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16-bit
In computer architecture, 16-bit integers, memory addresses, or other data units are those that are 16 bits (2 octets) wide. Also, 16-bit CPU and ALU architectures are those that are based on registers, address buses, or data buses of that size. 16-bit microcomputers are computers in which 16-bit microprocessors were the norm. A 16-bit register can store 216 different values. The signed range of integer values that can be stored in 16 bits is −32,768 (−1 × 215) through 32,767 (215 − 1); the unsigned range is 0 through 65,535 (216 − 1). Since 216 is 65,536, a processor with 16-bit memory addresses can directly access 64 KB (65,536 bytes) of byte-addressable memory
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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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Precision (computer Science)
In computer science, the precision of a numerical quantity is a measure of the detail in which the quantity is expressed. This is usually measured in bits, but sometimes in decimal digits. It is related to precision in mathematics, which describes the number of digits that are used to express a value. Rounding error[edit] Further information: Floating point Precision is often the source of rounding errors in computation. The number of bits used to store a number will often cause some loss of accuracy. An example would be to store "sin(0.1)" in IEEE single precision floating point standard
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Application Software
An application program (app or application for short) is a computer program designed to perform a group of coordinated functions, tasks, or activities for the benefit of the user. Examples of an application include a word processor, a spreadsheet, an accounting application, a web browser, a media player, an aeronautical flight simulator, a console game or a photo editor
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Bit
The bit (a portmanteau of binary digit)[1] 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
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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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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. Implementation[edit] Early processors used a wire for each bit of the address width
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Memory Address
In computing, a memory address is a reference to a specific memory location used at various levels by software and hardware
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32-bit 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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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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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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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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