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48-bit
In computer architecture, 4 8-bit integers can represent 281,474,976,710,656 (248 or 2.814749767×1014) discrete values. This allows an unsigned binary integer range of 0 through 281,474,976,710,655 (248 − 1) or a signed two's complement range of -140,737,488,355,328 (-247) through 140,737,488,355,327 (247 − 1). A 4 8-bit memory address can directly address every byte of 256 tebibytes of storage. 4 8-bit can refer to any other data unit that consumes 48 bits (6 octets) in width
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Bus (computing)
In computer architecture, a bus[1] (a contraction of the Latin omnibus) is a communication system that transfers data between components inside a computer, or between computers. This expression covers all related hardware components (wire, optical fiber, etc.) and software, including communication protocols.[2] Early computer buses were parallel electrical wires with multiple hardware connections, but the term is now used for any physical arrangement that provides the same logical function as a parallel electrical bus
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Decimal128 Floating-point Format
In computing, decimal128 is a decimal floating-point computer numbering format that occupies 16 bytes (128 bits) in computer memory. It is intended for applications where it is necessary to emulate decimal rounding exactly, such as financial and tax computations. Decimal128 supports 34 decimal digits of significand and an exponent range of −6143 to +6144, i.e. ±0.000000000000000000000000000000000×10^−6143 to ±9.999999999999999999999999999999999×10^6144. (Equivalently, ±0000000000000000000000000000000000×10^−6176 to ±9999999999999999999999999999999999×10^6111.) Therefore, decimal128 has the greatest range of values compared with other IEEE
IEEE
basic floating point formats. Because the significand is not normalized, most values with less than 34 significant digits have multiple possible representations; 1×102=0.1×103=0.01×104, etc
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256-bit Floating-point Format
In computing, octuple precision is a binary floating-point-based computer number format that occupies 32 bytes (256 bits) in computer memory. This 256-bit
256-bit
octuple precision is for applications requiring results in higher than quadruple precision
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Half-precision Floating-point Format
In computing, half precision is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory. In IEEE 754-2008 the 16-bit base 2 format is officially referred to as binary16
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Single-precision Floating-point Format
Single-precision floating-point format
Single-precision floating-point format
is a computer number format, usually occupying 32 bits
32 bits
in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. A floating point variable can represent a wider range of numbers than a fixed point variable of the same bit width at the cost of precision. A signed 32-bit
32-bit
integer variable has a maximum value of 231 − 1 = 2,147,483,647, whereas an IEEE 754
IEEE 754
32-bit
32-bit
base-2 floating-point variable has a maximum value of (2 − 2−23) × 2127 ≈ 3.402823 × 1038
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Double-precision Floating-point Format
Double-precision floating-point format
Double-precision floating-point format
is a computer number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. Floating point
Floating point
is used to represent fractional values, or when a wider range is needed than is provided by fixed point (of the same bit width), even if at the cost of precision. Double precision may be chosen when the range and/or precision of single precision would be insufficient. In the IEEE 754-2008 standard, the 64-bit base-2 format is officially referred to as binary64; it was called double in IEEE 754-1985. IEEE 754 specifies additional floating-point formats, including 32-bit base-2 single precision and, more recently, base-10 representations. One of the first programming languages to provide single- and double-precision floating-point data types was Fortran
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Quadruple-precision Floating-point Format
In computing, quadruple precision (or quad precision) is a binary floating-point-based computer number format that occupies 16 bytes (128 bits) in with precision more than twice the 53-bit double precision. This 128-bit quadruple precision is designed not only for applications requiring results in higher than double precision,[1] but also, as a primary function, to allow the computation of double precision results more reliably and accurately by minimising overflow and round-off errors in intermediate calculations and scratch variables. William Kahan, primary architect of the original IEEE-754 floating point standard noted, "For now the 10-byte Extended format is a tolerable compromise between the value of extra-precise arithmetic and the price of implementing it to run fast; very soon two more bytes of precision will become tolerable, and ultimately a 16-byte format..
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Octuple-precision Floating-point Format
In computing, octuple precision is a binary floating-point-based computer number format that occupies 32 bytes (256 bits) in computer memory. This 256-bit
256-bit
octuple precision is for applications requiring results in higher than quadruple precision
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Decimal Floating-point
Decimal
Decimal
floating-point (DFP) arithmetic refers to both a representation and operations on decimal floating-point numbers. Working directly with decimal (base-10) fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions (common in human-entered data, such as measurements or financial information) and binary (base-2) fractions. The advantage of decimal floating-point representation over decimal fixed-point and integer representation is that it supports a much wider range of values. For example, while a fixed-point representation that allocates 8 decimal digits and 2 decimal places can represent the numbers 123456.78, 8765.43, 123.00, and so on, a floating-point representation with 8 decimal digits could also represent 1.2345678, 1234567.8, 0.000012345678, 12345678000000000, and so on
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Decimal32 Floating-point Format
In computing, decimal32 is a decimal floating-point computer numbering format that occupies 4 bytes (32 bits) in computer memory. It is intended for applications where it is necessary to emulate decimal rounding exactly, such as financial and tax computations. Like the binary16 format, it is intended for memory saving storage. Decimal32 supports 7 decimal digits of significand and an exponent range of −95 to +96, i.e. ±0.000000×10^−95 to ±9.999999×10^96. (Equivalently, ±0000000×10^−101 to ±9999999×10^90.) Because the significand is not normalized (there is no implicit leading "1"), most values with less than 7 significant digits have multiple possible representations; 1×102=0.1×103=0.01×104, etc
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Decimal64 Floating-point Format
In computing, decimal64 is a decimal floating-point computer numbering format that occupies 8 bytes (64 bits) in computer memory. It is intended for applications where it is necessary to emulate decimal rounding exactly, such as financial and tax computations. Decimal64 supports 16 decimal digits of significand and an exponent range of −383 to +384, i.e. ±0.000000000000000×10^−383 to ±9.999999999999999×10^384. (Equivalently, ±0000000000000000×10^−398 to ±9999999999999999×10^369.) In contrast, the corresponding binary format, which is the most commonly used type, has an approximate range of ±0.000000000000001×10^−308 to ±1.797693134862315×10^308
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Computer Architecture
In computer engineering, computer architecture is a set of rules and methods that describe the functionality, organization, and implementation of computer systems
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64-bit Floating-point Format
Double-precision floating-point format
Double-precision floating-point format
is a computer number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point. Floating point
Floating point
is used to represent fractional values, or when a wider range is needed than is provided by fixed point (of the same bit width), even if at the cost of precision. Double precision may be chosen when the range and/or precision of single precision would be insufficient. In the IEEE 754-2008 standard, the 64-bit base-2 format is officially referred to as binary64; it was called double in IEEE 754-1985. IEEE 754 specifies additional floating-point formats, including 32-bit base-2 single precision and, more recently, base-10 representations. One of the first programming languages to provide single- and double-precision floating-point data types was Fortran
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Integer (computer Science)
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.Contents1 Value and representation 2 Common integral data types2.1 Bytes
Bytes
and octets 2.2 Words 2.3 Short integer2.3.1 Common short integer sizes2.4 Long integer2.4.1 Common long integer sizes2.5 Long long3 See also 4 Notes 5 ReferencesValue and representation[edit] The value of an item with an integral type is the mathematical integer that it corresponds to
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Unsigned Integer
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 half the possible values are non-positive values (so if an 8-bit is signed, positive unsigned values 128 to 255 are gone while -128 to 127 are present). Unsigned variables 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
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