EIT Electrical Review, Second Edition

Chapter 7: Digital Codes and Number Systems

Overview

The material in this chapter is of the level expected in a first or second course in digital logic. Most electrical engineers will already have at least one book on this subject. But for those who need references, two of the more popular books used in many universities in the United States are ones by Bartee [1] and by Roth [2]. Both of these books start with number systems and codes.

In digital systems, numbers and digital codes are carefully specified, since in these systems, the values are discrete unlike an analog system where values may be continuous. The number system for digital codes, rather than running from, say, 1 to 10, run from 0 to 9 for the standard base 10 system. Or, for the binary system 0 to 1, and 0 to 7 for the octal system. On the other hand, for a hexadecimal system (base 16) from 0 to 15; where representation beyond 9, need new symbols, such as "A" for 10, "B" for 11, etc., and "F" for 15. These will be discussed shortly.

[1]Bartee, DIGITAL COMPUTER FUNDAMENTALS, 6th ed., McGraw-Hill, 1985.

[2]Roth, FUNDAMENTALS OF LOGIC DESIGN, 3rd ed., West Publishing Co., 1985.

Number Systems:

The standard number system (base 10 or radix 10) that everyone is familiar with may be broken into powers of 10 and written as follows (say, the number fifteen hundred thirty two point four) is expressed as,

1,532.4=1x10 3 + 5x10 2 + 3x10...

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