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Two's complement is a method for representing signed integers in binary form. It is widely used in computer systems due to its simplicity and efficiency in performing arithmetic operations.
Key Principles
In two's complement, the most significant bit (MSB) is used as the sign bit. If the MSB is 0, the number is positive; if the MSB is 1, the number is negative1. This representation allows for a single representation of zero and simplifies arithmetic operations.
Conversion Process
To convert a positive binary number to its two's complement (negative form), follow these steps:
Invert all bits: Change every 0 to 1 and every 1 to 0.
Add 1: Add 1 to the inverted number, ignoring any overflow.
For example, to find the two's complement of 6 (binary 0110):
Invert all bits: 0110 becomes 1001.
Add 1: 1001 + 1 = 1010.
Thus, the two's complement of 6 is 1010, which represents -61.
Arithmetic Operations
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