Your Question:

implement the following boolean function with nor gate F(A,B,C,D) = sum (0,1,4,5,8,9,10,11)

Step By Step Answers with Explanation

To implement the given Boolean function F(A, B, C, D) = Σ(0, 1, 4, 5, 8, 9, 10, 11) using NOR gates, we will first find the complemented form of this function and then create a logic circuit using NOR gates to represent it.

We have the following complemented terms:

- A'BC'D'

- A'BC'D

- AB'C'D

1. NOR gate for A'BC'D':

- Inputs: A', B, C', D'

- Output: Q2

- Logic: Q2 = (A + B' + C' + D')'

4. NOR gate for AB'CD':

- Inputs: A, B', C, D

- Output: Q5

- Logic: Q5 = (A + B + C' + D')'

7. NOR gate for AB'C'D:

- Inputs: A, B', C', D

- Output: Q8

- Logic: Q8 = (A' + B + C + D)'

- Logic: F'(A, B, C, D) = (Q1 + Q2 + Q3 + Q4 + Q5 + Q6 + Q7 + Q8)'

This final NOR gate represents the complemented form of the given Boolean function F(A, B, C, D). If you want to obtain the original function F(A, B, C, D), you can invert the output of this final NOR gate using a NOT gate.