What does two's complement mean?

Definitions for two's complement
two's com·ple·ment

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Wikipedia

  1. Two's complement

    Two's complement is a mathematical operation to reversibly convert a positive binary number into a negative binary number with equivalent (but negative) value, using the binary digit with the greatest place value to indicate whether the binary number is positive or negative (the sign). It is used in computer science as the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. When the most significant bit is a one, the number is signed as negative. (see Converting from two's complement representation, below). Two's complement is executed by 1) inverting (i.e. flipping) all bits, then 2) adding a place value of 1 to the entire inverted number (not necessarily applied only to a singular bit). For example, say the number −6 is of interest. +6 in binary is 0110 (the leftmost most significant bit is needed for the sign; positive 6 is not 110 because it would be interpreted as -2). Step one is to flip all bits, yielding 1001. Step two is to add the place value one to the flipped number, which yields 1010. To verify that 1010 indeed has a value of −6, remember that two's complement makes the most significant bit represent a negative place value, then add the place values: 1010 = 1×(-23)+0×(22)+1×(21)+0×(20) = 1(-8) + 0 + 1(2) + 0 = −6. Always ignore overflow - failing to ignore overflow will produce the wrong value for the result.

Wikidata

  1. Two's complement

    Two's complement is a mathematical operation on binary numbers, as well as a binary signed number representation based on this operation. The two's complement of an N-bit number is defined as the complement with respect to 2, in other words the result of subtracting the number from 2. This is also equivalent to taking the ones' complement and then adding one, since the sum of a number and its ones' complement is all 1 bits. The two's complement of a number behaves like the negative of the original number in most arithmetic, and positive and negative numbers can coexist in a natural way. In two's-complement representation, negative numbers are represented by the two's complement of their absolute value; in general, negation is performed by taking the two's complement. This system is the most common method of representing signed integers on computers. An N-bit two's-complement numeral system can represent every integer in the range − to + while ones' complement can only represent integers in the range − to +. The two's-complement system has the advantage that the fundamental arithmetic operations of addition, subtraction, and multiplication are identical to those for unsigned binary numbers. This property makes the system both simpler to implement and capable of easily handling higher precision arithmetic. Also, zero has only a single representation, obviating the subtleties associated with negative zero, which exists in ones'-complement systems.

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Numerology

  1. Chaldean Numerology

    The numerical value of two's complement in Chaldean Numerology is: 5

  2. Pythagorean Numerology

    The numerical value of two's complement in Pythagorean Numerology is: 4

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"two's complement." Definitions.net. STANDS4 LLC, 2024. Web. 19 Apr. 2024. <https://www.definitions.net/definition/two%27s+complement>.

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