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Information about Double Precision

In computing, double precision is a computer numbering format that occupies two storage locations in computer memory at address and address+1. A double precision number, sometimes simply called a double, may be defined to be an integer, fixed point, or floating point.

Modern computers with 32-bit stores (single precision) provide 64-bit double precision. Double precision floating point is an IEEE 754 standard for encoding floating point numbers that uses 8 bytes.

Double precision memory format

Sign bit: 1 Exponent width: 11 Significand precision: 52 (53 implicit)

The format is written with an implicit integer bit with value 1 unless the written exponent is all zeros. With the 52 bits of the fraction mantissa appearing in the memory format the total precision is therefore 53 bits (approximately 16 decimal digits, ). The bits are laid out as follows:

Exponent encodings

Emin (0x001) = -1022 Emax (0x7fe) = 1023 Exponent bias (0x3ff) = 1023 The true exponent = written exponent - exponent bias

0x000 and 0x7ff are reserved exponents 0x000 is used to represent zero and denormals 0x7ff is used to represent infinity and NaNs

All bit patterns are valid encodings.

The entire double precision number is described by:

Double precision examples

0x3ff0 0000 0000 0000 = 1

0xc000 0000 0000 0000 = -2

0x7fef ffff ffff ffff ~ 1.7976931348623157 x 10308 (Max Double) 0x3fd5 5555 5555 5555 ~ 1/3 (1/3 rounds down instead of up like single precision, because of the odd number of bits in the significand.)

0x0000 0000 0000 0000 = 0 0x8000 0000 0000 0000 = -0

0x7ff0 0000 0000 0000 = Infinity 0xfff0 0000 0000 0000 = -Infinity

See also

computing is synonymous with counting and calculating. Originally, people that performed these functions were known as computers. Today it refers to a science and technology that deals with the computation and the manipulation of symbols.
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The term computer numbering formats refers to the schemes implemented in digital computer and calculator hardware and software to represent numbers. A common mistake made by non-specialist computer users is a certain misplaced faith in the infallibility of numerical computations.
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The integers (from the Latin integer, which means with untouched integrity, whole, entire) are the set of numbers including the whole numbers (0, 1, 2, 3, …) and their negatives (0, −1, −2, −3, …).
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"Fixed point" has many meanings in science, most of them mathematical.
  • Fixed point (mathematics)
  • Fixed point combinator
  • Fixed-point arithmetic, a manner of doing arithmetic on computers
  • For fixed points in physics, see Renormalization group

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In computing, floating-point is a numerical-representation system in which a string of digits (or bits) represents a real number. The most commonly encountered representation is that defined by the IEEE 754 Standard.
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BIT is an acronym for:
  • Bannari amman Institute of Technology
  • Bangalore Institute of Technology
  • Beijing Institute of Technology
  • Benzisothiazolinone
  • Bilateral Investment Treaty
  • Bhilai Institute of Technology - Durg

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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.
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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.
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standardization or standardisation can have several meanings depending on its context. Common use of the word standard implies that it is a universally agreed-upon set of guidelines for interoperability.
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In computing, floating-point is a numerical-representation system in which a string of digits (or bits) represents a real number. The most commonly encountered representation is that defined by the IEEE 754 Standard.
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byte (pronounced /baɪt/) is a unit of measurement of information storage, most often consisting of eight bits. In many computer architectures it is a unit of memory addressing.
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In computer science the sign bit is the bit in a computer numbering format which indicates the sign of the number. Typically the bit is the most significant bit in the format.
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Exponentiation is a mathematical operation, written an, involving two numbers, the base a and the exponent n.
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The significand (also coefficient or mantissa) is the part of a floating-point number that contains its significant digits. Depending on the interpretation of the exponent, the significand may be considered to be an integer or a fraction.
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The precision of a value describes the number of digits that are used to express that value. In a scientific setting this would be the total number of digits (sometimes called the significant digits) or, less commonly, the number of fractional digits or
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Mantissa can mean:
  • (According to the Oxford English Dictionary) "an addition of comparatively small importance, esp. to a text or discourse; a supplement"
  • The fractional part (i.e. the part after the separator) of a common logarithm.

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exponent bias. Biasing is done because exponents have to be signed values in order to be able to represent both tiny and huge values, but two's complement, the usual representation for signed values, would make comparison harder.
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0 (zero) is both a number and a numerical digit used to represent that number in numerals. It plays a central role in mathematics as the additive identity of the integers, real numbers, and many other algebraic structures.
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In computer science, denormal numbers or denormalized numbers (now often 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'.
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The word infinity comes from the Latin infinitas or "unboundedness." It refers to several distinct concepts (usually linked to the idea of "without end") which arise in philosophy, mathematics, and theology.
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Nan or NAN may refer to one of the following.

Acronym

  • NaN, "Not a Number" used in computer arithmetic and defined in the IEEE floating-point standard.

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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.
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In computing, half precision is a computer numbering format that occupies only half of one storage location (word) in computer memory at some address. A half-precision number may be defined to be a binary or decimal integer, fixed point, or floating point.
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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.
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In computing, quadruple precision (also commonly shortened to quad precision) is a computer numbering format that occupies four storage locations in computer memory at address, address+1, address+2, and address+3.
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In computing, floating-point is a numerical-representation system in which a string of digits (or bits) represents a real number. The most commonly encountered representation is that defined by the IEEE 754 Standard.
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