FULL ADDER
FULL ADDER
Full adder is a combinational circuit, which performs the addition of three bits A, B and Cin. Where, A & B are the two parallel significant bits and Cin is the carry bit, which is generated from previous stage. This Full adder also produces two outputs sum, S & carry, Cout, which are similar to Half adder.
The Truth table of Full adder is shown below.
| Inputs | Outputs | |||
|---|---|---|---|---|
| A | B | Cin | Cout | S |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 1 |
| 0 | 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 |
When we do the addition of three bits, the resultant sum can have the values ranging from 0 to 3 in decimal. We can represent the decimal digits 0 and 1 with single bit in binary. But, we can’t represent the decimal digits 2 and 3 with single bit in binary. So, we require two bits for representing those two decimal digits in binary.
Let, sum, S is the Least significant bit and carry, Cout is the Most significant bit of resultant sum. It is easy to fill the values of outputs for all combinations of inputs in the truth table. Just count the number of ones present at the inputs and write the equivalent binary number at outputs. If Cin is equal to zero, then Full adder truth table is same as that of Half adder truth table.
We will get the following Boolean functions for each output after simplification.
S=A⊕B⊕Cin
Cout=AB+(A⊕B)cin
