Logical Operations

Logical Operations

Logical Operations are used to make decisions in computing based on a set of conditions or rules.

  • AND Operation: The AND operation returns true if both conditions are true. For instance, (true AND true) is true, but (true AND false) is false.

  • OR Operation: The OR operation returns true if at least one condition is true. As an example, (false OR true) is true, and so is (true OR true).

  • NOT Operation: The NOT operation inverts the truth value. Essentially, if the input is true, it becomes false, and vice versa.

  • NAND Operation: The NAND operation is the opposite of the AND operation. It returns true unless both conditions are true. For instance, (true NAND true) is false.

  • NOR Operation: The NOR operation is the opposite of the OR operation. It only returns true when both conditions are false. By way of example, (false NOR false) is true.

  • XOR Operation: The XOR (exclusive OR) operation returns true if an uneven number of conditions are true. For instance, (true XOR false) is true, but both (true XOR true) and (false XOR false) are false.

  • XNOR Operation: The XNOR operation is the opposite of the XOR operation. It’s true only when an even number of conditions are true. So (true XNOR true) would be true.

Truth Tables

Truth Tables are used to summarise the outputs of logical operations for all possible inputs.

  • A truth table for AND, for instance, would show that A AND B is only true when both A and B are true.

  • A truth table for OR would show that A OR B is true when either A is true, B is true, or both are true.

  • You can also create truth tables for NAND, NOR, XOR, and XNOR operations.

Logic Gates

Logic Gates are used in physical systems to implement logical operations. They are the building blocks of digital circuits.

  • An AND gate outputs true (usually represented by 1) only when all its inputs are true.

  • An OR gate outputs true when at least one of its inputs is true.

  • A NOT gate (also known as an inverter) outputs the opposite of its input.

  • NAND, NOR, XOR, and XNOR gates can also be constructed.

It’s critically important to understand logical operations in computer science, as they provide the foundation for all computing logic and decision-making processes.