Question

How many gates, including inverters, are required to implement the equation, X = ACD + AB(CD + BC), before simplification?

A) 7
B) 9
C) 3
D) 5

Answer 1

To implement the equation X = ACD + AB(CD + BC) before simplification, a total of 7 gates, including inverters, are required.

Step-by-step explanation:

To implement the equation X = ACD + AB(CD + BC) before simplification, we can break it down into the following steps:

1. Implement the equation CD + BC using an OR gate, which requires 2 inputs and 1 output.
2. Implement the equation AB(CD + BC) using an AND gate, which requires 3 inputs and 1 output.
3. Implement the equation ACD using another AND gate, which requires 3 inputs and 1 output.
4. Add the outputs of the previous two steps using an OR gate, which requires 2 inputs and 1 output.
5. Implement the equation X = ACD + AB(CD + BC) using an OR gate, which requires 2 inputs and 1 output.
6. Implement the inverter for the X output, which requires 1 input and 1 output.

Therefore, a total of 7 gates, including inverters, are required to implement the equation before simplification.