Two's complement

Two's complement is the most popular method of signifying negative integers in computer science.

Related Topics:
Complement - Method of signifying negative integers - Computer science

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It is also an operation of negation (converting positive to negative numbers or vice versa) in computers which represent negative numbers using two's complement.

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Its use is ubiquitous today because it doesn't require the addition and subtraction circuitry to examine the signs of the operands to determine whether to add or subtract, making it both simpler to implement and capable of easily handling higher precision arithmetic.

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In the two's complement representation, the leftmost bit of a signed binary numeral indicates the sign. If the leftmost bit is 0, the number is interpreted as a non-negative binary number.

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If the most significant (leftmost) bit is 1, the bits contain a negative number in two's complement form.

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To obtain the absolute value of the negative number, all the bits are inverted then 1 is added to the result.

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A signed 8-bit binary numeral can represent any integer in the range −128 to +127. If the sign bit is 0, then the largest value that can be stored in the remaining seven bits is 27 − 1, or 127.

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Using two's complement as the method for representing negative numbers allows us to have only one representation of zero, and to have effective addition and subtraction while still having the most significant bit as the sign bit.

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