two outputs: S (Sum) and Cout (Carry-out).
4. Full Adder: Functionality
Inputs:
- A: First bit to be added.
- B: Second bit to be added.
- Cin: Carry-in bit from the previous bit position.
Outputs:
- S: The sum bit for the current bit position.
- Cout: The carry-out bit to be used as the carry-in for the next higher bit position.
5. Full Adder: Truth Table
| A |
B |
Cin |
S |
Cout |
| 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 |
Explanation: This table shows all possible input combinations (A, B, Cin) and the corresponding output values (S, Cout).
6. Full Adder: Implementation
- Realization: A full adder can be built using two half adders and one OR gate.
- Half Adder 1 (HA1): Adds A and B, producing a partial sum and a carry-out.
- Half Adder 2 (HA2): Adds the partial sum from HA1 and Cin, producing the final sum (S).
- OR Gate: The carry-out from the full adder (Cout) is 1 if either of the half adders produced a carry-out of 1. Therefore, the carry-out outputs of HA1 and HA2 are fed into an OR gate.
7. Encapsulation
Once constructed, the internal details of the full adder become hidden. You only need to understand its inputs (A, B, Cin) and outputs (S, Cout) to use it.
