Assuming complemented literals B̅ and F̅ are available, the total number of…

Concept

In a direct two-level sum-of-products implementation, each displayed product term is formed by an AND gate, and all displayed product outputs feed one final OR gate.

Without Boolean minimization, the total gate-input count is the sum of all literal inputs entering the AND gates and all displayed product outputs entering the OR gate. Complemented literals are treated as already available unless inverter inputs are explicitly included.

Application

1. The four displayed product terms require 3, 4, 2, and 2 AND-gate inputs respectively.

2. Therefore, the AND stage uses 3 + 4 + 2 + 2 = 11 inputs.

3. The four displayed product outputs enter a four-input OR gate, adding 4 gate inputs.

4. Hence the stated direct two-level realization uses 11 + 4 = 15 gate inputs.

Cross-check

Counting gate by gate gives 3 + 4 + 2 + 2 + 4 = 15. Boolean minimization would absorb AB̅CD into AD and yield a different count, but minimization is explicitly excluded here. Likewise, separately counting NOT gates would use another convention.

Result: 15 gate inputs.