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twos-compliment.md

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Two's Compliment

Two's complement is a mathematical operation on binary numbers, and it is the most common method of representing signed integers in binary form. It allows for simple arithmetic operations and easy detection of overflow.

How Two's Complement Works

  1. Positive Numbers:

    • Positive numbers are represented as usual in binary.

  2. Negative Numbers:

    • To represent a negative number, follow these steps:
      1. Write the absolute value of the number in binary.
      2. Invert all the bits (change 0 to 1 and 1 to 0).
      3. Add 1 to the least significant bit (LSB).

Example

  • Representing 5 in 8-bit binary:

    • 00000101

  • Representing -5 in 8-bit binary:

    1. Write 5 in binary: 00000101
    2. Invert the bits: 11111010
    3. Add 1 to the LSB: 11111011

Advantages of Two's Complement

  • Single Representation for Zero: Unlike other methods, two's complement has only one representation for zero.
  • Simple Arithmetic: Addition, subtraction, and multiplication are straightforward and do not require special rules for positive and negative numbers.
  • Overflow Detection: Overflow can be easily detected by examining the carry into and out of the most significant bit.

Usage

Two's complement is widely used in computer systems and programming languages to handle signed integers efficiently.