Information Technology Reference
In-Depth Information
further.you.start.over.again.with.zero.but.prepend.a.one,.so.
you.have.10..Thus,.the.irst.character.on.the.far.right.of.a.deci-
mal.number.equals.the.number.of.ones,.or.that.character.mul-
tiplied.by.one..The.second.character.will.equal.the.number.of.
tens;.the.next.character.will.be.the.number.of.100s,.and.so.on.
Binary. works. the. same. way,. but. because. you. have. only.
two. characters. to. work. with. (base-2),. every. increment. is. a.
multiple.of.two..So,.the.irst.character.on.the.far.right.of.the.
number.is.the.number.of.ones,.the.second.character.is.the.
number.of.twos,.the.third.is.the.number.of.fours,.the.next.is.
the.number.of.eights,.the.next.sixteens,.and.so.forth.
With. hexadecimal,. you.now.have.16. possible. characters.
(base-16).so.you.are.operating.in.multiples.of.16..For.instance,.
the.irst.10.characters,.0.to.9.have.a.value.that.matches.their.
number,.but.the.character.A.is.equal.to.10.(in.decimal.nota-
tion),.B.is.11,.C.is.12,.D.is.13,.E.is.14,.and.F.is.15..Then.to.
increment.to.the.next.number.you.go.back.to.0.prepended.
with.a.one,.but.10.in.hexadecimal.does.not.equal.10.in.deci-
mal.(of.course)..The.irst.character.on.the.right.is.the.number.
of.ones.as.always,.but.because.we.are.using.a.base-16.lan-
guage,.the.next.character.to.its.left.will.be.the.number.of.six-
teens..The.number.to.its.left.will.be.the.number.of.256s.(16.
×.16),.next.will.be.the.number.of.4096s.(16.×.256),.and.so.
on..Figure 3.2.compares.the.three.mathematical.languages.
used.for.recording.or.coding.digital.information.
Hopefully,.this.is.beginning.to.make.some.logical.sense..
The.reason.this.is.important.is.because.if.you.are.ever.in.the.
position. to. have. to. actually. look. at. digital. data. in. its. most.
basic. form,. it. will. probably. be. represented. in. hexadecimal.
notation..Behind.that.coding.are.the.basic.ones.and.zeros.of.
binary.code.that.the.computer.processors.work.with.to.create.
and.manipulate.the.information.that.you.see.on.your.screen.
or.that.is.used.to.run.your.programs.
Now,.consider.for.a.moment.why.those.hungry.engineers.
would. have. chosen. to. use. hexadecimal. notation. instead. of.
decimal.or.just.the.binary.code..Think.back.to.the.beginning.
of.this.section.when.we.were.irst.digging.into.the.culinary.
