Question

Show that the NOR gate is functionally complete by implementing a NOT gate, a two-input AND gate, and a two-input OR gate using only two-input NOR gates.

Answer 1

To show that the NOR gate is functionally complete, we can implement a NOT gate, a two-input AND gate, and a two-input OR gate using only two-input NOR gates.

Step-by-step explanation:

A NOR gate is functionally complete if it can be used to implement all other logic gates. To show that the NOR gate is functionally complete, we can implement a NOT gate, a two-input AND gate, and a two-input OR gate using only two-input NOR gates.

1. Implementing a NOT gate: To implement a NOT gate using a two-input NOR gate, we connect both inputs of the NOR gate together. The output will be the inverse of the input.
2. Implementing a two-input AND gate: To implement a two-input AND gate using two two-input NOR gates, connect the outputs of both NOR gates to the inputs of another NOR gate. The output of this NOR gate will be the result of the AND operation.
3. Implementing a two-input OR gate: To implement a two-input OR gate using two two-input NOR gates, connect the inputs of one NOR gate to each input of the OR gate, and connect the output of this NOR gate to both inputs of the other NOR gate. The output of this NOR gate will be the result of the OR operation.