The CPU & Instruction Formats

Total Page:16

File Type:pdf, Size:1020Kb

The CPU & Instruction Formats K Hinds 2018 www.kumarhinds.net Page 1 HEX to Decimal Conversion e.g.: Convert C0DE to Decimal Hexadecimal Digit Notes These values are statically assigned, they Digit Positions (n) 3 2 1 0 grow to the left. This part's easy, plug your hex values in Hex Digits Sorted C 0 D E from right-to-left. Convert A-F 12 0 13 14 Convert hex values A-F to 10-15. Multiply by 16n 12 × 163 0 × 162 13 × 161 14 × 160 The exponent of 16 is the position, n. The product of hex digit and the power of Resulting Products 49152 0 208 14 16. Sum Up All 49374 Our decimal equivalent! Products Computer Organization The Central Processing Unit (CPU) is also known as the microprocessor or processor. The processor contains three sections called the Arithmetic Logic Unit (ALU), the Control Unit and Registers. K Hinds 2018 www.kumarhinds.net Page 2 Random Access Memory (RAM) Read Only Memory (ROM) Definition Random Access Memory or RAM is a Read-only memory or ROM is also a form form of data storage that can be of data storage that can not be easily altered accessed randomly at any time, in any or reprogrammed. Stores instructions that order and from any physical location., are not necessary for re-booting up to make allowing quick access and the computer operate when it is switched manipulation. off. They are hardwired. Use RAM allows the computer to ROM stores the program required to read data quickly to run applications. It initially boot the computer. It only allows allows reading and writing. reading. Volatility RAM is volatile i.e. its contents are lost It is non-volatile i.e. its contents are retained when the device is powered off. even when the device is powered off. Types The two main types of RAM are static The types of ROM include PROM, EPROM RAM and dynamic RAM. and EEPROM. Control unit: The Control Unit makes decisions and sends the appropriate signal down its lines to other parts of the computer. It controls the timing of operations in the computer and controls the instructions sent to the processor and the peripheral devices. Arithmetic/logic unit (ALU): The ALU carries out arithmetic and logic functions. It carries out all the calculations and makes decisions on the data sent to the processor. CPU Registers/Memory Registers are lightning fast computer memory used to speed the execution of computer programs by providing quick access to stored values during program execution. These registers are the top of the memory hierarchy and are the fastest way for the system to manipulate data. They can drive their data onto an internal bus in a single clock cycle. The result of ALU operation is stored here and could be re-used in a subsequent operation or saved into memory. Registers are normally measured by the number of bits they can hold, for example, an “8-bit register” or a “32-bit register”. There are several other classes of registers: Accumulator: It is most frequently used register used to store data taken from memory. Its number varies from microprocessor to microprocessor. General Purpose registers: General purpose registers are used to store data and intermediate results during program execution. Its contents can be accessed through assembly programming. Special purpose Registers: Users do not access these registers. These are used by computer system at the time of program execution. Some types of special purpose registers are given below: Instruction Register (IR): IR holds the instruction currently being executed or decoded. When one instruction is completed, next instruction is fetched in memory for processing. Program Counter (PC): The program counter, PC, is a special-purpose register that is used by the processor to hold the address of the next instruction to be executed. The PC is continually updated to point to the next instruction during the op-code decode cycle. K Hinds 2018 www.kumarhinds.net Page 3 Fetch-decode-execute cycle The main job of the CPU is to execute programs using the fetch-decode-execute cycle (also known as the instruction cycle). This cycle begins as soon as you turn on a computer. To execute a program, the program code is copied from Secondary Storage into Primary Memory. The CPU's PC is set to the memory location where the first instruction in the program has been stored, and execution begins. The program is now running. In a program, each machine code instruction takes up a slot in the main memory. These slots (or memory locations) each have a unique memory address. The PC stores the address of each instruction and tells the CPU in what order they should be carried out. When a program is being executed, the CPU performs the fetch-decode-execute cycle, which repeats repeatedly until reaching the STOP instruction. Summary of the fetch-decode-execute cycle 1. The processor checks the PC to see which instruction to run next. 2. The PC gives an address value in the memory of where the next instruction is. 3. The processor fetches the instruction value from this memory location. 4. Once the instruction has been fetched, it is stored in the IR and it needs to be decoded and executed. For example, this could involve taking one value, putting it into the ALU, then taking a different value from a register and adding the two together. 5. Once this is complete, the processor goes back to the PC to find the next instruction to load into the IR. 6. This cycle is repeated until the program ends. K Hinds 2018 www.kumarhinds.net Page 4 Data Manipulation Data manipulation involves transferring data and operating on data with math Functions, data conversion, data comparison and logical operations. Each instruction requires two or more words of data memory for operation. The words of data memory are referred to as Registers. Input/Output The instruction copies data from a source word to a destination word and vice versa. Data transfer instructions involve the transfer of the contents from one word to another. Data transfer instructions are Output instructions. The MOVE instruction is used to copy the value in one word to another word. Conversely, the LOAD instruction inputs information to a register for processing Input/Output, Arithmetic & Logic commands can be summarized as follows: LOAD (Input) – Loads in a value to main memory MOV (Move) —Moves the source value to the destination. AND (And) —Performs a bitwise AND operation. OR (Or) —Performs a bitwise OR operation. NOT (Not) —Performs a bitwise NOT operation. ADD - MUL - SUB - Instruction Length – Fixed & Variable Fixed Length: On some machines, all instructions have the same length; Having all the instructions be the same length is simpler and make decoding easier but often wastes space Variable Length: On others there may be many different lengths based on the operation required; so, the Opcode and the Operand is varied. This method wastes less space and is more efficient, however they are more difficult to decode. Instruction Format Instructions are decoded as a set of sequenced Operations. These operations instruct the ALU and Control Unit inside the CPU. Operations consist of a set of instructions and data. Operations are made up of Opcodes and Operands. The opcode performs an action on an operand. K Hinds 2018 www.kumarhinds.net Page 5 Opcode The opcode tells the processor the job that needs to be done. A simple operation might be 'ADD', ‘MUL’ or 'SUB'. If we use the analogy of a recipe, the opcode might be 'chop' or 'mix'. Each opcode instruction is very limited in what it can tell the processor to do. A CPU's instruction set contains the opcodes that it will accept. There are two types of opcode: 1. An opcode that tells the circuitry which operation to carry out. E.g. POP, PUSH, ADD, SUB, MUL, MOD, DIV, LOAD 2. An opcode along with some data to be processed: e.g. ADD A,B; LOAD A Zero, One, Two and Three Address Instruction Computer perform task on the basis of instruction provided. An instruction in computer comprises of groups called fields. These field contains different information and depending on the computer – x86 or x64 architecture, everything is in 0 and 1; so each field has different significance on the basis of what a CPU decide to perform. Most machines however have similar instructions sets – instruction sets tell the CPU what to do: ADD, SUB, MOVE, LOAD, etc. An instruction format defines the layout of the bits of an instruction, in terms of its separate parts (Zero, One, two or Three). An instruction format must include an opcode and, implicitly or explicitly, zero or more operands. Typical operations in a computer system may either Infix, Prefix and Postfix Expressions Infix With an arithmetic expression such as B * C, the form of the expression states that variable B is being multiplied by the variable C, since the multiplication operator * appears between them. This type of notation is referred to as infix since the operator is in between the two operands. Order of Operations Consider an infix example, A + B * C. The operators + and * still appear between the operands, each operator has a precedence level. Operators of higher precedence are used before operators of lower precedence. The only thing that can change that order is the presence of parentheses. The precedence order for arithmetic operators’ places multiplication and division above addition and subtraction. If two operators of equal precedence appear, then a left-to-right ordering or associativity is used. Prefix Consider the infix expression A + B.
Recommended publications
  • High Performance Decimal Floating-Point Units
    UNIVERSIDADE DE SANTIAGO DE COMPOSTELA DEPARTAMENTO DE ELECTRONICA´ E COMPUTACION´ PhD. Dissertation High-Performance Decimal Floating-Point Units Alvaro´ Vazquez´ Alvarez´ Santiago de Compostela, January 2009 To my family A´ mina˜ familia Acknowledgements It has been a long way to see this thesis successfully concluded, at least longer than what I imagined it. Perhaps the moment to thank and acknowledge everyone’s contributions is the most eagerly awaited. This thesis could not have been possible without the support of several people and organizations whose contributions I am very grateful. First of all, I want to express my sincere gratitude to my thesis advisor, Elisardo Antelo. Specially, I would like to emphasize the invaluable support he offered to me all these years. His ideas and contributions have a major influence on this thesis. I would like to thank all people in the Departamento de Electronica´ e Computacion´ for the material and personal help they gave me to carry out this thesis, and for providing a friendly place to work. In particular, I would like to mention to Prof. Javier D. Bruguera and the other staff of the Computer Architecture Group. Many thanks to Paula, David, Pichel, Marcos, Juanjo, Oscar,´ Roberto and my other workmates for their friendship and help. I am very grateful to IBM Germany for their financial support though a one-year research contract. I would like to thank Ralf Fischer, lead of hardware development, and Peter Roth and Stefan Wald, team managers at IBM Deutchland Entwicklung in Boblingen.¨ I would like to extend my gratitude to the FPU design team, in special to Silvia Muller¨ and Michael Kroner,¨ for their help and the warm welcome I received during my stay in Boblingen.¨ I would also like to thank Eric Schwarz from IBM for his support.
    [Show full text]
  • Fully Redundant Decimal Arithmetic
    2009 19th IEEE International Symposium on Computer Arithmetic Fully Redundant Decimal Arithmetic Saeid Gorgin and Ghassem Jaberipur Dept. of Electrical & Computer Engr., Shahid Beheshti Univ. and School of Computer Science, institute for research in fundamental sciences (IPM), Tehran, Iran [email protected], [email protected] Abstract In both decimal and binary arithmetic, partial products in multipliers and partial remainders in Hardware implementation of all the basic radix-10 dividers are often represented via a redundant number arithmetic operations is evolving as a new trend in the system (e.g., Binary signed digit [11], decimal carry- design and implementation of general purpose digital save [5], double-decimal [6], and minimally redundant processors. Redundant representation of partial decimal [9]). Such use of redundant digit sets, where products and remainders is common in the the number of digits is sufficiently more than the radix, multiplication and division hardware algorithms, allows for carry-free addition and subtraction as the respectively. Carry-free implementation of the more basic operations that build-up the product and frequent add/subtract operations, with the byproduct of remainder, respectively. In the aforementioned works enhancing the speed of multiplication and division, is on decimal multipliers and dividers, inputs and outputs possible with redundant number representation. are nonredundant decimal numbers. However, a However, conversion of redundant results to redundant representation is used for the intermediate conventional representations entails slow carry partial products or remainders. The intermediate propagation that can be avoided if the results are kept additions and subtractions are semi-redundant in redundant format for later use as operands of other operations in that only one of the operands as well as arithmetic operations.
    [Show full text]
  • Algorithms and Architectures for Decimal Transcendental Function Computation
    Algorithms and Architectures for Decimal Transcendental Function Computation A Thesis Submitted to the College of Graduate Studies and Research in Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy in the Department of Electrical and Computer Engineering University of Saskatchewan Saskatoon, Saskatchewan, Canada By Dongdong Chen c Dongdong Chen, January, 2011. All rights reserved. Permission to Use In presenting this thesis in partial fulfilment of the requirements for a Postgraduate degree from the University of Saskatchewan, I agree that the Libraries of this University may make it freely available for inspection. I further agree that permission for copying of this thesis in any manner, in whole or in part, for scholarly purposes may be granted by the professor or professors who supervised my thesis work or, in their absence, by the Head of the Department or the Dean of the College in which my thesis work was done. It is understood that any copying or publication or use of this thesis or parts thereof for financial gain shall not be allowed without my written permission. It is also understood that due recognition shall be given to me and to the University of Saskatchewan in any scholarly use which may be made of any material in my thesis. Requests for permission to copy or to make other use of material in this thesis in whole or part should be addressed to: Head of the Department of Electrical and Computer Engineering 57 Campus Drive University of Saskatchewan Saskatoon, Saskatchewan Canada S7N 5A9 i Abstract Nowadays, there are many commercial demands for decimal floating-point (DFP) arith- metic operations such as financial analysis, tax calculation, currency conversion, Internet based applications, and e-commerce.
    [Show full text]
  • History of Binary and Other Nondecimal Numeration
    HISTORY OF BINARY AND OTHER NONDECIMAL NUMERATION BY ANTON GLASER Professor of Mathematics, Pennsylvania State University TOMASH PUBLISHERS Copyright © 1971 by Anton Glaser Revised Edition, Copyright 1981 by Anton Glaser All rights reserved Printed in the United States of America Library of Congress Cataloging in Publication Data Glaser, Anton, 1924- History of binary and other nondecimal numeration. Based on the author's thesis (Ph. D. — Temple University), presented under the title: History of modern numeration systems. Bibliography: p. 193 Includes Index. 1. Numeration — History. I. Title QA141.2.G55 1981 513'.5 81-51176 ISBN 0-938228-00-5 AACR2 To My Wife, Ruth ACKNOWLEDGMENTS THIS BOOK is based on the author’s doctoral dissertation, History of Modern Numeration Systems, written under the guidance of Morton Alpren, Sara A. Rhue, and Leon Steinberg of Temple University in Philadelphia, Pa. Extensive help was received from the libraries of the Academy of the New Church (Bryn Athyn, Pa.), the American Philosophical Society, Pennsylvania State University, Temple University, the University of Michigan, and the University of Pennsylvania. The photograph of Figure 7 was made available by the New York Public Library; the library of the University of Pennsylvania is the source of the photographs in Figures 2 and 6. The author is indebted to Harold Hanes, Joseph E. Hofmann, Donald E. Knuth, and Brian J. Winkel, who were kind enough to communicate their comments about the strengths and weaknesses of the original edition. The present revised edition is the better for it. A special thanks is also owed to John Wagner for his careful editorial work and to Adele Clark for her thorough preparation of the Index.
    [Show full text]
  • Ed 040 737 Institution Available from Edrs Price
    DOCUMENT RESUME ED 040 737 LI 002 060 TITLE Automatic Data Processing Glossary. INSTITUTION Bureau of the Budget, Washington, D.C. NOTE 65p. AVAILABLE FROM Reprinted and distributed by Datamation Magazine, 35 Mason St., Greenwich, Conn. 06830 ($1.00) EDRS PRICE EDRS Price MF-$0.50 HC-$3.35 DESCRIPTORS *Electronic Data Processing, *Glossaries, *Word Lists ABSTRACT The technology of the automatic information processing field has progressed dramatically in the past few years and has created a problem in common term usage. As a solution, "Datamation" Magazine offers this glossary which was compiled by the U.S. Bureau of the Budget as an official reference. The terms appear in a single alphabetic sequence, ignoring commas or hyphens. Definitions are given only under "key word" entries. Modifiers consisting of more than one word are listed in the normally used sequence (record, fixed length). In cases where two or more terms have the same meaning, only the preferred term is defined, all synonylious terms are given at the end of the definition.Other relationships between terms are shown by descriptive referencing expressions. Hyphens are used sparingly to avoid ambiguity. The derivation of an acronym is shown by underscoring the appropriate letters in the words from which the acronym is formed. Although this glossary is several years old, it is still considered the best one available. (NH) Ns U.S DEPARTMENT OF HEALTH, EDUCATION & WELFARE OFFICE OF EDUCATION THIS DOCUMENT HAS BEEN REPRODUCED EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION ORIGINATING IT POINTS OF VIEW OR OPINIONS STATED DO NOT NECES- SARILY REPRESENT OFFICIAL OFFICE OF EDU- CATION POSITION OR POLICY automatic data processing GLOSSA 1 I.R DATAMATION Magazine reprints this Glossary of Terms as a service to the data processing field.
    [Show full text]
  • Report Association for Computing Machinery
    June 1954 REPORT TO THE ASSOCIATION FOR COMPUTING MACHINERY FIRST GLOSSARY of PROGRAMMING TERMINOLOGY Committee on Nomenclature 'Co Wo Adams R. FoOsborn J 0 W 0 Backus G. W. Patterson J 0 W. Carr, III J. Svigals J. Wegstein Grace Murray Hopper, Chairman COPIES Copies of this glossary are available at 25, each. When ordered by mail, the price is 50~for the first copy and 25<'f for each 'additional copy sent to one address. Please address all orders, with cash or -check enclosed" to the Association for Computing Machinery" 2 East 63rd Street, New York 2'1" N.Y. ACKNOWLEDQ]lJIENT This (·programmer's glossary" had its ,inception in a glos­ sary compiled by Dr. Grace Murray Hopper for the Workshops on AutomaticOoding held in 1953 under the sponsorship of the Bur­ eau of Oensus, the Office of the Air Comptroller, and Remington Rand" Inc. '!he answers to the plea for criticisms and sugges­ tions made in that first version were most generous o Everyef­ fort has been made to include all of them or to arbitrate fairly those in conflict. Both versions have borrowed heavi~y from the "St1mdards on Electronic Computers: l)efinitionsof' Terms" 1950"" Proceedipgs of the I.R.E." Vol. 39 No.3" pp. 271-277" March 1951" and from the "Glossary", Computers and Automation~ Vol. 2" Nos. 2" 4 and 9" March" May, and December" 1953. The commit­ tee extends its thanks to the authors ,of those glossaries and to the many others who have contributed their time and thoughts to the preparation of this glossary.
    [Show full text]
  • Is Hirihiti?H DECIMAL
    May 1, 1962 J. F. COULEUR 3,032,266 DECIMAL TO BINARY CONVERSION OF NUMBERS LESS THAN UNITY Filed July 12, l960 2 Sheets-Sheet l FG.I. TENTHS DECADE HUNDREDTHS DECADE THOUSANDTHS DECADE 4. 2 is hirihiti?h DECIMAL TERAF DODE MATRIX DODE MATRIX DODE MATRIX TEST PULSE BUS CLOCK - MULTIVBRATOR AND BNARY COUNTER ACCUMULATOR NVENTOR: JOHN F. COULEUR, BY (4-f (? W2----- HIS AT TORNEY. May 1, 1962 J. F. COULEUR 3,032,266 DECIMAL TO BINARY CONVERSION OF NUMBERS LESS THAN UNITY Filed July 12, 1960 2. Sheets-Sheet 2 F.G.3. BINARY BINARY CODED DECMAL TENTHS HUNDREDTHS THOUSANDTHS Row 3 2 8 NUMBER O O OOO OOO () OO OOO O T (2) O O O O O OO S (3) O OO OOO OO T (4) O OO OOO OOO S (5) O OO OOO OOO T (6) OO O O OOO OOO S (7) OO OO OOO OOO T (8) OO OOO OO O OOO S (9) OO OOO OOO O T (O) OOO OOO OO OO S (I) OOO OOO OO OO T (2) OOOO OO OO OOO S (3) OOOO OO OO OOO T (4) OOOO OO OOO OO O S (5) OOOO OO O OOO. T (6) OOOO OO OO OOO S (7) OOOO OO OO O T (8) OOOO OO OO O O S (9) OOOO OO OO OO T (20) OOOO OOO O OO O S (2) T MEANS TEST AND ADD THREE TO ANY DECADE 2 5 S MEANS SHIFT FIG.4. BINARY BNARY CODED DECMA -------------------IO- IO-2 IO-3 IO-4 10-5 O-6 (3) (2) (8) () (2) (5) OO OOO OOO OOO OOO OO OO OOO O OOO OOO OOO T O O O Oi Oi O O OOO O.
    [Show full text]
  • Design and Architecture of New 11:2 Decimal Compressors
    Sådhanå (2019) 44:125 Ó Indian Academy of Sciences https://doi.org/10.1007/s12046-019-1110-4Sadhana(0123456789().,-volV)FT3](0123456789().,-volV) Design and architecture of new 11:2 decimal compressors PRABIR SAHA* and PUJA SAMANTA National Institute of Technology Meghalaya, Shillong, India e-mail: [email protected]; [email protected] MS received 5 January 2018; revised 11 March 2019; accepted 19 March 2019; published online 25 April 2019 Abstract. Design and architectures of new 11:2 decimal compressors have been reported in this paper. Two design methodologies viz. delay and area optimized compressors have been introduced and implemented through tree structure of decimal number system. The architectures have been realized through vertical carry save addition algorithm, wherein to build up such addition of unconventional (4221 and 5211) binary coded decimal technique has been incorporated. Configurations of such compressors have been prototyped and tran- sistor level implementation have been carried out to evaluate performance parameters like speed (propagation delay), power dissipation, area and area delay product. The architecture has been validated by Cadence virtuoso platform using 90 nm, 65 nm and 45 nm CMOS technology which provides useful statistics to determine the compressor’s performance parameters. The propagation delay of the delay optimized compressor equals to *0.094 ns while the propagation delay of the area optimized compressor is *0.124 ns using 90 nm CMOS technology at 1 V supply voltage. The reported architectures are *24% and *41% faster from its counterpart. Keywords. Cadence; decimal compressor; layout area; power consumption; propagation delay. 1. Introduction multiplication; hence it reduces the overall delay of the multiplication.
    [Show full text]
  • Binary Number System
    Binary Number System Most of the time, we use the decimal number system: there are 10 digits, denoted by 0, 1, ..., 9, and we say 10 is the base of the decimal system. E.g., 314:159 ≡ (314:159)10 = 3 · 102 + 1 · 101 + 4 · 100 + 1 · 10−1 + 5 · 10−2 + 9 · 10−3: Most computers use the binary number system: there are two digits, denoted by 0 and 1, called bits, for binary digits, and we say 2 is the base of the binary system. E.g., 3 2 1 0 −1 −2 (1101:11)2 = 1 · 2 + 1 · 2 + 0 · 2 + 1 · 2 + 1 · 2 + 1 · 2 = 13:75: DECIMAL FLOATING-POINT NUMBERS Floating point notation is akin to what is called scientific notation in high school algebra. For a nonzero number x, we can write it in the form x = σ · ξ · 10e with e an integer, 1 ≤ ξ < 10, and σ = +1 or −1. Thus 50 = (1:66666 ··· ) · 101; with σ = +1 3 10 On a decimal computer or calculator, we store x by instead storing σ, ξ, and e. We must restrict the number of digits in ξ and the size of the exponent e. For example, on an HP-15C calculator, the number of digits kept in ξ is 10, and the exponent is restricted to −99 ≤ e ≤ 99. BINARY FLOATING-POINT NUMBERS We now do something similar with the binary representation of a number x. Write x = σ · ξ · 2e with 1 ≤ ξ < (10)2 = 2 and e an integer. For example, −4 (:1)10 = (1:10011001100 ··· )2 · 2 ; σ = +1 The number x is stored in the computer by storing the σ, ξ, and e.
    [Show full text]
  • Downloading from Naur's Website: 19
    1 2017.04.16 Accepted for publication in Nuncius Hamburgensis, Band 20. Preprint of invited paper for Gudrun Wolfschmidt's book: Vom Abakus zum Computer - Begleitbuch zur Ausstellung "Geschichte der Rechentechnik", 2015-2019 GIER: A Danish computer from 1961 with a role in the modern revolution of astronomy By Erik Høg, lektor emeritus, Niels Bohr Institute, Copenhagen Abstract: A Danish computer, GIER, from 1961 played a vital role in the development of a new method for astrometric measurement. This method, photon counting astrometry, ultimately led to two satellites with a significant role in the modern revolution of astronomy. A GIER was installed at the Hamburg Observatory in 1964 where it was used to implement the entirely new method for the meas- urement of stellar positions by means of a meridian circle, then the fundamental instrument of as- trometry. An expedition to Perth in Western Australia with the instrument and the computer was a suc- cess. This method was also implemented in space in the first ever astrometric satellite Hipparcos launched by ESA in 1989. The Hipparcos results published in 1997 revolutionized astrometry with an impact in all branches of astronomy from the solar system and stellar structure to cosmic distances and the dynamics of the Milky Way. In turn, the results paved the way for a successor, the one million times more powerful Gaia astrometry satellite launched by ESA in 2013. Preparations for a Gaia suc- cessor in twenty years are making progress. Zusammenfassung: Eine elektronische Rechenmaschine, GIER, von 1961 aus Dänischer Herkunft spielte eine vitale Rolle bei der Entwiklung einer neuen astrometrischen Messmethode.
    [Show full text]
  • Binary Number System
    Binary Number System Most of the time, we use the decimal number system: there are 10 digits, denoted by 0, 1, ..., 9, and we say 10 is the base of the decimal system. E.g., 314:159 ≡ (314:159)10 = 3 · 102 + 1 · 101 + 4 · 100 + 1 · 10−1 + 5 · 10−2 + 9 · 10−3: Most computers use the binary number system: there are two digits, denoted by 0 and 1, called bits, for binary digits, and we say 2 is the base of the binary system. E.g., 3 2 1 0 −1 −2 (1101:11)2 = 1 · 2 + 1 · 2 + 0 · 2 + 1 · 2 + 1 · 2 + 1 · 2 = 13:75: DECIMAL FLOATING-POINT NUMBERS Floating point notation is akin to what is called scientific notation in high school algebra. For a nonzero number x, we can write it in the form x = σ · ξ · 10e with e an integer, 1 ≤ ξ < 10, and σ = +1 or −1. Thus 50 = (1:66666 ··· ) · 101; with σ = +1 3 10 On a decimal computer or calculator, we store x by instead storing σ, ξ, and e. We must restrict the number of digits in ξ and the size of the exponent e. For example, on an HP-15C calculator, the number of digits kept in ξ is 10, and the exponent is restricted to −99 ≤ e ≤ 99. BINARY FLOATING-POINT NUMBERS We now do something similar with the binary representation of a number x. Write x = σ · ξ · 2e with 1 ≤ ξ < (10)2 = 2 and e an integer. For example, −4 (:1)10 = (1:10011001100 ··· )2 · 2 ; σ = +1 The number x is stored in the computer by storing the σ, ξ, and e.
    [Show full text]
  • A High Performance Binary to BCD Converter
    ISSN (Print) : 2320 – 3765 ISSN (Online): 2278 – 8875 International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering (An ISO 3297: 2007 Certified Organization) Vol. 4, Issue 8, August 2015 A High Performance Binary to BCD Converter A. Hari Priya1 Assistant Professor, Dept. of ECE, Indur Institute of Engineering. and Technology, Siddipet, Medak, India1 ABSTRACT: Decimal data processing applications have grown exponentially in recent years thereby increasing the need to have hardware support for decimal arithmetic. Binary to BCD conversion forms the basic building block of decimal digit multipliers. This paper presents novel high speed low power architecture for fixed bit binary to BCD conversion which is at least 28% better in terms of power-delay product than the existing designs. KEYWORDS:Decimal Arithmetic, Binary to BCD Converter I.INTRODUCTION In commercial business and internet based applications, decimal arithmetic is receiving significant importance. Decimal arithmetic is important in many applications such as banking, tax calculation, insurance, accounting and many more. Even though binary arithmetic is used widely, decimal computation is essential. The decimal arithmetic is not only required when numbers are presented for inspection by humans, but also it is a necessity when fractions are being used. Rational numbers whose denominator is a power of ten are decimal fractions and most them cannot be represented by binary fractions. For example, the value 0.01 may require an infinitely recurring binary number. Even though the arithmetic is correct, but if binary approximation is used instead of an exact decimal fraction, results can be wrong. This extensive use of decimal data indicates that it is important to analyse how the data can be used and how the decimal arithmetic can be defined.
    [Show full text]