In
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 practical disciplines (includin ...
, 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 represented a ...
in a
signed number representation that indicates the
sign of a number. Although only
signed numeric data types have a sign bit, it is invariably located in the
most significant bit 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: 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 inequality (mathematics), less than 0 (number), zero. Negative numbers are often used to represent the magnitude of a loss ...
.
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 q ...
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 be ...
numbers, such as IEEE format
The Institute of Electrical and Electronics Engineers (IEEE) style is a widely accepted format for writing research papers, commonly used in technical fields, particularly in computer science. IEEE style is based on the Chicago Style. In IEEE ...
, 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
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