Universal Gates (NAND, NOR Gate)

Universal Gates

The NAND and NOR gates are known as universal gates, since any logic function can be implemented using NAND or NOR gates.

1. NAND Gate

The NAND gate can be used to generate the NOT function, the AND function, the OR function, and the NOR function.

NOT function :

An inverter can be made from a NAND gate by connecting all of the inputs together and creating, in effect, a single common input, as shown in Fig. 2.5.1, for a two–input gate.

AND function :

An AND function can be generated using only NAND gates. It is generated by simply inverting output of NAND gate i.e.  = AB. Fig. 2.5.2 shows the two input AND gate using NAND gates.

OR function :

OR function is generated using only NAND gates as follows: We know that Boolean expression for OR gate is

Y = A + B

The above equation is implemented using only NAND gates as shown in Fig. 2.5.3.

Note : Bubble at the input of NAND gate indicates inverted input.

NOR function :

NOR function is generated using only NAND gates as follows : We know that Boolean expression for NOR gate is

The above equation is implemented using only NAND gates, as shown in Fig. 2.5.4.

2. NOR Gate

Similar to NAND gate, the NOR gate is also a universal gate, since it can be used to generate the NOT, AND, OR and NAND functions.

NOT function :

An inverter can be made from a NOR gate by connecting all of the inputs together and creating, in effect, a single common input, as shown in Fig. 2.5.5.

OR function :

An OR function can be generated using only NOR gates. It can be generated by simply inverting output of NOR gate; i.e.  = A + B. Fig. 2.5.6 shows the two input OR gate using NOR gates.

AND function :

AND function is generated using only NOR gates as follows : We know that Boolean expression for AND gate is

Y = A . B

The above equation is implemented using only NOR gates as shown in Fig. 2.5.7.

Note : Bubble at the input of NOR gate indicates inverted input.

NAND function :

NAND function is generated using only NOR gates as follows: We know that Boolean expression for NAND gate is

The above equation is implemented using only NOR gates, as shown in Fig. 2.5.8.

Review Questions

1. What are universal gates? Give examples.

2. Why NAND and NOR gates are called universal gates?

3. Why digital circuits are more frequently constructed with NAND or NOR gates than with AND and OR gates?

4. Realize (i) AND gate (ii) NOR gate using only NAND gates.

5. Show how to connect NAND gates to get an AND gate and OR gate ?

6. Realize (i) OR gate (ii) AND gate using only NOR gates.