Information Technology Reference
In-Depth Information
22. Base systems
Computers use a variety of different number b ase systems to operate, including
the familiar base 10. In addition, binary or base 2, octal or base 8 and hexadecimal, which
is base 16, are also used. If you are going to get an appreciation of just how computers
work, you will need some comprehension of the different number systems. We will begin
by doing some counting in all four of these bases.
We will count in each from 0 to 23 and we shall start with the familiar base 10. If
you have a PC, access the calculator on your system by clicking on start and then go up to
programs. From there go to accessories and then click on calculator. Once there, click on
view and change your calculator to scientific and you should be in base 10 or decimal. If
not, set the calculator to that base by turning on
Dec
from the four choices Hex, Dec, Oct, and Bin. If the last choice is Bin Laden, call the
FBI. You are now ready to begin counting. If you don't have a PC, you may be able to
accomplish the same results with an ordinary calculator by doing the following:
click on 0, then +, then 1 and then =.
The result will be 1. If you then repeat clicking on the = sign, you will get the same result
as if we were counting from 0 to 23. The result from your PC's calculator, your ordinary
calculator, or if you have neither should be
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23.
This is what we expect to get if we were to count from 0 to 23 in that familiar number
base 10.
Now we shall repeat the process for binary or base 2. First set the PC calculator to
base 2 by turning on the switch for
Bin
.
Proceed as before and the result will be
0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 10000
10001 10010 10011 10100 10101 10110 10111
and this is counting from 0 to 23 in base 2. Again if you don't have the scientific
calculator, take my word for it and I will return to these numbers shortly.
We will now repeat the process for octal and hexadecimal. Switch on base 8 by
setting the calculator to
Oct
and repeat the process as before. The result will be
0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 20 21 22 23 24 25 26 27
and that list represents counting from 0 to 23 in base 8. Next set the calculator to base 16
by clicking on
Hex
- don't worry, nothing bad will happen to you - and by once again repeating the exercise,
the result is
0 1 2 3 4 5 6 7 8 9 A B C D E F 10 11 12 13 14 15 16 17.
This is the sequence of numbers you get if you count from 0 to 23 in base 16 or
hexadecimal.
