In computing, signedness is a property of data types representing numbers in computer programs. A numeric variable is signed if it can represent both positive and negative numbers, and unsigned if it can only represent non-negative numbers (zero or positive numbers).
As signed numbers can represent negative numbers, they lose a range of positive numbers that can only be represented with unsigned numbers of the same size (in bits) because roughly half the possible values are non-positive values, whereas the respective unsigned type can dedicate all the possible values to the positive number range.
For example, a two's complement signed 16-bit integer can hold the values −32768 to 32767 inclusively, while an unsigned 16 bit integer can hold the values 0 to 65535. For this sign representation method, the leftmost bit (most significant bit) denotes whether the value is positive or negative (0 for positive, 1 for negative).
For most architectures, there is no signed–unsigned type distinction in the machine language. Nevertheless, arithmetic instructions usually set different CPU flags such as the carry flag for unsigned arithmetic and the overflow flag for signed. Those values can be taken into account by subsequent branch or arithmetic commands.
The C programming language, along with its derivatives, implements a signedness for all integer data types, as well as for "character". For Integers, the unsigned modifier defines the type to be unsigned. The default integer signedness is signed, but can be set explicitly with signed modifier. By contrast, the C standard declares signed char, unsigned char, and char, to be three distinct types, but specifies that all three must have the same size and alignment. Further, char must have the same numeric range as either signed char or unsigned char, but the choice of which depends on the platform. Integer literals can be made unsigned with U suffix. For example, 0x FFFFFFFF gives −1, but 0xFFFFFFFFU gives 4,294,967,295 for 32-bit code.
Compilers often issue a warning when comparisons are made between signed and unsigned numbers or when one is cast to the other. These are potentially dangerous operations as the ranges of the signed and unsigned types are different.
In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of bits, usually four or eight. Sometimes, special bit patterns are used for a sign or other indications.
In computing, floating-point arithmetic (FP) is arithmetic using formulaic representation of real numbers as an approximation to support a trade-off between range and precision. For this reason, floating-point computation is often found in systems which include very small and very large real numbers, which require fast processing times. A number is, in general, represented approximately to a fixed number of significant digits and scaled using an exponent in some fixed base; the base for the scaling is normally two, ten, or sixteen. A number that can be represented exactly is of the following form:
In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are commonly represented in a computer as a group of binary digits (bits). The size of the grouping varies so the set of integer sizes available varies between different types of computers. Computer hardware, including virtual machines, nearly always provide a way to represent a processor register or memory address as an integer.
IEEE 754-1985 was an industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008, and then again in 2019 by minor revision IEEE 754-2019. During its 23 years, it was the most widely used format for floating-point computation. It was implemented in software, in the form of floating-point libraries, and in hardware, in the instructions of many CPUs and FPUs. The first integrated circuit to implement the draft of what was to become IEEE 754-1985 was the Intel 8087.
In computer programming, an arithmetic shift is a shift operator, sometimes termed a signed shift. The two basic types are the arithmetic left shift and the arithmetic right shift. For binary numbers it is a bitwise operation that shifts all of the bits of its operand; every bit in the operand is simply moved a given number of bit positions, and the vacant bit-positions are filled in. Instead of being filled with all 0s, as in logical shift, when shifting to the right, the leftmost bit is replicated to fill in all the vacant positions.
A computer number format is the internal representation of numeric values in digital device hardware and software, such as in programmable computers and calculators. Numerical values are stored as groupings of bits, such as bytes and words. The encoding between numerical values and bit patterns is chosen for convenience of the operation of the computer; the encoding used by the computer's instruction set generally requires conversion for external use, such as for printing and display. Different types of processors may have different internal representations of numerical values and different conventions are used for integer and real numbers. Most calculations are carried out with number formats that fit into a processor register, but some software systems allow representation of arbitrarily large numbers using multiple words of memory.
In computer science and computer programming, a data type or simply type is an attribute of data which tells the compiler or interpreter how the programmer intends to use the data. Most programming languages support basic data types of integer numbers, floating-point numbers, characters and Booleans. A data type constrains the values that an expression, such as a variable or a function, might take. This data type defines the operations that can be done on the data, the meaning of the data, and the way values of that type can be stored. A data type provides a set of values from which an expression may take its values.
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral at the level of its individual bits. It is a fast and simple action, basic to the higher level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands.
Two's complement is a mathematical operation on binary numbers, and is an example of a radix complement. It is used in computing as a method of signed number representation.
In computer science, primitive data type is either of the following:
In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after the radix point. Fixed-point number representation can be compared to the more complicated floating-point number representation.
The syntax of the C programming language is the set of rules governing writing of software in the C language. It is designed to allow for programs that are extremely terse, have a close relationship with the resulting object code, and yet provide relatively high-level data abstraction. C was the first widely successful high-level language for portable operating-system development.
In computing, signed number representations are required to encode negative numbers in binary number systems.
The computer programming languages C and Pascal have similar times of origin, influences, and purposes. Both were used to design their own compilers early in their lifetimes. The original Pascal definition appeared in 1969 and a first compiler in 1970. The first version of C appeared in 1972.
In computer programming, an integer overflow occurs when an arithmetic operation attempts to create a numeric value that is outside of the range that can be represented with a given number of digits – either higher than the maximum or lower than the minimum representable value.
In the C programming language, data types constitute the semantics and characteristics of storage of data elements. They are expressed in the language syntax in form of declarations for memory locations or variables. Data types also determine the types of operations or methods of processing of data elements.
Many protocols and algorithms require the serialization or enumeration of related entities. For example, a communication protocol must know whether some packet comes "before" or "after" some other packet. The IETF RFC 1982 attempts to define "Serial Number Arithmetic" for the purposes of manipulating and comparing these sequence numbers.
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 −0 and +0, regarded as equal by the numerical comparison operations but with possible different behaviors in particular operations. This occurs in the sign and magnitude and ones' complement signed number representations for integers, and in most floating-point number representations. The number 0 is usually encoded as +0, but can be represented by either +0 or −0.
A negative base may be used to construct a non-standard positional numeral system. Like other place-value systems, each position holds multiples of the appropriate power of the system's base; but that base is negative—that is to say, the base b is equal to −r for some natural number r.
The computer programming languages C and Object Pascal have similar times of origin, influences, and purposes. Both were used to design their own compilers early in their lifetimes.