Question

Show how AND, OR Not gate functions can be implemented using only:

NOR gate

Answer 1

1. NOT Gate using NOR

Connect both inputs of a NOR gate to the same input A.

Y = (A + A)′ = A′

2. OR Gate using NOR

First apply A and B to a NOR gate:

X = (A + B)′

Now use another NOR gate as a NOT gate:

Y = (X + X)′ = A + B

Therefore,

A + B = [(A +B )′ + (A + B)′]′

3. AND Gate using NOR

First obtain A′ and B′ using NOR gates:

A′ = (A + A)′ 

B′ = (B + B)′

Then apply these to another NOR gate:

Y = (A′ + B′)′

By De Morgan's theorem,

Y = A ⋅ B