### Definition

• Logic gates are fundamental building blocks of digital circuits that perform logical operations on binary inputs to produce a binary output.

### Features

• Logic gates are the core components of electronic devices or circuits that implement Boolean functions, which are mathematical functions that operate on binary variables (0 and 1).
• The logic gates can be combined in various ways to create more complex circuits and implement different logical functions.
• By connecting the inputs and outputs of these gates, it is possible to build digital systems capable of performing calculations, making decisions, and processing data in binary form.

### Type of Logic Gates

There are several types of logic gates, including:

#### (A) Fundamental Logic Gates:

• The fundamental logic gates are basic building blocks of digital circuits and are used to manipulate binary data.
• These fundamental logic gates, along with additional gates such as NAND, NOR, and XOR, form the foundation for constructing more complex digital circuits and performing logical operations.
• AND Gate:
• The AND gate takes two or more input signals and produces an output signal.
• The AND gate produces an output of 1 (or “true”/”high”) only when all of its inputs are 1; otherwise, the output is 0 (or “false”/”low”).
• It can be represented by the symbol “∧”.
• The AND logic gate can be represented by a Boolean expression as F=A.B
• It can be represented by the Truth table:  Boolean Input Variable A Boolean Input Variable B Output(F) 0 0 0 0 1 0 1 0 0 1 1 1
• OR Gate:
• The OR gate also takes two or more input signals and produces an output signal.
• The OR gate produces an output of 1 (or “true”/”high”) if at least one of its inputs is 1 (or “true”/”high”); otherwise, the output is 0 (or “false”/”low”).
• It can be represented by the symbol “∨”.
• The AND logic gate can be represented by a Boolean expression as F=A+B
• It can be represented by the Truth table:  Boolean Input Variable A Boolean Input Variable B Output (F) 0 0 0 0 1 1 1 0 1 1 1 1
• NOT Gate/Inverter:
• The NOT gate has a single input and produces an output that is the complement of the input.
• The NOT gate, also known as an inverter, produces the logical complement of its input.
• If the input is high(1), the output is low(0), and vice versa.
• It can be represented by the symbol “¬” or “!”.
• The AND logic gate can be represented by a Boolean expression as F=!A
• It can be represented by the Truth table:  Single Boolean Input Variable A Output (F) 0 1 1 0
• XOR Gate:
• The XOR (Exclusive OR) logic gate is a fundamental digital logic gate that produces a true (logic high) output only when the number of true inputs is odd.
• It can be represented using the symbol “⊕” or as an arrangement of transistors in electronic circuits.
• The XOR (exclusive OR) gate produces an output of 1 if the number of 1 input is odd; otherwise, the output is 0. In other words, the output of the XOR gate is true only when the inputs A and B are different.
• It can be represented by the symbol “⊕”.
• It can be represented by the Truth table:  Boolean Input Variable A Boolean Input Variable B Output (F) 0 0 0 0 1 1 1 0 1 1 1 0
• The XOR gate is commonly used in digital circuits for various applications, including data encryption, error detection, parity generation, and arithmetic operations.
• It is a fundamental building block in digital circuit design and is used in combination with other logic gates to create more complex circuits.

#### (B) Derived/Universal Logic Gates:

• NAND Gate:
• The NAND (NOT AND) gate is an AND gate followed by a NOT gate.
• It is called NAND because it performs the combination of the logical operations NOT and AND.
• It produces an output of 0 only when all of its inputs are 1; otherwise, the output is 1.
• A NAND gate has two or more inputs and one output.
• The output of a NAND gate is the inverse (logical NOT) of the AND operation of its inputs.
• In other words, the output is true (logic high) unless all of its inputs are true. If all inputs are true, the output is false (logic low).
• It can be represented by the Truth table-
 Boolean Input Variable A Boolean Input Variable B Output (F) 0 0 1 0 1 1 1 0 1 1 1 0

• The NAND gate is a versatile gate and can be used to implement any other type of gate, including AND, OR, NOT, XOR, etc.
• By connecting NAND gates together in specific configurations, we can create complex logic circuits and perform various logical operations.
• It is widely used in digital circuit design and forms the basis for many digital systems.
•
• NOR Gate:
• The NOR (NOT OR) gate is an OR gate followed by a NOT gate.
• It produces an output of 1 if all of its inputs are 0; otherwise, the output is 0.
• It is called NOR because it performs the combination of the logical operations NOT and OR.
• A NOR gate has two or more inputs and one output.
• The output of a NOR gate is true (logic high) only when all of its inputs are false. If any of the inputs are true, the output is false (logic low).
• The symbol for a NOR gate is an OR gate with a small circle at its output, similar to the symbol for a NAND gate.
• It can be represented by the Truth table-
 Boolean Input Variable A Boolean Input Variable B Output (F) 0 0 1 0 1 0 1 0 0 1 1 0

• Like the NAND gate, the NOR gate is a versatile gate and can be used to implement any other type of gate, including AND, OR, NOT, XOR, etc.
• By connecting NOR gates together in specific configurations, we can create complex logic circuits and perform various logical operations.
• It is widely used in digital circuit design and forms the basis for many digital systems.
• XNOR Gate:
• The XNOR (exclusive NOR) gate is a logic gate that produces an output of 1 if the number of 1 input is even; otherwise, the output is 0.
• It is the complement of the XOR gate.
• The XNOR gate can be represented by the symbol “⊙” or “≡”.
• The truth table for a two-input XNOR gate is as follows:  Boolean Input Variable A Boolean Input Variable B Output (F) 0 0 1 0 1 0 1 0 0 1 1 1
• The XNOR gate can also be expressed using Boolean algebra as:

Output = (A AND B) OR (NOT A AND NOT B)

Categories: Computer Organization