Implement (A+B+C)(A+B+D) by Factoring
Logic synthesis tools routinely collapse complex Product-of-Sums expressions by identifying shared subexpressions to minimize area and delay. Recognizing and factoring out common terms at the schematic level prevents unnecessary gate duplication in critical data paths.
The circuit implements the Boolean function Y = (A + B + C)(A + B + D).
| A | B | C | D | Y | |-----|-----|-----|-----|-----| | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 1 | | 0 | 1 | 0 | 0 | 1 | | 0 | 1 | 0 | 1 | 1 | | 0 | 1 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 0 | 1 | | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 1 | | 1 | 1 | 0 | 1 | 1 | | 1 | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | 1 |
Constraints
- Implement the optimized function using a maximum of 3 logic gates.
- Do not expand the expression into a full Sum-of-Products form.
- Use only combinational logic.
Topics
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Place the gates, wire them up and watch the signals settle. Every submission runs on the same simulation engine that grades it.
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