Logic Gates: 7 Types, Truth Table & Symbols, Boolean Expression [PDF]

Are you Confused about the Logic Gates? Today we will study the Complete details of Logic Gates-(NOT, OR, AND, NOR, NAND, X-OR, X-NOR GATE), their types, symbols, and boolean expression of each logic gate. We have also provided a PDF for the same.

Definition of Logic Gates

A logic gate is a circuit with one or more input voltages but only one output voltage. logic gates are fundamental building blocks of the digital system. NOT, OR, and AND Gates are the basic types of gates.

The interconnection of gates to perform various logical operations is called logic design. A truth table lists all possible combinations of inputs and the corresponding outputs. All logic gates obey their truth table.

Types of Logic Gates

There are 7 types of logic gates. These are the fundamental ones:

AND Gate: When each and every input is true then it gives a true output.
OR Gate : When at least one input is true, it produces a true output.
NOT Gate: Produces the opposite output by reversing the input.
XOR Gate: If the inputs are different, it produces a true output.

Moreover, these gates may be combined to create more complex ones:

NAND gate: It is an AND gate’s reverse.
NOR Gate: It is the opposite of an OR gate.
XNOR Gate: Exclusive NOR operation 
Developing an understanding of these gates helps effective digital circuit construction and analysis.

AND gate

An AND gate is sometimes called the “all or nothing gate”. It has 2 or more input signals. It produces 1/High/On as output when all inputs are 1/High/On. Otherwise, it creates a 0 output (nothing).In other words, it creates a 0/Low/Off output when any input is 0/Low/Off. An AND gate corresponds to the action of series switches for the input. The below table shows the four commonly used methods for expressing the AND operation.

ABY
000
010
100
111
Truth Table of AND Gate

Logic gates
AND GATE
AND gate Boolean expression 
AND Gate Symbol
AND gate Circuit Diagram

OR Gate

An OR gate is sometimes called the “any or all gate”. It has 2 or more input signals. It produces a 1/High/On output if any or all inputs are 1/High/On. It produces a 0/Low/Off output when all inputs are 0/Low/Off. An OR gate corresponds to the action of parallel switches for the input. The below table shows the four commonly used methods for expressing the OR operation.

ABY
000
011
101
111
Truth Table of OR Gate
Logic gates
OR GATE
OR gate Boolean expression 
OR Gate Symbol
OR gate Circuit Diagram

NOT Gate

A NOT gate produces an output that is the complement of the input. It has only one input signal. It produces a 1/High/On output when the input is 0/Low/Off and produces a 0/Low/Off output when the input is 1/High/On. The four commonly used methods of expressing the NOT operation as shown in the figure.

AY
01
10
Truth Table of NOT Gate

Logic gates
NOT GATE
NOT gate Boolean expression 
NOT Gate Symbol
NOTE gate Circuit Diagram

NOR Gate

A NOR gate represents an OR gate followed by an inverter. It has 2 or more input signals. It produces a 1/High/On when all the inputs are 0/Low/Off. It produces a 0/Low/Off output when any or all of the inputs are 1/High/On. It therefore also acts as a negative (bubbled) AND gate. The below table shows the four commonly used methods for expressing the NAND operation.

ABY
001
010
100
110
Truth Table of NOR Gate

NAND Gate

A NAND gate presents an AND gate followed by an inverter. It has 2 or more input signals. It produces a 0/Low/Off output only when all the inputs are 1/High/On. It creates a 1/High/On output when any of the inputs is 0/Low/Off.De Mergon’s second theorem says that the NAND gate is equivalent to a negative (bubbled) OR gate. The below table shows the four commonly used methods for expressing the NAND operation.

ABY
001
011
101
110
Truth Table of NAND Gate

X-OR Gate

An exclusive-OR (X-OR) gate is an anti-coincidence gate. It produces a 1 output only when the odd number of 1 is present at a time. A 2-input X-OR gate is an inequality detector.

It produces a 1/High/On output only when its two inputs are not equal i.e. when one input is 1/High/On or 0/Low/Off. An X-NOR gate can be used as a controlled inverter by connecting one input terminal to logic 1/High/On and feeding the signal to be inverted to the other terminal. The below table shows the four commonly used methods for expressing the X-OR operation.

ABY
001
010
100
110
Truth Table of X-OR Gate

X-NOR Gate

An exclusive-NOR (X-NOR) gate is a coincidence gate. It produces a 1/High/On output only when an even number of 1/High/On is present at the input. A 2-input X-NOR gate is an equality detector.

It produces a 1/High/On output only when its two inputs are equal i.e. when both inputs are 1/High/On or 0/Low/Off. An X-NOR gate can be used as a controlled inverter by connecting one input terminal to logic 0/Low/Off and feeding the signal to be inverted to the other terminal. The below table shows the four commonly used methods for expressing the X-NOR operation.

ABY
001
010
100
111
Truth Table of X-NOR Gate

Conclusion

Logic gates are fundamental components in digital electronics, enabling the creation and manipulation of complex circuits. The seven types of logic gates (AND, OR, NOT, NAND, NOR, XOR, and XNOR) each have their own truth table symbols and Boolean expressions, representing their behavior. These symbols and expressions provide a standardized language for engineers to communicate and document circuit designs. By understanding and leveraging the principles of logic gates, engineers can design efficient and innovative digital systems. It is important to apply these concepts with integrity and originality, promoting ethical practices in the field of digital electronics.

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