Data Representation: Logic

Data Representation: Logic

Basics of Logic in Computing

  • At its core, computing is based on binary logic, which deals with binary values - 0 and 1, True and False, Yes and No.
  • This binary logic structure is dependent on logic gates, electronic switches that execute logical operations.

Basics of Logic Gates

  • Logic gates process signals, representing them as binary values (0 is off/false and 1 is on/true).
  • The most basic types include the AND, OR and NOT gates. Other gates include the NAND, NOR, XOR and XNOR gates.
  • Each gate has a specific rule that it follows, known as the truth table that outlines the gate’s logic.

AND Gate

  • The AND gate outputs 1 only if both its inputs are 1. Otherwise, it outputs 0.

OR Gate

  • The OR gate outputs 1 if at least one of its inputs is 1. If both inputs are 0, it outputs 0.

NOT Gate

  • The NOT gate, or inverter, has only one input and one output. It inverts the value of the input, outputting 1 if the input is 0 and vice versa.

NAND, NOR, XOR, and XNOR Gates

  • NAND and NOR gates are the inverse of AND and OR gates respectively. NAND outputs 0 only if both inputs are 1, while NOR outputs 1 only if both inputs are 0.
  • XOR, or exclusive OR gate, outputs 1 only if exactly one of its inputs is 1. If both inputs are 0 or 1, it outputs 0.
  • The XNOR gate is the inverse of XOR. It outputs 1 if both inputs are the same, and 0 if they are different.

Use of Logic Gates

  • Logic gates form the basis of digital circuits, and are used in creating system memory, processors, and all the fundamental components of computers.
  • Entire flow of operations in a computer is guided by logic gates. This includes applications from simple calculator operations to complex gaming algorithms.
  • Understanding the operation of logic gates and the representation of logic in binary form is essential for understanding the operation of computer systems.