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LOGIC GATES‐ DEFINITIONS, TYPES AND USES

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Vatsal edited this page Dec 24, 2024 · 1 revision

What are Logic Gates?

Logic gates are an electronic circuit that are designed by using electrical components like diodes, transistors, resistors, and more. It is used to perform logical operations based on the inputs provided to it and gives logical output that can be either high(1) or low(0). The operation of logic gates is based on the Boolean algebra or mathematics. Logic gate finds its uses in our day to day basis such as in the architecture of our telephone, laptops, tablets an memory devices.

Types of Logic Gates

Logic gates can be broadly classified into seven main categories:

AND Gate

An AND gate performs logical multiplication of binary inputs. The output of the AND gate is high (1) if both inputs are high (1); otherwise, the output is low (0).

Boolean Expression

The Boolean expression for the AND gate is:
A . B = X

The value of X will be true when both inputs are true.
image

Properties of AND Gate

  1. AND gate can accept two or more input values at a time.
  2. When all inputs are logic 1, the output is logic 1.

OR Gate

An OR gate performs logical addition. The output of the OR gate is high (1) if any of the inputs are high (1); otherwise, the output is low (0).

Boolean Expression

The Boolean expression for the OR gate is:
X = A + B

The value of X will be high (true) when at least one input is high (true).
image

Properties of OR Gate

  1. OR gate can have two or more input lines.
  2. When all inputs are low or logic 0, the output is low or logic 0.

NOT Gate

The NOT gate, also called an inverter, has a single input and output. It outputs the complement of the input: when the input is low, the output is high, and vice-versa.

Boolean Expression

The Boolean expression for the NOT gate is:
Y = Ā or Y = A’

The value of Y will be high when A is low.
image

Properties of NOT Gate

  1. The output is the complement of the input.
  2. NOT gate takes only one input.

NOR Gate

The NOR gate is a universal logic gate that gives a high (1) output when all inputs are low (0). It is the complement of the OR gate.

Boolean Expression

For inputs A and B, the expression for a NOR gate is:
O = (A + B)’

The value of O will be true when all inputs are low (0).
image

Properties of NOR Gate

  1. NOR gate can have two or more inputs.
  2. It gives a high output only when all inputs are low.

NAND Gate

The NAND gate, or "NOT AND," is a universal logic gate that gives a high (1) output unless all inputs are high (1). It is the complement of the AND gate.

Boolean Expression

For inputs A and B, the expression for a NAND gate is:
X = (A . B)’
image

Properties of NAND Gate

  1. NAND gate can take two or more inputs and produces one output.
  2. It produces a low output only when all inputs are high.

XOR Gate

The XOR (Exclusive OR) gate outputs high (1) when the inputs are dissimilar (one input is low and the other is high).

Boolean Expression

For inputs A and B, the expression for an XOR gate is:
X = A’B + AB’
image

Properties of XOR Gate

  1. XOR gate accepts only two inputs.
  2. The output is high when the inputs are dissimilar.

XNOR Gate

The XNOR (Exclusive NOR) gate outputs high (1) when the inputs are similar (both are high or both are low). It is the complement of the XOR gate.

Boolean Expression

For inputs A and B, the expression for an XNOR gate is:
Y = A ⊙ B
Or equivalently:
Y = AB + A’B’
Or using XOR gate logic:
Y = (A ⊕ B)’
image

Properties of XNOR Gate

  1. XNOR gate accepts only two inputs.
  2. The output is high when the inputs are similar.

Applications of Logic Gates

Logic gates are the fundamental building blocks of all digital circuits and devices. Here are some key digital devices that utilize logic gates in their circuits:

  • Computers
  • Microprocessors
  • Microcontrollers
  • Digital and smart watches
  • Smartphones, etc.

Advantages of Logic Gates

  1. Basic Functions
    Logic gates perform basic logical functions like AND, OR, NOT, XOR, NAND, and NOR. All digital operations and respective data processing rely on these functions.

  2. Speed
    Their extremely high-speed operation makes them essential in today's information processing systems, enabling quick data analysis.

  3. Reliability
    The behavior of logic gates is accurately defined, ensuring predictable operation when integrated into systems.

  4. Scalability
    The complexity of digital systems can be increased by interconnecting and replicating logic gates without significant changes in size or complexity.

  5. Low Cost
    The production cost of logic gates is relatively low, making them a cost-effective choice for constructing digital circuits.

  6. Low Power Consumption
    Logic gates consume minimal power, making them ideal for battery-operated gadgets or low-power consumption applications.

Created and maintained by Open Horizon® under the GNU AGPLv3 licence. Visit the full repository at https://github.com/openhorizonrobotics/ece-1.

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