Build the Same Function in Both Minimum-Gate and Minimum-Depth Versions and Compare

EDA tools synthesize logic based on strict design constraints, trading off silicon area for signal propagation speed. A designer must structure the logic differently depending on whether the target is minimal gate count or minimal logic depth.

Implement the boolean function F = AB + ACD + BCD twice. Route the area-optimized (minimum-gate) version to F_area. Route the timing-optimized (minimum-depth) version to F_speed.

| A | B | C | D | F_area | F_speed | |-----|-----|-----|-----|----------|-----------| | 0 | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 1 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 0 | 0 | 0 | 0 | | 0 | 1 | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | 0 | 0 | | 0 | 1 | 1 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | 0 | 0 | | 1 | 0 | 0 | 1 | 0 | 0 | | 1 | 0 | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | 1 | 1 | | 1 | 1 | 1 | 0 | 1 | 1 | | 1 | 1 | 1 | 1 | 1 | 1 |

Constraints

• Implement F_area using a factored Boolean expression to minimize total gate count.
• Implement F_speed using a strict two-level sum-of-products (SOP) form to minimize logic depth.
• Do not share any logic gates between the F_area circuit and the F_speed circuit.
• Use only basic AND, OR, and NOT gates.

Topics

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