What are Universal Gates? NAND and NOR Gate

What are Universal Gates?

Universal gates are those gates that can perform the tasks of other gates with minor adjustments. Universal gates are widely used in formulating NAT-based questions in the GATE exam. There are two universal gates:

• NAND Gate
• NOR Gate

Let us understand these universal gates in detail in the coming sections.

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NAND Gate

The NAND gate is one of the universal gates. The NAND gate is a AND gate followed by a NOT gate. Thus, we can say it is a AND NOT operation. It may have two or more inputs but only one output. The logical symbols of a NAND Gate and the truth table are shown below.

• Thus, the logical expression for the output is

It is clear from the truth table of the two-input NAND gate that the output is 1 when either A or B or both the inputs are at logic ‘0’. We can say that if Ā = 1 = B are, both A and B are 1, and the output is 1. Therefore, the NAND gate can perform the OR function by inverting the inputs.

• The output is the exact inverse of the AND gate for all possible input combinations in the NAND gate.
• The OR gate with inverted inputs is called bubbled OR gate or negative OR gate. The NAND gate is also called an active low OR gate.
• The switching circuit diagram for a NAND gate is shown below:

The bulb will glow when any of the switches A or B will open (logic 0).

• NAND gate follows the commutative law as (AB)’ = (BA).’

• NAND gate will not follow the associative law as

• Enable and disable inputs:

For a NAND Gate

For control = 0;

A	Control	Y
0	0	1
1	0	1

Thus, logic ‘0’ is the disabled input for the NAND gate.

For control = 1;

A	Control	Y
0	1	1
1	1	0

Thus, logic ‘1’ is the enable input for the NAND gate.

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NOR Gate

The NOR gate is one of the universal gates. A NOR gate combines two basic logic gates: an OR gate and a NOT gate. So we can say it is an OR-NOT operation. It may have two or more inputs and an output. The logical symbols of the NOR Gate are shown:

• It is clear from the truth table that the output is ‘1’ only if all the inputs are at logic ‘0’. It can also say that if the inputs A’ = B’ = 1, the output Y is 1. Thus, the NOR gate is equivalent to the AND gate with inverted inputs, and it can be realized by a bubbled AND gate, as shown above.
• The logical expression for the output is 

• The NOR gate is also called as the active LOW AND gate.
• The switching circuit of a NOR gate is as shown:

When any of the switches, either A or B, is closed, the bulb will not glow.

• NOR gate follows the commutative law as follows:
  

However, it does not follow the associative law.

• Enable and disable inputs:
  For a NOR Gate

If control = 0;

A	Control	Y
0	0	1
1	0	0

Thus, logic ‘0’ enables input.
If control = 1;

A	Control	Y
0	1	0
1	1	0

Thus, logic ‘1’ is disabled input.

Realization of the Logic Gate Using NAND Gate and NOR Gate

The realization of the logic gates is essential to the GATE CSE syllabus. These realizations using the NAND gate and NOR gate will help in building the strong conceptual base for the forthcoming exam.

NOT Gate Realization

Using NAND Gate

For the NOT gate realization, we require 1 NAND gate, as shown in the circuit diagram:

Using NOR Gate

For the NOT gate realization, we require 1 NOR gate, as shown in the circuit diagram:

AND Gate Realization

Using NAND gate

For the AND gate realization, we require 2 NAND gates, as shown in the circuit diagram:

Using NOR Gate

For the AND gate realization, we require 3 NOR gates if the inputs are not available in complement form, as shown in the circuit diagram:

OR Gate Realization

Using NAND Gate

For the OR gate realization, we require 3 NAND gates if the inputs are not available in complement form, as shown in the circuit diagram:

Using NOR Gate 

For the OR gate realization, we require 2 NOR gates, as shown in the circuit diagram:

 

EX-OR Gate Realization

Using NAND Gate

For the EX-OR gate realization, we require 4 NAND gates, as shown in the circuit diagram:

 

Using NOR Gate

For the EX-OR gate realization, we require 5 NOR gates, as shown in the circuit diagram:

EX-NOR Gate Realization

Using NAND Gate

 For the EX-NOR gate realization, we require 5 NAND gates, as shown in the circuit diagram: 

Using NOR Gate

For the EX-NOR gate realization, we require 4 NOR gates, as shown in the circuit diagram:

 

NOR Gate Realization Using NAND Gate

For the NOR gate realization using the NAND gate, we require 4 NAND gates, as shown in the circuit diagram:

NAND Gate Realization Using NOR Gate

For the NAND gate realization using the NOR gate, we require 4 NAND gates, as shown in the circuit diagram:

 

Shortcuts for the realization of logic gates are as follows:

GATES	Number of NAND gate	Number of NOR gate
NOT	1	1
AND	2	3
OR	3	2
EX-OR	4	5
EX-NOR	5	4

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