computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

, the sign bit is a

bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...

in a signed number representation that indicates the

sign A sign is an object, quality, event, or entity whose presence or occurrence indicates the probable presence or occurrence of something else. A natural sign bears a causal relation to its object—for instance, thunder is a sign of storm, or ...

of a number. Although only signed numeric data types have a sign bit, it is invariably located in the

most significant bit In computing, bit numbering is the convention used to identify the bit positions in a binary number. Bit significance and indexing In computing, the least significant bit (LSB) is the bit position in a binary integer representing the binar ...

position, so the term may be used interchangeably with "most significant bit" in some contexts. Almost always, if the sign bit is 0, the number is non-negative (positive or zero). If the sign bit is 1 then the number is negative, although formats other than

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 (the leftmost bit in big- endian ...

integers allow a

signed zero Signed zero is zero with an associated sign. In ordinary arithmetic, the number 0 does not have a sign, so that −0, +0 and 0 are identical. However, in computing, some number representations allow for the existence of two zeros, often denoted by ...

: distinct "positive zero" and "negative zero" representations, the latter of which does not correspond to the mathematical concept of a

negative number In mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed ma ...

. In the two's complement representation, the sign bit has the

weight In science and engineering, the weight of an object is the force acting on the object due to gravity. Some standard textbooks define weight as a vector quantity, the gravitational force acting on the object. Others define weight as a scalar qua ...

where is the number of bits. In the ones' complement representation, the most negative value is , but there are two representations of zero, one for each value of the sign bit. In a sign-and-magnitude representation of numbers, the value of the sign bit determines whether the numerical value is positive or negative.

Floating-point In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can ...

numbers, such as IEEE format, IBM format, VAX format, and even the format used by the Zuse Z1 and Z3 use a sign-and-magnitude representation. When using a complement representation, to convert a signed number to a wider format the additional bits must be filled with copies of the sign bit in order to preserve its numerical value, a process called '' sign extension'' or ''sign propagation''.

References

Binary arithmetic Computer arithmetic {{Comp-sci-stub