Industrial Data Communications 4th Edition

Appendix A: Number Review Systems

This appendix is concerned with number systems, primarily the binary number system. To
understand digital systems, an acquaintance with the binary number system is necessary
(however, it should not be terribly painful). While becoming familiar with binary, some of
the other systems of interest will be brought up, such as "hexadecimal" systems. All of
these find use in data communications systems.

The Decimal System

All number systems follow the same rules. You are probably quite familiar with one number
system, namely the decimal system. Decimal means that the number system is based on 10
digits. Its base is 10. The only numbers allowed in the decimal system are 0,1,2,3,4,5,6,7,8,9.
All the numbers that we can use to describe numerical quantities in decimal are made up of
those 10 numbers and no others.

Figure A-1 illustrates the powers of ten. Notice that a number, such as 4,302.63 is really
4000 + 300 + 2 +.6 + .03 or more correctly, 4 × 1000 (10 to the 3rd power) + 3 ×100 (10
to the 2nd power) + 0 ×10 (10 to the 1st power) + 2 ×1 (10 to the 0 power or 1) + 6 ×1 X
1/10 (10 to the -1 power) + 3 ×1 ×1/100 (10 to the -2 power).

Figure A-1. Powers of 10 Example

All other number systems will be constructed the same, except rather than 10 as the base,
they are based on a different number. For example, the base will be 2 if binary or 16 if
hexadecimal.

For this review of number systems, it is important that the emphasis be on the use of the
number system as a means of pattern recognition. The number systems chosen here are the
ones used presently in data communications. Binary is the number system used by computers;
decimal is used to represent binary values so they make sense to humans; and
hexadecimal is used to reduce binary streams to recognizable patterns. Computers presently
only work with only binary patterns, and humans really understand only decimal.

The arithmetic functions for the binary system will be explained next.

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