Integer Numbers

Understanding Integer Numbers

  • Integer numbers are a group of numbers that include all the whole numbers along with their negatives.
  • They are represented on the number line where each integer has a distinct predecessor and successor.
  • Difference between two integers is an integer.
  • Product of two integers is also an integer.
  • Note that integers include zero and negative values, unlike natural numbers.

Binary Representation of Integer Numbers

  • Positive integer numbers are represented in the binary system similar to natural numbers.
  • Dealing with negative integers in binary requires a system like two’s complement, which includes ‘flipping’ the bits and adding 1 to the binary representation.
  • Understanding this binary representation of integers, both positive and negative, is crucial to understanding the fundamental operation of computers.

Encoding and Decoding Integer Numbers

  • Encoding an integer number requires transforming a number from its original base (usually decimal) to another base, such as binary or hexadecimal.
  • Different protocols might be deployed for positive and negative numbers, with Two’s Complement being common for negatives.
  • Decoding follows the reverse process, where the integer is brought back to its original base from the encoded base representation.

Importance of Integer Numbers in Computing

  • Integer numbers are used to represent quantities that may be increased or decreased, such as account balances or game scores.
  • Specific instructions, called integer instructions, deal with integer data in machine-level operations.
  • Understanding integers is crucial to understanding arithmetic underflows and overflows in computing.
  • They also play a vital role in digital signal processing, graphics, and scientific computing.