Double precision - Citizendia

In computing, double precision is a computer numbering format that occupies two adjacent storage locations in computer memory. Computing is usually defined like the activity of using and developing Computer technology Computer hardware and software. The term computer numbering formats refers to the schemes implemented in Digital computer and Calculator hardware and software to represent numbers A common A double precision number, sometimes simply called a double, may be defined to be an integer, fixed point, or floating point. The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French In Computing, floating point describes a system for numerical representation in which a string of digits (or Bits represents a Real number.

Modern computers with 32-bit stores (single precision) provide 64-bit double precision. A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication In Computing, single precision is a Computer numbering format that occupies one storage location in computer memory at a given address Double precision floating point is an IEEE 754 standard for encoding floating point numbers that uses 8 bytes. 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 Standardization (or standardisation) is the process of developing and agreeing upon technical standards. In Computing, floating point describes a system for numerical representation in which a string of digits (or Bits represents a Real number. A byte (pronounced "bite" baɪt is the basic unit of measurement of information storage in Computer science.

1 Double precision memory format
- 1.1 Exponent encodings
2 Double precision examples
3 See also

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. In Computer science, the sign bit is a Bit (usually the Most significant bit) in a Computer numbering format that indicates the sign The significand (also Coefficient or 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 With the 52 bits of the fraction mantissa appearing in the memory format the total precision is therefore 53 bits (approximately 16 decimal digits, $l o g 10 (2 53)$ ). The bits are laid out as follows:

Exponent encodings

E_min (0x001) = -1022
E_max (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. In IEEE 754 Floating point numbers the Exponent is Biased in the engineering sense of the word – the value stored is offset from the actual value by the In Computer science, denormal numbers or denormalized numbers (now often called subnormal numbers) fill the gap around zero in Floating Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness In Computing, NaN ( N ot a N umber is a value or symbol that is usually produced as the result of an operation on invalid input operands

The entire double precision number is described by:

$(-1)^{sign} \times 2^{exponent - exponent~bias} \times 1.mantissa$

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. In Computing, single precision is a Computer numbering format that occupies one storage location in computer memory at a given address )

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

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

Contents

Double precision memory format

Exponent encodings

Double precision examples

See also