NUMERATION SYSTEMS in Digital

Chapter 1 NUMERATION SYSTEMS

Lessons In Electric Circuits Volume IV – Digital Book
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Summary of Contents

Lessons In Electric Circuits Volume IV – Digital Book

  • Chapter 1NUMERATION SYSTEMSContents 10,1.1 10,Numbers 10,and 10,symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . .1 15,1.2 15,Systems 15,of 15,numeration . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 17,1.3 17,Decimal 17,versus 17,binary 17,numeration . . . . . . . . . . . . . . . . . . . . .8 19,1.4 19,Octal 19,and 19,hexadecimal 19,numeration . . . . . . . . . . . . . . . . . . . . .10 21,1.5 21,Octal 21,and 21,hexadecimal 21,to 21,decimal 21,conversion. . . . . . . . . . . . . .12 22,1.6 22,Conversion 22,from 22,decimal 22,numeration. . . . . . . . . . . . . . . . . . .13”There are three types of people: those who can count, and those who can’t.”Anonymous1.1Numbers and symbolsThe expression of numerical quantities is something we tend to take for granted. This is both agood and a bad thing in the study of electronics. It is good, in that we’re accustomed to the useand manipulation of numbers for the many calculations used in analyzing electronic circuits. Onthe other hand, the particular system of notation we’ve been taught from grade school onward isnot the system used internally in modern electronic computing devices, and learning any differentsystem of notation requires some re-examination of deeply ingrained assumptions.First, we have to distinguish the difference between numbers and the symbols we use to representnumbers. A number is a mathematical quantity, usually correlated in electronics to a physicalquantity such as voltage, current, or resistance. There are many different types of numbers. Hereare just a few types, for example:WHOLE NUMBERS:1, 2, 3, 4, 5, 6, 7, 8, 9 . . .INTEGERS:-4, -3, -2, -1, 0, 1, 2, 3, 4 . . .1