3-Variable Function via Decoder
Look-up tables and programmable logic arrays rely on generating all possible input combinations and selectively routing them to outputs. A decoder paired with an OR gate acts as a universal logic generator capable of synthesizing any arbitrary Boolean function without requiring complex gate networks.
Implement the specific 3-variable Boolean function defined by the truth table below. The inputs are A (MSB), B, and C (LSB). The output is Y.
| A | B | C | Y | |-----|-----|-----|-----| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 0 |
Constraints
- Use exactly one 3:8 decoder.
- Use exactly one OR gate.
- Do not use any AND, NAND, NOR, or XOR gates.
- Leave all unused decoder outputs completely unconnected.
Topics
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