Star Micronics 8 Series Binary and hexadecimal arithmetic, Decimal Binary Hexadecimal Decimal

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,therefore,youcanhaveanumberthat lookslike 2C7C,or evenFACE.

Here’showthedecimal,binaryandhexadecimalnumbersystemscompare:

Decimal	Binary	Hexadecimal Decimal		Binary	Hexadecimal
o		o	8	1(W3	8
1	Ooo1	1,	9	1001	9
2	0010	2	10	1010	A
3	0011	3	11	1o11	B
4	0100	4	12	1100	c
5	0101	5	13	1101	D
6	0110	6	14	1110	E
7	0111	7	15	1111	F

5