Design & Implementation of a One-Bit Full-Adder
Objective
To design and implement a full-adder circuit. A full-adder circuit computes the sum of three one-bit boolean inputs. Note that the sums of three one-bit inputs can be at most (3)10, which in binary is (11)2, thus the full-adder circuit has 3 inputs and still only two outputs.
Input/Outputs
Three one-bit inputs (A, B, C)
Two one-bit outputs (Sum and Carry)
Truth Table
INPUTS |
OUTPUTS |
|||
A |
B |
C |
Carry |
Sum |
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 |
Karnaugh Maps
Carry |
|||||
C |
A B |
||||
0 0 |
0 1 |
1 1 |
1 0 |
||
0 |
1 |
||||
1 |
1 |
1 |
1 |
||
Carry = AB+BC+AC
Sum |
|||||
C |
A B |
||||
0 0 |
0 1 |
1 1 |
1 0 |
||
0 |
1 |
1 |
|||
1 |
1 |
1 |
|||
Sum = A’B’C+A’BC’+ABC+AB’C’
= A’ . ( B
Å C) + A . ( B Å C )= A
Å ( B Å C )
Circuit Implementation