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STAR LASERPRINTER 8 SOFTWARE
Binary and hexadecimal arithmetic
If you already know what hexadecimalnumbers are, you can skip this
sectionand go aheadto read aboutASCII.
The decimalnumbersystemwith which we're all familiaris a positional
counting system. There's the "ones" position, the "tens" position, the
"hundreds"positionandsoon. Eachhigherpositionis worthtcntimesmore
thanthe positionto therightof it, sincethedecimalsystemusesthe baseof
ten. Moreover,we need ten symbolsto showthe actualvaluesthat maybe
in each position.
The binarysystemis positionaltoo.There'sthe"ones"position,the"twos"
position,the"fours"position,the"eights"positionandsoon. Inbinaryeach
positionis worthonlytwicethatofthepositiontoitsright.Andweonlyneed
twosymbols-O (zero)and 1(one)-to showthevaluesthatmaybe in any
position.So in binary we get numbersthat look like 1010or 10001100.
The hexadecimalsystemis madeof base-sixteennumbers.Hexadecimalis
positionalliketheothercountingsystems.Andeachhigherpositionis worth
sixteentimes as much as the positionto its right.
We need sixteen different symbols to show all the possible values one
hexadecimaldigit could have. We can use our decimal system's ten
symbols,but we'vehad to borrowa few more from our alphabetto get all
thesymbolsweneed.Inhexadecimal, t herefore,youcanhaveanumberthat
lookslike 2C7C,or evenFACE.
Here'showthedecimal,binaryandhexadecimal n umbersystemscompare:
Decimal
o
1
2
3
4
5
6
7
Binary
Ooo1
0010
0011
0100
0101
0110
0111
Hexadecimal
o
1,
2
3
4
5
6
7
Decimal
8
9
10
11
12
13
14
15
Binary
1(W3
1001
1010
1o11
1100
1101
1110
1111
Hexadecimal
8
9
A
B
c
D
E
F
5
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