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48-bit
In computer architecture , 48-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 48-BIT memory address can directly address every byte of 256 tebibytes of storage. 48-BIT can refer to any other data unit that consumes 48 bits (6 octets ) in width. Examples include 4 8-bit CPU and ALU architectures are those that are based on registers , address buses , or data buses of that size. WORD SIZEComputers with 4 8-bit words include the AN/FSQ-32 , CDC 1604/upper-3000 series , BESM-6 , Ferranti
Ferranti
Atlas , and Burroughs large systems (B5xxx-B8xxx, most of which additionally had a 3- or 4-bit type tag)
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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 octuple precision is for applications requiring results in higher than quadruple precision . This format is rarely (if ever) used and very few things support it
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Decimal Floating Point
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. Zero has 192 possible representations (384 when both signed zeros are included)
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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. Because the significand is not normalized, most values with less than 16 significant digits have multiple possible representations; 1×102=0.1×103=0.01×104, etc. Zero has 768 possible representations (1536 if you include both signed zeros )
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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, 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
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Double-precision Floating-point Format
DOUBLE-PRECISION FLOATING-POINT FORMAT is a computer number format that occupies 8 bytes (64 bits) in computer memory and represents a wide, dynamic range of values by using a floating point . Double-precision floating-point format
Double-precision floating-point format
usually refers to BINARY64, as specified by the IEEE 754 standard , not to the 64-bit decimal format DECIMAL64. In older computers, different floating-point formats of 8 bytes were used, e.g., GW-BASIC 's double-precision data type was the 64-bit MBF
64-bit MBF
floating-point format
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128-bit 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, 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
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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 octuple precision is for applications requiring results in higher than quadruple precision . This format is rarely (if ever) used and very few environments support it
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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. It is intended for storage of many floating-point values where higher precision is not needed, not for performing arithmetic computations. Although implementations of the IEEE Half-precision floating point are relatively new, several earlier 16-bit floating point formats have existed including that of Hitachi's HD61810 DSP of 1982, Scott's WIF and the 3dfx Voodoo Graphics processor . Nvidia
Nvidia
and Microsoft
Microsoft
defined the HALF datatype in the Cg language , released in early 2002, and implemented it in silicon in the GeForce FX , released in late 2002
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Single-precision Floating-point Format
SINGLE-PRECISION FLOATING-POINT FORMAT is a computer number format that occupies 4 bytes ( 32 bits ) in computer memory and represents a wide dynamic range of values by using a floating point . In IEEE 754-2008 the 32-bit
32-bit
base-2 format is officially referred to as BINARY32. It was called SINGLE in IEEE 754-1985 . In older computers, different floating-point formats of 4 bytes were used, e.g., GW-BASIC 's single-precision data type was the 32-bit
32-bit
MBF floating-point format. One of the first programming languages to provide single- and double-precision floating-point data types was Fortran . Before the widespread adoption of IEEE 754-1985 , the representation and properties of the double float data type depended on the computer manufacturer and computer model
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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. Zero has 12288 possible representations (24576 if you include both signed zeros )
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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 . Some definitions of architecture define it as describing the capabilities and programming model of a computer but not a particular implementation. In other definitions computer architecture involves instruction set architecture design, microarchitecture design, logic design , and implementation
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Bit
The BIT (a portmanteau of BINARY DIGIT) is a basic unit of information used in computing and digital communications . A binary digit can have only one of two values , and may be physically represented with a two-state device. These state values are most commonly represented as either a 0or1. The two values of a binary digit can also be interpreted as logical values (true/false, yes/no), algebraic signs (+/−), activation states (on/off), or any other two-valued attribute. The correspondence between these values and the physical states of the underlying storage or device is a matter of convention, and different assignments may be used even within the same device or program . The length of a binary number may be referred to as its bit-length . In information theory , one bit is typically defined as the uncertainty of a binary random variable that is 0 or 1 with equal probability, or the information that is gained when the value of such a variable becomes known
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Octet (computing)
The OCTET is a unit of digital information in computing and telecommunications that consists of eight bits . The term is often used when the term byte might be ambiguous, as the byte has historically been used for storage units of a variety of sizes. The term octad(e) for eight bits is no longer common. CONTENTS* 1 Definition * 1.1 Octad * 2 Unit multiples * 3 Use in internet protocol addresses * 4 References * 5 External links DEFINITIONA variable-length sequence of octets, as in Abstract Syntax Notation One (ASN.1), is referred to as an octet string. The international standard IEC 60027-2, chapter 3.8.2, states that a byte is an octet of bits. However, the unit byte has historically been platform -dependent and has represented various storage sizes in the history of computing. Due to the influence of several major computer architectures and product lines, the byte became overwhelmingly associated with eight bits
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Address Bus
An ADDRESS BUS is a computer bus (a series of lines connecting two or more devices) that is used to specify a physical address . When a processor or DMA -enabled device needs to read or write to a memory location, it specifies that memory location on the address bus (the value to be read or written is sent on the data bus ). The width of the address bus determines the amount of memory a system can address. For example, a system with a 32-BIT address bus can address 232 (4,294,967,296) memory locations. If each memory location holds one byte, the addressable memory space is 4 GB. IMPLEMENTATIONEarly processors used a wire for each bit of the address width. For example, a 16-bit address bus had 16 physical wires making up the bus. As the buses became wider and lengthier, this approach became expensive in terms of the number of chip pins and board traces. Beginning with the Mostek 4096 DRAM, address multiplexing implemented with multiplexers became common
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