Four-Variable K-Map: Multi-Output Minimization Identifying Shared Product Terms
Hardware synthesis tools minimize logic across multiple outputs simultaneously to reduce silicon area and power consumption.
The logic block below defines two outputs, F1 and F2, based on four inputs A, B, C, and D.
F1 = Σm(0, 1, 2, 3, 4, 5, 8, 9, 10, 11) F2 = Σm(0, 1, 4, 5, 12, 13, 14, 15)
Analyze the Boolean functions to identify their prime implicants. Determine the optimal shared product term that minimizes the total gate count when implementing both functions in shared logic. Calculate the hardware savings compared to independent minimization.
Constraints
- Assume all inputs are available natively in both true and complemented forms.
- Assume the standard cell library only contains 2-input AND and 2-input OR gates.
- Do not count NOT gates used for input inversion.
Topics
Solve this problem
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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