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Encyclopedia > Single precision It has been suggested that this article or section be merged into IEEE floating-point standard. (Discuss)

In computing, single precision is a computer numbering format that occupies one storage location in computer memory at a given address. A single-precision number, sometimes simply a single, may be defined to be an integer, fixed point, or floating point. Wikipedia does not have an article with this exact name. ... The IEEE Standard for Binary Floating-Point Arithmetic (IEEE 754) is the most widely-used standard for floating-point computation, and is followed by many CPU and FPU implementations. ... Originally, the word computing was synonymous with counting and calculating, and a science and technology that deals with the original sense of computing mathematical calculations. ... One of the common misunderstandings among computer users is a certain faith in the infallibility of numerical computations. ... The integers consist of the positive natural numbers (1, 2, 3, â€¦), their negatives (âˆ’1, âˆ’2, âˆ’3, ...) and the number zero. ... In mathematics, a fixed point of a function f is an argument x such that f(x) = x; see fixed point (mathematics). ... A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. ...

Modern computers with 32-bit stores (single precision) provide 64-bit double precision. Single precision floating point is an IEEE 754 standard for encoding floating point numbers that uses 4 bytes. BIT is an acronym for: Bangalore Institute of Technology Bilateral Investment Treaty Bhilai Institute of Technology - Durg Birla Institute of Technology - Mesra Battles in Time (Doctor Who magazine) Category: ... The IEEE Standard for Binary Floating-Point Arithmetic (IEEE 754) is the most widely-used standard for floating-point computation, and is followed by many CPU and FPU implementations. ... Standardization, in the context related to technologies and industries, is the process of establishing a technical standard among competing entities in a market, where this will bring benefits without hurting competition. ... A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. ... A byte is commonly used as a unit of storage measurement in computers, regardless of the type of data being stored. ...

## Single precision memory format GA_googleFillSlot("encyclopedia_square");

` Sign bit: 1 Exponent width: 8 Significand precision: 23 `

The format is written with an implicit most-significant bit with value 1 unless the written exponent is all zeros. Thus only 23 bits of the fraction mantissa appear in the memory format but the total precision is 24 bits. In computer science the sign bit is the bit in a computer numbering format which indicates the sign of the number. ... In mathematics, exponentiation is a process generalized from repeated multiplication, in much the same way that multiplication is a process generalized from repeated addition. ... The significand (also coefficient or, more informally, mantissa) is the part of a floating-point number that contains its significant digits. ... The precision of a value describes the number of digits that are used to express that value. ... Image File history File links Float_example. ...

### Exponent encodings

` Emin (0x01) = -126 Emax (0xfe) = 127 Exponent bias (0x7f) = 127 `

The true exponent = written exponent - exponent bias In IEEE 754 floating point numbers the exponent is biased in the engineering sense of the word â€“ the value stored is offset from the actual value by the exponent bias. ...

` 0x00 and 0xff are reserved exponents 0x00 is used to represent zero and denormals 0xff is used to represent infinity and NaNs `

All bit patterns are valid encodings. 0 (zero) is both a number â€” or, more precisely, a numeral representing a number â€” and a numerical digit. ... In computer science, denormal numbers (also called subnormal numbers) fill the gap around zero in floating point arithmetic: any non-zero number which is smaller than the smallest normal number is sub-normal. Producing a denormal is sometimes called gradual underflow because it allows the calculation to lose precision slowly... The infinity symbol âˆž in several typefaces The word infinity comes from the Latin infinitas or unboundedness. ... // Acronym NaN, an abbreviation of Not a Number used in computer arithmetic and defined in the IEEE floating-point standard. ...

## Single precision examples in hexadecimal

` 3f80 0000 = 1 `
` c000 0000 = -2 `
` 7f7f ffff ~ 3.4028234 x 1038 (Max Single) `
` 3eaa aaab ~ 1/3 `

By default, 1/3 rounds up instead of down like double precision, because of the even number of bits in the significand. So the bits beyond the rounding point are `1010...` which is more than 1/2 of a unit in the last place. In mathematics and computer science, base-16, hexadecimal, or simply hex, is a numeral system with a radix or base of 16 usually written using the symbols 0â€“9 and Aâ€“F or aâ€“f. ... In computing, double precision is a computer numbering format that occupies two storage locations in computer memory at address and address+1. ...

` 0000 0000 = 0 8000 0000 = -0 `
` 7f80 0000 = Infinity ff80 0000 = -Infinity ` Results from FactBites:

 lapack/single (4427 words) gams d4b1 file sspgv.f sspgv.f plus dependencies prec single for Computes all eigenvalues and eigenvectors of a generalized, symmetric-definite generalized eigenproblem, Ax= lambda, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed, storage. gams d4b1 file sspgvd.f sspgvd.f plus dependencies prec single for Computes all eigenvalues and eigenvectors of a generalized, symmetric-definite generalized eigenproblem, Ax= lambda, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed, storage. gams d4a1 file sspgvx.f sspgvx.f plus dependencies prec single for Computes selected eigenvalues, and optionally, eigenvectors of, a generalized symmetric-definite generalized eigenproblem, Ax= lambda, Bx, ABx= lambda x, or BAx= lambda x, where A and B are in packed, storage.
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