DataRepresentation - Data Representation Data...

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Data Representation Beta Draft - Do not distribute © 2001, By Randall Hyde Page 53 Data Representation Chapter Three A major stumbling block man y be ginners encounter when attempting to learn assembly language is the common use of the binary and he xadecimal numbering systems. Man y programmers think that he xadecimal (or he x 1 ) numbers represent absolute proof that God ne v er intended an yone to w ork in assembly language. While it is true that he xadecimal numbers are a little dif ferent from what you may be used to, their adv an - tages outweigh their disadv antages by a lar ge mar gin. Ne v ertheless, understanding these numbering systems is important because their use simplifi es other comple x topics including boolean algebra and logic design, signed numeric representation, character codes, and pack ed data. 3.1 Chapter Overview This chapter discusses se v eral important concepts including the binary and he xadecimal numbering sys - tems, binary data or g anization (bits, nibbles, bytes, w ords, and double w ords), signed and unsigned number - ing systems, arithmetic, logical, shift, and rotate operations on binary v alues, bit fi elds and pack ed data. This is basic material and the remainder of this te xt depends upon your understanding of these concepts. If you are already f amiliar with these terms from other courses or study , you should at least skim this material before proceeding to the ne xt chapter . If you are unf amiliar with this material, or only v aguely f amiliar with it, you should study it carefully before proceeding. All of the material in this c hapter is important! Do not skip o v er an y material. In addition to the basic material, this chapter also introduces some ne w HLA state - ments and HLA Standard Library routines. 3.2 Numbering Systems Most modern computer systems do not represent numeric v alues using the decimal system. Instead, the y typically use a binary or tw o’ s complement numbering system. T o understand the limitations of computer arithmetic, you must understand ho w computers represent numbers. 3.2.1 A Review of the Decimal System Y ou’ v e been using the decimal (base 10) numbering system for so long that you probably tak e it for granted. When you see a number lik e “123”, you don’ t think about the v alue 123; rather , you generate a mental image of ho w man y items this v alue represents. In reality , ho we v er , the number 123 represents: 1*10 2 + 2 * 10 1 + 3*10 0 or 100+20+3 In the positional numbering system, each digit appearing to the left of the decimal point represents a v alue between zero and nine times an increasing po wer of ten. Digits appearing to the right of the decimal point represent a v alue between zero and nine times an increasing ne g ati v e po wer of ten. F or e xample, the v alue 123.456 means: 2 + 2*10 1 0 + 4*10 -1 + 5*10 -2 + 6*10 -3 or 100 + 20 + 3 + 0.4 + 0.05 + 0.006 1. Hexadecimal is often abbreviated as hex even though, technically speaking, hex means base six, not base sixteen.
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Chapter Three Volume 1 Page 54 © 2001, By Randall Hyde Beta Draft - Do not distribute 3.2.2 The Binary Numbering System Most modern computer systems (including PCs) operate using binary logic.
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This note was uploaded on 08/08/2011 for the course CS 101 taught by Professor Jitenderkumarchhabra during the Summer '11 term at National Institute of Technology, Calicut.

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DataRepresentation - Data Representation Data...

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