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80x86
Probably the biggest stumbling block most beginners encounter when attempting to learn assembly language is the common use of the binary and hexadecimal numbering systems. Many programmers think that hexadecimal (or hex1 ) numbers represent absolute proof that God never intended anyone to work in assembly language. While it is true that hexadecimal numbers are a little different from what you may be used to, their advantages outweigh their disadvantages by a large margin. Nevertheless, understanding these numbering systems is important because their use simplifies other complex topics including boolean algebra and logic design, signed numeric representation, character codes, and packed data.
1.0 Chapter Overview This chapter discusses several important concepts including the binary and hexadecimal numbering systems, binary data organization (bits, nibbles, bytes, words, and double words), signed and unsigned numbering systems, arithmetic, logical, shift, and rotate operations on binary values, bit fields and packed data, and the ASCII character set. This is basic material and the remainder of this text depends upon your understanding of these concepts. If you are already familiar with these terms from other courses or study, you should at least skim this material before proceeding to the next chapter. If you are unfamiliar with this material, or only vaguely familiar with it, you should study it carefully before proceeding. All of the material in this chapter is important! Do not skip over any material.
1.1 Numbering Systems Most modern computer systems do not represent numeric values using the decimal system. Instead, they typically use a binary or two’s complement numbering system. To understand the limitations of computer arithmetic, you must understand how computers represent numbers.
1.1.1 A Review of the Decimal System You’ve been using the decimal (base 10) numbering system for so long that you probably take it for granted. When you see a number like “123”, you don’t think about the value 123; rather, you generate a mental image of how many items this value represents. In reality, however, the number 123 represents:
1*10^2 + 2 * 10^1 + 3*100
100+20+3
Each digit appearing to the left of the decimal point represents a value between zero
and nine times an increasing power of ten. Digits appearing to the right of the decimal
point represent a value between zero and nine times an increasing negative power of ten.
For example, the value 123.456 means:
1*10^2 + 2*10^1 + 3*10^0 + 4*10^-1 + 5*10^-2 + 6*10^-3
100 + 20 + 3 + 0.4 + 0.05 + 0.006
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