Question

Simplify the following function and implement it with a two-level NOR gate circuit.

F(x,y,z) = [(x+y)(x+z)]'

Answer 1

To simplify the function F(x,y,z) = [(x+y)(x+z)]', we can apply Boolean algebra. The simplified expression is F(x,y,z) = x'y' + x'z'. We can implement this with a two-level NOR gate circuit.

Step-by-step explanation:

To simplify the function F(x,y,z) = [(x+y)(x+z)]', we need to apply Boolean algebra. Let's start by expanding the expression:

F(x,y,z) = [(x+y)(x+z)]' = (x+y)' + (x+z)'

Using De Morgan's laws, we can simplify further:

F(x,y,z) = x'y' + x'z'To implement this function with a two-level NOR gate circuit, we need to derive the Boolean expression and then convert it into NOR gates. The simplified expression is F(x,y,z) = x'y' + x'z'. We can implement this using 3 NOR gates:

Output = NOR(NOR(x', y'), NOR(x', z'))