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Comparison Of CPU Architectures
An instruction set architecture (ISA) is an abstract model of a computer, also referred to as computer architecture. A realization of an ISA is called an ''implementation''. An ISA permits multiple implementations that may vary in performance, physical size, and monetary cost (among other things); because the ISA serves as the interface between software and hardware. Software that has been written for an ISA can run on different implementations of the same ISA. This has enabled binary compatibility between different generations of computers to be easily achieved, and the development of computer families. Both of these developments have helped to lower the cost of computers and to increase their applicability. For these reasons, the ISA is one of the most important abstractions in computing today. An ISA defines everything a machine language programmer needs to know in order to program a computer. What an ISA defines differs between ISAs; in general, ISAs define the supported dat ...
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Instruction Set Architecture
In computer science, an instruction set architecture (ISA) is an abstract model that generally defines how software controls the CPU in a computer or a family of computers. A device or program that executes instructions described by that ISA, such as a central processing unit (CPU), is called an ''implementation'' of that ISA. In general, an ISA defines the supported instructions, data types, registers, the hardware support for managing main memory, fundamental features (such as the memory consistency, addressing modes, virtual memory), and the input/output model of implementations of the ISA. An ISA specifies the behavior of machine code running on implementations of that ISA in a fashion that does not depend on the characteristics of that implementation, providing binary compatibility between implementations. This enables multiple implementations of an ISA that differ in characteristics such as performance, physical size, and monetary cost (among other things), but t ...
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Binary Number
A binary number is a number expressed in the Radix, base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one). A ''binary number'' may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two. The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computer, computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thoma ...
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36-bit Computing
36-bit computers were popular in the early mainframe computer era from the 1950s through the early 1970s. Starting in the 1960s, but especially the 1970s, the introduction of 7-bit ASCII and 8-bit EBCDIC led to the move to machines using 8-bit computing, 8-bit bytes, with word sizes that were multiples of 8, notably the 32-bit computing, 32-bit IBM System/360 mainframe computer, mainframe and VAX, Digital Equipment VAX and Data General Eclipse MV/8000, Data General MV series superminicomputers. By the mid-1970s the conversion was largely complete, and microprocessors quickly moved from 8-bit to 16-bit to 32-bit over a period of a decade. The number of 36-bit machines rapidly fell during this period, offered largely for backward compatibility purposes running legacy system, legacy programs. History Prior to the introduction of computers, the state of the art in precision scientific and engineering calculation was the ten-digit, electrically powered, mechanical calculator, such a ...
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24-bit Computing
Notable 24-bit machines include the CDC 924 – a 24-bit version of the CDC 1604, CDC lower 3000 series, SDS 930 and SDS 940, the ICT 1900 series, the Elliott 4100 series, and the Datacraft minicomputers/ Harris H series. The term SWORD is sometimes used to describe a 24-bit data type with the S prefix referring to sesqui. The range of unsigned integers that can be represented in 24 bits is 0 to 16,777,215 ( in hexadecimal). The range of signed integers that can be represented in 24 bits is −8,388,608 to 8,388,607. Usage The IBM System/360, announced in 1964, was a popular computer system with 24-bit addressing and 32-bit general registers and arithmetic. The early 1980s saw the first popular personal computers, including the IBM PC/AT with an Intel 80286 processor using 24-bit addressing and 16-bit general registers and arithmetic, and the Apple Macintosh 128K with a Motorola 68000 processor featuring 24-bit addressing and 32-bit registers. The eZ ...
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18-bit Computing
Eighteen binary digits have 262,144 (1000000 octal, 40000 hexadecimal) distinct combinations. Eighteen bits was a common word size for smaller computers in the 1960s, when large computers often using 36 bit words and 6-bit character sets, sometimes implemented as extensions of BCD, were the norm. There were also 18-bit teletypes experimented with in the 1940s. Example computer architectures Possibly the most well-known 18-bit computer architectures are the PDP-1, PDP-4, PDP-7, PDP-9 and PDP-15 minicomputers produced by Digital Equipment Corporation from 1960 to 1975. Digital's PDP-10 used 36-bit words but had 18-bit addresses. The UNIVAC division of Remington Rand produced several 18-bit computers, including the UNIVAC 418 and several military systems. The IBM 7700 Data Acquisition System was announced by IBM on December 2, 1963. The BCL Molecular 18 was a group of systems designed and manufactured in the UK in the 1970s and 1980s. The NASA Standard Spacecraft ...
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12-bit Computing
Before the widespread adoption of ASCII in the late 1960s, six-bit character codes were common and a 12-bit word, which could hold two characters, was a convenient size. This also made it useful for storing a single decimal digit along with a sign. Possibly the best-known 12-bit CPUs are the PDP-8 and its descendants (such as the Intersil 6100 microprocessor), which were produced in various forms from August 1963 to mid-1990. Many Analog-to-digital converter, analog to digital converters (ADCs) have a 12-bit resolution. Some PIC microcontrollers use a 12-bit instruction word but handle only 8-bit data. 12 binary digits, or 3 nibbles (a 'tribble'), have 4096 (10000 octal, 1000 hexadecimal) distinct combinations. Hence, a microprocessor with 12-bit memory addresses can directly access 4096 Word (computer architecture), words (4 kW) of word-addressable memory. IBM System/360 instruction formats use a 12-bit displacement field which, added to the contents of a base register, can ...
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IEEE 754
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard #Design rationale, addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and Software portability, portably. Many hardware floating-point units use the IEEE 754 standard. The standard defines: * ''arithmetic formats:'' sets of Binary code, binary and decimal floating-point data, which consist of finite numbers (including signed zeros and subnormal numbers), infinity, infinities, and special "not a number" values (NaNs) * ''interchange formats:'' encodings (bit strings) that may be used to exchange floating-point data in an efficient and compact form * ''rounding rules:'' properties to be satisfied when rounding numbers during arithmetic and conversions * ''operations:'' arithmetic and other operatio ...
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IBM Hexadecimal Floating-point
Hexadecimal floating-point arithmetic, floating point (now called HFP by IBM) is a format for encoding floating-point numbers first introduced on the IBM IBM System/360, System/360 computers, and supported on subsequent machines based on that architecture, as well as machines which were intended to be application-compatible with System/360. In comparison to IEEE 754 floating point, the HFP format has a longer significand, and a shorter Exponentiation, exponent. All HFP formats have 7 bits of exponent with a exponent bias, bias of 64. The normalized range of representable numbers is from 16−65 to 1663 (approx. 5.39761 × 10−79 to 7.237005 × 1075). The number is represented as the following formula: (−1)sign × 0.significand × 16exponent−64. Single-precision 32-bit A single-precision floating-point format, single-precision HFP number (called "short" by IBM) is stored in a 32-bit word: : In this format the initial bit is not suppressed, and the radix (hexadecimal) poin ...
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Significand
The significand (also coefficient, sometimes argument, or more ambiguously mantissa, fraction, or characteristic) is the first (left) part of a number in scientific notation or related concepts in floating-point representation, consisting of its significant digits. For negative numbers, it does not include the initial minus sign. Depending on the interpretation of the exponent, the significand may represent an integer or a fractional number, which may cause the term "mantissa" to be misleading, since the ''mantissa'' of a logarithm is always its fractional part. Although the other names mentioned are common, ''significand'' is the word used by IEEE 754, an important technical standard for floating-point arithmetic. In mathematics, the term "argument" may also be ambiguous, since "the argument of a number" sometimes refers to the length of a circular arc from 1 to a number on the unit circle in the complex plane. Example The number 123.45 can be represented as a decimal floati ...
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Exponent
In mathematics, exponentiation, denoted , is an operation involving two numbers: the ''base'', , and the ''exponent'' or ''power'', . When is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, is the product of multiplying bases: b^n = \underbrace_.In particular, b^1=b. The exponent is usually shown as a superscript to the right of the base as or in computer code as b^n. This binary operation is often read as " to the power "; it may also be referred to as " raised to the th power", "the th power of ", or, most briefly, " to the ". The above definition of b^n immediately implies several properties, in particular the multiplication rule:There are three common notations for multiplication: x\times y is most commonly used for explicit numbers and at a very elementary level; xy is most common when variables are used; x\cdot y is used for emphasizing that one talks of multiplication or when omitting the multiplication sign would ...
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Method Of Complements
In mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm (or mechanism) for addition throughout the whole range. For a given number of places half of the possible representations of numbers encode the positive numbers, the other half represents their respective additive inverses. The pairs of mutually additive inverse numbers are called ''complements''. Thus subtraction of any number is implemented by adding its complement. Changing the sign of any number is encoded by generating its complement, which can be done by a very simple and efficient algorithm. This method was commonly used in mechanical calculators and is still used in modern computers. The generalized concept of the ''radix complement'' (as described below) is also valuable in number theory, such as in Midy's theorem. The ''nines' complement'' of a number given in decimal representation is fo ...
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