Logic Gates

LOGIC GATES

Logic gates are the fundamental building blocks of digital systems. Logic gates are electronic circuits that perform the most elementary Boolean operations. Before understanding the logic gates, we must understand the meaning of positive and negative logic.

Types of Logic Gates

Logic gates are electronic circuits with a number of inputs and one output. There are three basic logic gates, namely

1. OR gate,
2. AND gate,
3. NOT gate

Other logic gates that are derived from these basic gates are

1. NAND gate,
2. NOR gate,
3. EXCLUSIVE-OR gate,
4. EXCLUSIVE-NOR gate

AND Gate

An AND gate is a logic circuit with two or more inputs and one output that performs ANDing operation. The output of an AND gate is HIGH only when all of its inputs are in the HIGH state. In all other cases, the output is LOW. For a positive logic systems, it means that the output of the AND gate is a logic ‘1’ only when all of its inputs are in logic ‘1’ state. In all other cases, the output is logic ‘0’. The logic symbol and the truth table of a two-input AND gate are shown in Figure 2.3 and Table 2.6 respectively.

OR Gate

An OR gate is a logic circuit with two or more inputs and one output that performs ORing operation. The output of an OR gate is LOW only when all of its inputs are LOW. For all other possible input combinations, the output is HIGH. For a positive logic system, the output of an OR gate is a logic ‘0’ only when all of its inputs are at logic ‘0’. For all other possible input combinations, the output is a logic ‘1’. The logic symbol and the truth table of a two-input OR gate are shown in Figure 2.4 and Table 2.7 respectively.

NOT Gate

A NOT gate, also called an inverter is a one-input, one-output logic circuit whose output is always the complement of the input. That is, a LOW input produces a HIGH output, and vice versa. It means that for a positive logic system, a logic ‘0’ at the input produces a logic ‘1’ at the output, while a logic ‘1’ at the input produces a logic ‘0’ output. It is also known as a complementing circuit or an inverting circuit. The logic symbol and the truth table of an inverter are shown in Figure 2.5 and Table 2.8 respectively.

NAND Gate

The term NAND implies NOT-AND. A NAND gate is equivalent to AND gate followed by a NOT gate. The standard logic symbol for a 2-input NAND gate is shown in Figure 2.6. This symbol is same as AND gate symbol except for a small circle (bubble) on its output. This circle represents the NOT function.

The truth Table 2.9 of a NAND gate is obtained from the truth Table of an AND gate by complementing the output entries. The output of a NAND gate is a logic ‘0’ when all its inputs are a logic ‘1’.

For all other input combinations, the output is a logic ‘1’. NAND gate operation is logically expressed as

NOR Gate

The term NOR implies NOT-OR. A NOR gate is equivalent to OR gate followed by a NOT gate. The standard logic symbol for a 2-input NOR gate is shown in Figure 2.7. This symbol is same as OR gate symbol except for a small circle (bubble) on its output. This circle represents the NOT function.

The truth Table 2.10 of a NOR gate is obtained from the truth Table of an OR gate by complementing the output entries. The output of a NOR gate is a logic ‘1’ when all its inputs are logic ‘0’. For all other

input combinations, the output is a logic ‘0’. The output of a two-input NOR gate is logically expressed as

Exclusive-OR (XOR) Gate

The Exclusive-OR gate, commonly known as EX-OR gate, is a twoinput, one-output gate. The logic symbol for the Ex-OR gate is shown in Figure 2.8 and the truth table for a two-input EX-OR operation is given in Table 2.11.

From the truth table it can be stated that, the output of an EXOR gate is a logic ‘1’ when the two inputs are at different logic and a logic ‘0’ when the two inputs are at the same logic.

NOTE :

1. The exclusive-OR and equivalence gates both can be extended to more than two inputs. However, multiple-input exclusive OR gates are uncommon from the hardware standpoint.
2. For a multiple output-input EX-OR logic function we can conclude that the output of a multiple-input EX-OR logic function is a logic ‘1’ only when an odd number of input variables are ‘1’.

Exclusive-NOR (XNOR) Gate

The exclusive-NOR gate, commonly known as Ex-NOR, is an Ex-OR gate, followed by an inverter. It has two inputs and one output. The logic symbol for the Ex-NOR gate is shown in Figure 2.9, and the truth table for the two-input Ex-NOR operation is given in Table 2.12.

The output of a two-input EX-NOR gate is a logic ‘1’ when the inputs are same and a logic ‘0’ when they are different.

NOTE :

1. Likewise Ex-OR gates, three or more variable Ex-NOR gates also do not exist. Normally, multiple-input EX-NOR logic functions can be implemented using more than one 2-input Ex-NOR gates.
2. For a multiple output-input EX-NOR logic function we can conclude that the output of a multiple-input EX-NOR logic function is a logic ‘1’ only when an even number of input variables are ‘0’. Note if all inputs are 0, then also output will be ‘1’.

REFERENCES

1.        Digital Design by M. Morris Mano, Michael D Ciletti, Pearson

2.        Digital Fundamentals by Thomas L. Floyd, R. P. Jain, Pearson

3.        Digital Circuits and Design by S Salivahanan, S Arivazhagan, Vikas Publishing House Pvt Ltd.

4.        Digital Systems by Ronald J. Tocci, Neal S. Widmer, Gregory L. Moss, Pearson

5.        Digital Electronics Principles And Integrated Circuits by Anil K. Maini

6.        Fundamentals of Digital Circuits by Anand Kumar

7.        Digital Electronics by John Morris

8.        Digital Electronics : An Introduction To Theory And Practice By William Gothmann.