In Two's Complement, the leftmost (most significant) bit is used as the sign bit. If the sign bit is 0, the number is positive, and if it is 1, the number is negative. The remaining bits represent the absolute value of the number, just like in Sign and Magnitude, however the way the binary representation is generated is more complication..
Calculating Two's Complement
To calculate the negative value of a Two's Complement binary number:
invert (flip) all the bits
and add 1 to the resulting number.
This process converts the positive number into its negative counterpart.
Notes
when you add one to the number you perform a carry just like in normal binary addition.
Ignore any binary overflow from beyond the digits you use
A positive number needs to begin with a zero before conversion, so if it doesn't start with zero you will need to add a zero to the left.
Which bit is flipped when finding two's complement of a binary number?
The twos compliment binary representation of -15 is .
The 2's complement binary number 1001 is equivalent to in denary
Advantages of Two's Complement
1. Simplicity
Two's complement is a simple method of representing both positive and negative numbers using binary digits. It allows for easy arithmetic operations and logical manipulations.
2. Range of Representation
With two's complement, a wider range of values can be represented using a fixed number of bits compared to other number systems. This allows for efficient storage and manipulation of data.
3. Efficiency in Circuit Design
Two's complement is widely used in digital circuit design for arithmetic operations in processors, microcontrollers, and other electronic devices. Its efficient representation of negative numbers simplifies circuit design and reduces the complexity of hardware implementation.
4. Compatibility
Two's complement is compatible with various arithmetic algorithms and logic circuits, making it suitable for use in both hardware and software implementations. It is widely supported in computers, calculators, and digital systems.
Why is two's complement used instead of sign-magnitude representation?
