Implementing Boolean Functions with Truth Tables
Problem 1: Implement the following function F(A, B, C) = Σ(2, 5, 6, 7) using a truth table with:
Truth Table for Function F(A, B, C)
| A | B | C | F |
|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
a. Decoder Implementation
A decoder is used to select one of the outputs based on the input combination. In this case, we have 3 inputs (A, B, C) and 8 possible combinations. The truth table shows that F = 1 for input combinations (010), (101), (110), and (111), and F = 0 for all other combinations. To implement this, we connect the corresponding decoder outputs to an OR gate.
b. Multiplexer Implementation
A multiplexer (MUX) selects one of the input lines and passes it to the output. The selection is controlled... Continue reading "Implementing Logic Functions with Decoders and MUXs" »