Laser Printer User Manual

1.2 STARLASERPRINTER4 SOFTWARE
1.2.1Binaryand hexadecimalarithmetic
1fyou alreadyknow what hexadecimalnumbersare, you can skip this
sectionandgo aheadto read aboutASCII.
The decimalnumbersystemwith whichwe’reall familiaris a positional
counting system. There’s the “ones” position, the “tens” position, the
“hundreds”positionandsoon. Eachhigherpositionisworthtentimesmore
thanthepositiontotherightof it,sincethedecimalsystemusesthe baseof
ten.Moreover,we needtensymbolsto showthe actualvaluesthatmaybe
in eachposition.
Thebinarysystemispositionaltoo.There’sthe“ones”position,the“twos”
position,the“fours”position,the“eights”positionandsoon. Inbinaryeach
positionisworthonlytwicethatofthepositiontoitsright.Andweonlyneed
twosymbols- O(zero)and1(one)- toshowthevaluesthatmaybe inany
position.So in binarywe getnumbersthatlooklike 1O1Oor 10001100.
Thehexadecimalsystemis madeof base-sixteennumbers.Hexadecimalis
positionalliketheothercountingsystems.Andeachhigherpositionisworth
sixteentimesasmuchas thepositionto itsright.
We need sixteen differentsymbolsto show all the possiblevalues one
hexadecimaldigit could have. We can use our decimal system’s ten
symbols,but we’vehad to borrowa fewmorefromour alphabetto get all
thesymbolsweneed.Inhexadecimal,therefore,youcanhaveanumberthat
lookslike2C7C,or evenFACE.
Here’showthedecimal,binaryandhexadecimalnumbersystemscompare:
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
1000
1001
1010
1o11
11(X)
1101
1110
1111
Hexadecimal
8
9
A
B
c
D
E
F
5