Logic Gates & its Type

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-

• • • 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-

• • • 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)