Two's complement representation is a method of representing signed integers in binary form. It is based on the idea that the leftmost bit of a binary number represents the sign, with 0 indicating a positive number and 1 indicating a negative number. This method allows for efficient mathematical operations on signed integers in computer systems.
To calculate the two's complement representation of a number, the following steps can be followed:
The final result is the two's complement representation of the original number.
With n bits, two's complement representation can represent numbers in the range of -2n-1 to 2n-1 - 1. For example, with 8 bits, the range is -128 to 127.
Two's complement representation is used in computer systems because it allows for efficient mathematical operations on signed integers. It also simplifies the logic needed for addition and subtraction, making it a more practical choice for computers.
The advantages of using two's complement representation include its ability to represent both positive and negative numbers using the same binary system, simplifying mathematical operations, and the ability to represent a wider range of numbers compared to other signed integer representations. Additionally, two's complement is the most commonly used method for representing signed integers in computer systems, making it a standardized and widely understood system.