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The 1s complement of a number is found by changing all ones to zeros and all zeros to ones. This is called as taking complement or 1's complement.
The 2s complement of binary number is obtained by adding 1 to the Least Significant Bit (LSB) of ones complement of the number.
2s complement=1s complement + 1
In mathematics, negative numbers in any base are represented by prefixing them with a − sign (negative sign). However, in computer hardware, numbers are represented in binary without any extra symbols, requiring a method of encoding the minus sign. In computing, 1's complement is one of the method to represent the negative numbers. However, 2's complement is dominant today. 1's complement could not have widespread use because of issues like negative zero, end-around borrow, etc.
1's complement has no special usage for negative integers. 2's complement makes sense because it can be used in natural addition and subtraction arithmetic without any need to change the bits. Providing that no overflow occurs, the sign bit of the result is just the right value.
Primary Advantage of two's complement is that the it has one value for zero while one's complement has 2 values for zero each for "Positive" zero & "Negative" zero. Another advantage is that 2's complement doesn't require carry values.