Digital Logic - Old Questions

7. Show that both NAND gate and NOR gate are universal gates.

An universal gate is a gate which can implement any Boolean function without need to use any other gate type. The NAND and NOR gates are universal gates.

NAND gate

NAND gate is the combination of NOT gate and AND gate. If the two input values for an NAND gate are both 1, the output is 0; otherwise, the output is 1.

Fig: Various representations of a NAND gate

NAND gate as a Universal Gate

To prove that any Boolean function can be implemented using only NAND gates, we will show that the AND, OR, and NOT operations can be performed using only these gates.

Thus, the NAND gate is a universal gate since it can implement the AND, OR and NOT functions.

NOR gate

NOR gate is the combination of NOT gate and OR gate. If the two input values for NOR gate are both 0, the output value is 1; otherwise, the output is 0.

Fig: Various representations of a NOR gate

NOR gate as a Universal Gate

To prove that any Boolean function can be implemented using only NOR gates, we will show that the AND, OR, and NOT operations can be performed using only these

Thus, the NOR gate is a universal gate since it can implement the AND, OR and NOT functions.