Thiết kế mạch bằng máy tính part 1 docx

TRUONG
DAI
HQC
BAcH
KHOA
HA
Nor
7
LlNH
GIANG
/'
K
•
TRUONG
D~I
HQC
BAcH
KHOA HA
N(n
NGUYEN LINH GIANG
A'
-'
THIET
KE
,
H
BANG
MAy
TiNH
• Giao trluh cho sinh vien Cong
ngh~

Thong tin,
I)i~n
tit
Vien thong
cae
truOng
d~i
hQc,
cao dfing
ky
thu~t
thuQc
cae
h~
dolo
t.w
,
NHA.
XU'\T
nAN
KHOA
HOC
vA
KY
THUST
HA
N(JI
6-6C2-01-6T7.3
113-244-03
KHKT-03

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VFRILOG,
VIIDL

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trill
It
bdy
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trong
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ngtr
VIIDL
ld tIl(Jt
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T,le
gia
TS.
N~uycn
Linh
G-i:mg
4
MI,lC
ll,lC
Trang
LO'j
noi dati
Chlwng
I.
Ma
dati vao thiet
kc
In<:,ch
vi
di¢n
tu
* 1.1. Cae
pl1[lll
d(x~n
trong thiet
kc
d.c
mach lfeh
lwp
~

1.2. :\16 hlnh
hoa
nwch
di¢n
~
1.3. T6ng
hQP
va
'oi
uu
hoa
111' lCh
dung
Imi), tinh
Chuang
II. Co' sit
toan
h<;lc
*2.1.
f)~.li
so
Bool
YU
I}'
thuyct chuyen
mt.teh
~2.2.
Cae
h~un
logic

va
d'.lIlg
chufln
uk
*2.3. T6i thicu h6a
de
bieu Ihue
logic
7
7
,
III
12
IY
19
22
27
Clllwn~
III.
Co
so
ella thiCt
kc
logic :t'i
*3.1.
D.)c
diem
cLIa
qu!.!
trlnh

thic"t
kc
m~\ch
miiy
tinh
35
*3.2. Cae phan
IU
logic
C0
ban
40
~3.3.
Thiel
ke
d.e nwch
t6
hQ'p
'-1-3
*3.4.
Nh(l'ng \'un
de
khi thie'l
ke
mach
to
hqp
51
*3.5. Thiel
ke

cae
mt.teh
tuan
tl! 54
*3.6.
Nhung
van
de
khi
lhi~-t
ke
Ci.lc
m<',lch
tufin
t~r
67
Chuong
IV.
NhO:ng
khai
ni~m
chung
,"'c
mb hloh hoa
phan
77
drng
*4.1.
M6
hlnh

hoa
philn
cung
~4.2.
Otc ngon ngu m6 hinh hoa phun
cu:ng
~4.3.
Otc
mo
hiBh
tnlu tuqng
Chtwng
V.
eric
phuong
phap
mt>
hlnh hoa logic
~5
.1.
Co
sa
ma
hillh hoa logic
~5.2.
Phuong
phip
ma
hinh
hoa

hi
en
djch
§5.3. Phuong
phip
mo
hlnh
hOil
hu6ng sl! ki4n
77
78
87
95
97
106
I
II
5
~5.4.
M(l hlnh hoa
qua
trlnh tre tin hi¢u trong cae philo
tLr
1T1i.Kh
115
~5.5.
M6
hlnh
hoa
tren mtre cae phan

tV
logie 114
Chll"tJllg
VI.
I'oigon
ngu
ml>
hinh
hoa
VHOL
131
96.1.
~vll~
<.UtU
ng<.'m
ngO
VUOL
131
~6.2.
Cic
c:{u truc co so
trang
VHOL
136
~6.3.
Cae kie'u
dO
ll('u 153
~6.4.
Toao

tv
\';1
bic'u
thue 162
~6.5.
etc
cAu
true
tuiin
tv
171
~6.6.
Dic
cilu true
song
.
,ong
1X7
~6.7.
Cic
chu"Ong
trlnh con Vil cae goi
clnwng
trlnh 196
Chmmg
VIl.
~lo
hlnh
hoa
m~.lch

bill1g ng(ln
ngu
VHUL
207
~7
.1.
~vl0
hlnh
hoa Iren mile crlu true
207
~7.2.
\16
hlnh
hoa
trC:n
ll1Lrc
thanh ghi truycn
dq.t
219
~7
.3.
~16
hlnh
hoa
de
610111<11
hiJu Iwn 231
Chmmg
VIll.
C{IC

phuong
ph,ip
kic'm
tra
loi
ml,lch logic 243
§8.1. Cae
1116
hlnh
lui logic
243
§8.2. Bai to;io phat
hiGn
16i
250
§8.3.
Cie
phu<.1ng
ph<.lp
thu,~t
toan
tong
h<,l"p
uk
gia tr! thiI
nghi¢111
264
~g.4.
PlllfO'ng
ph<ip!TI6

hinh
h6a
101
277
§8.5.
M(l1.
so
pilU'0ng
phap
lam
d<.m
gian
hoa
qua
trlnh kiem tra
phat
hi911
16i
288
Tai
li~u
tham
kluio
297
(,
CHUONG
I.
MO
DAU
VAO

THIET
KE
M,.,CH
VI
DI~N
Til
§1.1. Cae
ph:!n
do:;t"
trung thiet ke cae mach tich
hqp
SV
ra
(\i:J'j
ella
de
mach \'i di2n
Ill'
di'i
l:un
co'
~h
phel!
tri~ll
phCill
cll'll~
\,~I
phi-til
I1lCIll
Cllil

de
h~
th6ng tillh t,xtn
tl'Ong
nhl1"ng
th(tp
k~-
g;lll d,ly. Vll'l'
\,\ng hen
n,le
meTe
d6 Ifch hqp ella
de
lll<.lch
c1i¢n
til' IrcH
tnt'll
1ll::11
don
d~l
dua
t6i
\'i~c
che
1<,10
nhilng
I-u;
thong
\'O'i
d(l

phdc
1' 1]1
ngay
c~lllg
t:Ing
COll)!
ngh!.,'
che
I~\O
m,~ch
Itch
heyp
tren
eel sb'
uie
chflt han d,ln pluit
trj~ll
\'U
hao.
T(1i
gifb.l
nhfrng
n[\[11
RO
elta the k)'
20
nglf(1i
la
dil
dl

lh~
chc
tao
liU'(,il'
llhung
\11',lch
1ich
h9P
chu-a lui
h(\I1g
tri~u
liuh kicn di¢n
lU
trcn
mot
lmh
the
ch~-ll
b:ln
d,ll1.
I\'hU11g
llwch
dl)
duq'C
gqi
El
m'.Icil
lich
hQ'p
cao(VLSl)

ho~c
\a
mi tell
vi
cti¢n
IU.
Vi~c
ra dui
etla
nhung
111' leh
vi
di~n
Ill'
(hi him nay sinh
"~f
can
Ihid
ph,!i
co
ITIQI
phuong
ph{ip
luan va quy trinh thie't
ke'.
ehe
1<,tO
thieh h9V.
Trong eoog
nghi~p.

v,~c
che'
t, tO
uie
nweh lich
IH)p
dU'Q"c
thL!e
IlJ¢n
qua
hon giai
dm~n:
• Giai dmm thie't ke.
•
Giai
c1o<',m
che'
h.W.
• Giai
do<.~n
ki~m
tra.
• Giai
c1m.1I1
dong go!.
o giai
do,.111
thiel kc.
Itr
de

ehue nang ma
me.teh
sc
tlll.re
hi¢n.
('hClng
ta
x,ly dung
mCl
hinh ella
me.leh
tren
nhi~u
mue
de)
chi liet khac nhau. Cae muc
de)
chi tiet co the
(hrqc
ehia thanh muc kie'n true,
mu:e
logic,
mCre
V(lt
15;.
Ket
qua
eLla
giai
dO<'111

thiet
ke
la cac
rm'l
hlnh ella m,wh
(El
duvc xac
lIil(1ll
kh6ng
ehu:a loi tren phuong
di~n
thiel kc.
Gi<.li
<.10<.111
th(r hai iiI giai
c1O<.I11
che'
h.l0.
6 giai
c10,.111
nay, m'.Ich tieh hqp se
duqe
che
\'.10
th :o
dc
e(mg ngh¢
eflY
ghcp
d.e

phfin
tLf
lllC.lCh
iClI
dIe
tinh
tht
chat
bi.in
d<'ill
btll1g phmmg phap
m~11
na che
phLI
vi'I
cong ngh¢
X{IY
dung cae
mach
nhi~u
la-po
Ke't
q\l(i ella giai
c1m.l!1
llay
lit
nhung
vi
mach time
hi~n

nhfrng
ehLfe
n[mg
nhu
trong thie't kc.
Giai doan
ba
la
gi<'lI
c1m,1I1
kiem Ira. 6 giai
dO<'.111
nay, nhu'ng m',lch d5 che'
t"to
se
dU\J'C
kidm nghi¢m ngau nhicn
c1d
khiing dtnh
dll1g
l1l<:tch
kh6ng
ebu:a
loi ve
m,)!
ehe
!<;Io.
Trang
truung hqp co nhilng
10,

g(lp
nllleu litn
c6
the rut ra
7
1<:6'1
lutlll
loi
do
eo
Ih~
la loi lrong qua Irlnh
che
l<;to.
Dl!<I
\'aO
VI¢C
kitm
Ira
quy Il'lnb
eong
ngh¢ la
e6
Ihe
rUI
ra
ke'l
lU(1l1
\'e cae kh,lu c6
Ih~

>;mh
ra luI.
Cil;\[
doan
euai
clll1g
I~I
gml
c10an
dong
g6i.
Ll:ic
lki
de
vi
mach sc ducfe
phfll1
laeh \'il
du~jC
I,.to
Vl') hoe.
Trong
ehu'ong trlnh ta
s2
nghi2n
eCru
ky
giai
dm~ll
dill! ti2n iii giai duan

thict
kC.
Qua trlnh thic't
kc'
nie
mach
vi
lti¢n tti lrung
cong
nghicp
c1uqc
ehia
Elln
ba
ph;ll1
dOi ll1:
• Mo hlnh h6a.
• T()ng
hqp
vii
lai
Ull
ho'\.
•
Kl~m
nghi¢m vii
phi':
eilu£ln.
Trong
do ehung

la
1(lp
trung
vi:1O
blli
loan
m()
hlnh hoa maeh
\,~I
1611g
hl.lp.
t6i
ll'll
ho;i mach.
Pluin
du~n
dUll
lien:
1\-11'.
hlnh
hO{1
6 giai
dm.1i1
n~\y.
nh~1
thie't
ke
X[IY
(hyng
de

mo hinh dIll trllc
l11<,lch
\'il
de
ch(re
n~lllg
ma
mi lell
>;is
tlll.re
hi¢n.
Cic
mI.)
hlnh
m;.leh
iii
c{)1l1:!
cu
bi(o'u
di~n
d.e
;'
tu'('mg
thiel ke. Mo hinh ho,\ el6ng \'al tn) quail lrong Irong
LI1II.':1
kc'
m:.Ich
\'i di¢n
ILl'
blii

\'1
cac m6 hlnh
Iii
nhung phuong lien mang Ih6ng
Lin
\'(~
dc
mach
s0
duue
xiI)'
d~rng
m6t
deh
Cl) dong
VlI
ehinh x,ic. Do
d6
Ill()
hinh
e[m
ph;ii ehinh
x<.i.c.
ch[lt ehl' eOng nlur
c6
ml['e
ell)
16ng quat. trong su6t
\'(1
de

hl~U
c10i
w':ii
ngl['()"i
thiC·'t
kc "il may.
V{)'i
sl,l'
phat
L["J~n
eUd
cae
k5'
Ihu,:tl
mo
phong,
me)
hlnh
111<,1ch
c6
the duqc
xi.ly
d~rng
treil
cO'
so'
Ciic
ngon
ngL'i"
1110

l;i
ph[in
eU:llg
HDL
(harclwar~
description language>;). Trollg nhicu tnIll'ng hnp,
Ciic
mo
hlnh
de)
hqa nhu bieu do dong thong tin.
so'
de)
m,.teh
V(I
1lll)
I;i
hinh
d'.lI1g
hlnh
hQc
eLla
cae d6i
tU'(5!lg
cung
nhu
deh
sAp
xcp cluing
Lj'~n

Ixin
mach
dell
eo
Ihe
dUQ'e
dllllg
d~
hidu
<lien
m;.Ich.
D6i
vt'fi
llhi}'ng
llli,leh
co
dt)
lich
h0'P
sieu
lall
do dl)
phLi'c
t:.lp ella
mach
n'ft
eao
nen
\'l~e
X[IY

(h.rn,!!
111l')
hinh
mach
Ihuang
Iheo
eae
IllLrC
d()
chI
li2'1
kh,ic nhau.
Dieu
d6 elm
ph<'sp
nglf(\i Ihiel
ke'
I:~p
trung
\'aO
tung
ph,'ln
Cl'la
mo
hinh
I;.li
1[l'llg
giai
dO:.lIl
thiet

kC:'.
Ph;'l11
d()~n
hai:
Tong
hqp
va
t6i
I(lI
hila
Tl)llg
lWp
mach iii giai
cto'.111
>;;ing
I'.l()
thCr
hai ella qll,i trlllh
ll1le-l
ke'.
('lal
dOi.lI1
dill! lu[m theo
cae
\'
lUl'mg:
cllil
nh;1
Ihici kc
hl1111

111>l1h
(hin
de
kh;ii
ni¢m
Y~
111<.lch
Y~I
xay
dvng
nhung
mo
hlnh
sO'
h9
dfiu lien
ye
m'.\'.:I1.
Ml.lc
dleh
ehinh
cLla
giai
dO<;ln
t6ng
h\Jp
mach
I~I
xfly dVng
1116

hlnh
chi
liel
ella
111<.1ch.
v\
dl,l
nhu
cae
chi
liel
\'C
dang
hlnh
hqe
phl,le
vu
cho
cong
dO'.I11
Illp
nip
viI
tao
vi)
bge
eho
mach.
Dicll
n~IY

d'.lt
c1l(.iC
thong
qua
yu.\.
trinh
xay
dung:
V~I
chfnh
xac
hm\.
thiet
kc
ti:rng:
bu6e
trong
d6
m0
hlnh
truu wq"ng
ban
diiu
dW"iC
ngui\i
thiet
ke
chi
tiel
ho<1.

tung
bu6c
I~p
(11
I~p
l<:li.
Khi thVe hi¢1l
qUi.
Idnh
t6ng
Iwp
111'.lch
theo
dc
blfac Gii tie'n
m6
hinh,
ngu(1i thi('1
kc"
dn
nillcu
thC)ng
tin lien
quan
16'i
cae
e(lIlg
ngh~
che
tao

YLI
cac
phong
cach
thi(,t
kc
1l10ng l11u6n.
Ta
co
Iht
thtiy e.lc
ehCre
nang
ella
lll<.\eh
e6
Iht
dge
!{Ip
\'Cii
cae
chi
tic"t
thut
hiC'n,
trong
khi
do
Cile
d~lt1g

hi6u
dien
hinh
h~)C
ella
nwch
hO~1ll
toi\l1
pliu
thU(lC
\'LIO
cac
d;)c
tinh
ella cemg ngh¢
vi
dl,l
nhu
kfch
Ihu6c
cLla
de
d[ry dim IroJlg
miKh
plll.l
thuQe
dto
cbng
nghc
ehe' 1

•.
10.
Bai Imin
t6i
It'U
mach
IUllll
ke"t
IWp
cll(lt
che
\'6i bili Imin t(')ng
IWp
m'.lch.
Qu;.i
trlnh
16i
lilt
dOl
h(')i
phill
Il,l''-l
chQn
nhung
chi
lict
dc
djnh
eua
1l1i lell

\'()"i
ml.lC
rlieh
lam
Hill';
kh,'1
Il~ing
ella
m'.leh
"e
phuong
<.lJ¢n
thie"t
ke
tuong
Crng
v6i nhiJng d(l
do
x,ie
djnh.
Vai
Ir()
ella
tcii
lru
IiI
n[mg
cao
chell
IUq"ng

ella
mach
dien
Hlur
tOL
uu
\'~
chue
nan".
\'C
dj~n
ttch,
\'C
tll1h
d~
kiem
n"hicm
\'i'l
. _ b . b ,
ph,it hi¢ll
il')i.
ehuc
nimg lien
quail
t6i
thl"ii
gian
rl6
Ilwe
hi~n

Ill(lt qu(\
trlnh
:Xlr
I)' th(lJIg tin
cung
nhlf
~ci
IUQ"ng
Ih6ng
lin
c()
lh6
dU<;ic
XLe
Iy
trong
111(11
d{1ll
Y!
Ih(l"i
gian.
Cilc tlnh
n,-mg
ella
mach
Iii
anh
lur6ng
16n
t(1i

kha
nfulg
eanh
tranh
ella
m'.leh
trC:n
th; trui:5ng. V.tll
dc
ch{lt
Iuong
ella
n1<,leh
cOng !ten
qllan
t6i
kkh
Hllr6c
cling
nhlr
di~n
tfeh clla
n1<,leh.
Di¢n
Ikh
cung
IiI
d6i
Wong
cLla

16i
uu
mach.
Kfeh
Ihu6e
nhl) ella
me.lell
eho
phcp
co
Ih6 ph.ln
b6
nhicu
mach
tren
IIl9t
lap.
dicu
d6
IZlln
gli.im gl.l
IhLtnh
che'
lao
\'a
d6ng
g(ll.
Trong
dmg
nghi~p

ehe'
1,.\0
chung
la
Il10l1g
muCln
c<.'l
nhung
IhiL::t
ke'
eho
phcp
ph.it
h:cn
10]
\'a
x.ie
djnh
\'i
tI'l
16i
ella
nl<.\eh
sau
khi
ehe' tao. Kh.'t nfmg
!lilY.
lrong
nhicu
truil'ng hup, :lJlil imtJ'ng

16n
t6'i
eh:it
IIJ'~l'Ilg
ella
l11~leh.
M(ll
tht'H1g
~6
quan
trqng
lrong
\'eln
de
plUl1
hi¢n loi ella
Il1i.\eh
li\
ph[ill Inllll loi
e6
th6 duo'e
ph(11
hien
doi
,,6'i
mot
h()
g]a trj
thLe
nghi¢lll. l\'oi

chung,
ngU'{Ji
thic"t
k.c
mung
mu()n
c6
nhung
m,.ICh
de
ki~m
nghi¢\D,
dieu
d{)
lam
glillll gi(l
thLlllil
chung:
ella
qUil
tl"lnh
~,\n
xuelt.
PhilO
dOl,l1l
3:
Kicm
nghi~m
"'a
phe

chmln
Qui
Iflnh
phe
chuan
m'.lch
ILl
vi¢c (t,lt
dw.IC
<'1
m()1
mLre
(t() eh(lc eh{lll
hop
1)'
rang
111<.1ch
dicn
sc
lam
\'i¢c
dung
v6j gi,\
Ihic"t
khong
c6
loi
clie"
t,.lo.
TrC:n

')
phtlll
dm.lI1
nay
ml.le
dich
d~t
ra b\ pluii
IO<:J.i
hI')
m9i
16i
thi6t
kc
co
the
e6
tru6"e
klll
dua
van
san
xUtlL Qua tflllh phe ehwin
mi.lei"t
bao
g6m
vi¢e xdy dl;Ing mo
hlnh
mo
phong mi!eh

elva
tn~n
thiet
ke
va
tlive hi¢n klem Ira. Mo phollg
1l1<;lch
bao
g6m
phii.n
tich
die
dlen bien hanh vi ella
!ll~leh
di':ll then Ihni gian
doi \'6i
mQI
ho~c
nhieu
h(J
gia trj
dAu
vao.
Qua
trlnh
Jl)()
ph6ng
c()
the:
,ip

dl;lllg tn:n nhicu mue thiet
ke
kh5.c
nhau tuy theo
de
mue
truu
tu~mg
eLla
mo
hlnh.
§1.2. M6 hlnh
hoa
m;:tch
di~n
Mo hinh
!TIl.tch
la
bieu
di~n
trlru tuqng trang
d(j
chi
thich
hqp mi\ kh6ng
c6
nhung chi tiet tmrng (rng.
QUii
tdnh
t6ng

ht;1p
m<;leh
la
qua trlnh
t~IO
m6
hinh
111i.\Ch
bal
driu
Itl
nhung
bitu
dien
sa
luqe nha!.
Cae
m6
hlnh
duae
phun
Im.li
then cae
mLrC
dl)
mo
Iii
triru tuqng
Vll
de

g6c
dq
quan
~a1.
• Cae
!TICre
d(l
1116
til
trtlu tuqng:
duqc
chi a
lam ba
merc
nhu
sau:
•
Mere
kien true
6
1I1U'C
kie"n
wk.
mi.lch
di¢n duqe
tht
hi¢n qua t(lp
hqp
de
thao

tic
nhu
d.c
tfnh 10iln tren
dfr
h¢u,
de
phep
ehuyen
dbi \'ll Iruycn thong
tin. Vi
ell,!,
tren mlrc
kien true,
m~\Ch
co
the'
duqc bi6u
dien
qua
nhu11g
mo
hlnh tren
de
ngon
ngCr
1116
lil
phan
cUng. nhung bieu

diS
luang
thong
tin.
• Muc logic
6 m(re logic,
Illl.ICh
dlen duqc the hl¢n
ra nhlin" dac linh
c .
Mtl"e
kien true
PC~PC+I
Fetch (PC)

Muc 16gic
1>
1=L8=
Mu-c
hinh
hqe
I~I
nlHt
ti)p
hqp
dc
chu'c nang /(lgic
va
duqe
ehuy6n

Ihill1h
de
ham
logic. Vi
UI.1.
Iren
m(rc logic
Illi;lch
co
the
dlflJC
bicu uien
thong
qua cac bicu
do
ehuyen
tl"i Hlg
thai,
ulc
sa
do
mi.1Ch
logic.
I1lllh
1.1
Ba
llllk
Ol)
tri:ru
IlllYn)!

biell dicn mach (llen.
to
•
Muc
hlnh hoc
6 mue hlnh
h9C,
Im~eh
co
th~
dUQc
bitu
dicn
nhu
t<~p
hQp
dc
d6i
tlrqng hlnh
h9c.
Vi
dl)
don
gian ctia bic'u
di~n
hlnh h9c e6 the la
e:k
lop trong
mq.eh
nhicu

lOp,
dang
vc be ngoai
V~l
phfm
b6
clla
dc
phfin
tu
cau thanh
Im.leh.
• Cae goe
d<)
quan sat
ding
dUQ'e
ehia
thanh ba goc d():
•
Goe
elC;!
hanh
vi
Goe di} hanh
vi
mt')
t:i
de
ehde niing eua

m<:leh
ma
kh(lng
quan
tAm
tai
vi~c
tlwc hi¢n cae dll1c
n~Hlg
do.
• Goe
ell)
diu
true
Goe
tIC;!
diU true
1110
hi
mo
hlnh
m,~eh
bang
cae
th~H1h
pld.n
CO"
b,in ella
Im~eh
va cae lien

ke"t
gii1"a
de
thanh phan
d().
• Goe
tIt)
V1.)t
1)'
Goe
tIt)
V\l.t
Iy
co lien quan t6i cae d6i
tuQ'ng
v,~t
1"9
XU[lt
hi~n
trung thiel
k'::.
Cae rno hinh co
dc
Il1de
m6
tA
truu tu9ng khae nhau
v~\
co
the

el\.fl,l'e
quan
sat
thco nhung goe
<.19
khae nhau.
Vi
dl}.,
a
iTIdc
kie'n true theo goc
d()
hanh
vi
thl
me.lell
di¢n
l~l
tftp
hqp
c;ic phcp toan va
S\ T
licn quan
glll"i.1
chung
v6i nhau,
con
thl.Oo
gt)e
d()

cAu
true thl nweh Iii
t~IP
hqp
de
khoi
co
sa
va
ute
lien k6t, ghep n6i gilia
de
khai
co
so
do.
N0"u
xct truO)lg h0P thiet
kc"
d.e
mq.eh
ching
uQ
thl voi
d.e
mo
hlnh trcn muc logiC,
g{)C
d()
hZmh

vi
co
th~
la
cac
lUll
do
chuyc'n
tqmg
tlul.i,
con
goe
de;.
diu
true
la
cae ph[in
tiT
Il)gic
V~t
c,ic
kct noi giua
ca.e
phun
tlr
do. M6i quan
h¢
giua cae mue
d()
Huu

twmg
va
uie
goc dl) qUan sat
C{HI
mo hinh duqe
bie'u
dl~n
h,\ng
s(}
de)
ehu
Y ell.::t Gajski-
Kuhn.
G6e
dQ
h2uiQ
vi
G7~c
de)
eAu
true
r\1UC
kie'n true
;/
lIinh
1.2
ele
g(}c
do

qllan
~al
vii
d.c
llllrc
lllO
ti
trlill tlrong
nia
blC:u
dien
1110
hillh mach.
, ,
\ ,
, /
/
Mile hh{h hoe
11
I
lInh
1.2
eho
ta
(htlY
rnoi
lien
h~
giCra
cae

rn(re
hi~u
dien
m()
hlnh
\·;t
de
gae d()
quan
S(It. 6
muc
kien
true
va
l6gic.
rno
hlnh
1l1'.leh
tillro-ng
oll"<}e
hicu
dicn
tll<.:o
de
g6e
elt)
hiU1h
yj
V~t
ctlu

truc,
eon
0
Il1li"e
hI
nil
hqe
IlH')
hlnh
thui'mg
duqe
bicll then
qua
g6e
dQ
c:iu
true
va
V(lt
IY·.
Tr2n
hinh
1.3
cho
ta
d
tll.1
\6
dc
nnk

bieu
dlcn
ella
m6
hlnh
bQ
xu
iy
V~I
c(le
g/lC
dQ
qUdll
~,'lttuang
(mg. 0 lTIlIC
kitn
true,
thea
g6e
oQ
hanh vi, rn6
hinh
Iii
Uic dong i¢nh Iren
ng6n
ngiJ
mo
li\ phfln
eung
HDL;

theo
gac
d(l
cAll
true,
m6
illllh
ban
g6m
1.:lr
iHJr
cae
khoi
ea
sCi
nhu
h6
t[nh
lmill
so
hQc,
h9
(tieu
kilien,

yJ.
de
lien
kc-'t
giiJa

de
ph:in
tLr
d6,
6
mLre
16gie,
thea
goe
<.19
h~lllh
\'1,
mo
hlnh
ban
g()ll1
dc
so
de)
ehuyen
tf'.lllg Ihiii clla
cae
ot6mat
bieu diclI
hm.lt
dQllg
ella
mach:
then
gae

ct()
c:\u
true.
me)
hlnh
dW)'e
hi~u
elien btmg
de
so
d6
mi.ll'h 16gie gilra
de
rh'lll
tlt'
16gic
e(/
biill.
~~~
G6c
dc)
h~H1h
vi
G6c
de)
Cftll
lrllC
(,ell'
~ ~\1
~

~-
I
[fl'
~
~~
- -
ri
WJL
I
PC~PC+I
L
Mu-c
kicn true
Felch (PC)
I
ADD
I I
I
I
Contra I
~
'"to
0)
:3>
F x
GW1~
1 ),,"
,)
Mlrc
lC)gic

D D-'
(Slale
2)
lIinh
I.J
C~ic
IlllfC
bi~lI
di~lI111()
hillh
vil
[ill'
goc
ell)
qU.lll
\iil
llfon)'.
l'mg.
§ I.J,
Ton.t:::
hap
\-'a
t(ii
1ru
hoa
mach
dim.t:::
m:i,v
Huh
Cil'

e{mg
(\1
trq
giup
thiet
kc
hfmg may tfnh
eho
ph~p
ntmg
eao
mlng
",uSt
thi0't
ke',
Cie
k5'
thw.}t
Ihiet
k6
eho
rher gl,llll Ih(ri glall. n:mg
eao
chu
trinh
Ihi6t
k6
\'(\
giii!l1
e6ng

SLre
COil
nguo-i,
Cac
ky
thu(lt l(ii
tru
I~l!n
I;"mg
el1ftt
ll((),ng
tlli(1
hY.
Dn
do
de
ky
thU(lt t(;llg
hQ'p
vu
toi
u'u
hOii
1ll:.lch
\'6"i
~V
IIV
12
giup ella 1ll.ly linll
dUO'e

su
dung
trong
hriu
he'l
de
qua
trinh
IhilYI
"-0-
1ll',lCh
diell
ILl'
,,,6,
I.
'U,ng
hVp
IIW(h
di~n
ViL:e
phtm lo
•.
1l
de
m(l
hlnh
Ih~lJlh
cae
mu-e
IrLI'U

ILI'(.mg
\';1
CIC
g/lC
It{)
quan
,,:.il
eho
c1u1ng la
phwmg
phi.tp xtly dlJng
de
Ihie"1
k2'
tren gtai
dO'.I11
16ng
11O'p
mi,lCh.
(iiai
dm.m
h:;ng
h(,1P
maeh
e(l
Ihe
d\I(J'C
p!l[lJ\
ehla
Ih~lllh

Gle ph.tn
dO'.Il1
-",IU:
T()ng
l1\rp
d
Illll"c
kic'n Irue ban
gClm
vi~e
t',IO
ra g6e
d()
Cill
Ink
eLla
me)
hlllh
0'
mue
kien
tnle.
Dieu
[\;lj
IU'lmg
vuong
H1i
\'icc X,{lC
dmh
\'~I

phil!!
de
c1uic n{wg elm
mach
Ihi'tnh
de
ph0p
10,ln. etc
pll0p to,tn
n~ly
du{ye
g0i
IiI
6i
nguyen ella
Ihiel
kC:.
Tmllg
nHl
hlnh
cung bao
g6m
e.1
dc
kc'l
n6i
giCfil
de
phcp
10.11\

<I
trinh
Itr
Ihu'l'
hi~n.
Philn doan
ll~IY
IllLl'(mg
duqe gQI
IiI
(('lng
hop
(\
Illl're
L'<I()
h<l\'
ICing
IH,rp
eAu
true
VI
(1
d{)
ngu'i)"i
lhiel
kc
phJ.i
de
d!nh
C;'IC

du
lrue
\'J
m(l
( tren
ll1lfe
d()
dc
-;0
d6
khoi )
eLla
]11'.Ich.
'U;ng
h~1p
d rnlIe k)gie
IiI
ph[m
do,,111
1,.10
ra
g6e
d()
C<lU
Ink
ella
Illl)
hinh
(~
mlrc 16gie.

l\~l1g
hqp
logic hao
g6111
de
Ihao I,le
sLJ'
dung
ky
Ihu(ll logic
de'
1,.10
nen J11()
hlob
logIc.
M6
hlnh
n~IY
g6m
e{)
e,\c
ph,In
III
l6gic
co·
bin
\'a
kel
116i
giO'a

eie
ph.:in
Ill'
d6.
Nluf \':1)'
bu6e
long
hap
16gic
Et
hU"l_)-c
x,ie
dinh
c[['u
Irue
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(
t'),
Il1lfC
de
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It!
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1110
hlnh

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nghc
hay
1,'1
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IllU'
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().
mu-e
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hqe
hao g6m
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1',10
ra g6e
ct()
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1.\
ella
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()
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du"t,J'c
In()

Iii
Ihong qua
de
dilc Ifnh ella
1[11
c;i
de
m[lLl
hlllh hoc
lao ncn (t,lllg
Clla
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llli,lch.
ph[ln
h6
de
m'.lCh
1J\~1l
b:ill Ill'Kh.
Phtm
do'.111
nay Ihu(l'ng (tw!e goj
I~I
Ilm:;1
ke'
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l~'.
""
Goe d6 hanh
\1"

Mere
kicn
t~
Mile logic
"
//
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de)
diu
trl\C
T6ng
h0P
kien true
~/
MCre
hlnh
hQc
Thie't k6
V[tt
IS'
lI'inh 1.4
Cic
goc d
ll
quan \,\1.
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Iri:ru
Ilroll£'.
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ciic phrtn dmlll
!hie",
ke.
a.
Tong
lHlP
kicn trllC
G6c d9
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ly
M6 hinh hanh
VI
Ci
mut
kiei1 true
co
th0
(hf~X:
the
hi~n
qua
\{Ip
h()p
de
phcp loan
vi:11l10i
quan
h¢
phLJ
thuc)c

giiJa chung. Tong hqp kicn trllc
yell
d.lI
ph,ii
X,lc
dinh cae laj
nguyen
phdn
cung
dn
llLrqc
sit'
dyng
dJ
tlure !Il¢n
de
phep tmin.
,fn
dinh trinh
tty
t1wc
hien cae phcp loan va gtlll
kG!
chting
vt'J"j
de
l~li
nguyen.
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tlll;JC

hi¢n
Xfly
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m'Jch s,w !lay
phl,!
thuQC
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v,~y,
de
!hie'!
bY
ve
il1{I\ kicn true
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xac djnh
mlre
d()
Ilwc
hi~ll
,-;ong
song ella
(,.\c
phcp
toano
TllI;IC
hi¢n toi

1111
hOit
111C.\ch
11"en
llllk
nZly
Ch'lllg
\"ai
tro het suc
quan
trQng trong qua
tdnh
thlet
le".
Ta hay xct
y[
d~1
sau:
til
thiet
ke
m;\Ch
IhljC
hi¢n
Yi¢c
gi:li phuong
Irlnl1
\'1
ph[m),
-;

3x)'
-j
3y=O tren
c1m.m
[0, u]
bi'l.llg
phuong phap s6
"{5i
but'J·c
dich
d\
va dlc gia tf! ban
(.Hiu
x(O)=-x.
y(O)-y,
y (OJ II.
M<'ICh
di~n
co
the
duac
bi~u
dien btmg ng6n ngfr m6
til
ph[in cling llhu
sau:
Diffcq 1
I~
Read( x. y. dx,
i.l):

Repeat {
xl==x+dx:
u 1
==
u - 3*x*u*dx - 3*y*dx;
yl
=y+u*dx
C = x <
a:
x =
xl:
u=uL
y = yJ:
Until
(c ):
Writd
y):
~
119
dieu
khicn
I
I
':'
I
I
Bo
nh(1
t
ALL

I
I
Trong
VI
<lL,l
n~ly.
de
dOll gi,in.
ta
ctl
till:;
coi
c<le
c111'ong
dfr li¢ll Clb
mach
;.;uSt
phattlr
hai
nguon:
til
oQ
nhtm
",'a
lir
h9
tinh
to,in
so
hoc

ALU.
fill
ALL
1l;1~'
co
th~
tl11fc
hi~n
dc
phcp
tmin
cong.
trir
\'il
so
s<-ln11.
M~\ch
s0 g()ll1
c6
dc
thanh
ghi.
h9
X,lc
dinh
dia
chi
va
or)
dieu

khi~n.
Goc
dO
diu
Ink
ella
mo
hlnh
mi teh
(1
mlTe
kic"n
truc
cho
ta Ihtiy
dc
cau
trllc
VI
mo
etta
lhi0"l
kc".
:\16
hlnh
0'
m(re
logic
ella
111<,leh

co
thc
duqc
hieu
dicn
btll1g
dlc
sO"
c16
chuyen
trang
thai
Clla
dc
o16mat hilu h;.ln.
b,'ll1g
doc
sa
d6
h'lgic
1JO~iC
btll1g
de
ngon
ngCi"
m6
t,\ rhrin c(rng
HDL.
Cic
lllO

hlnh
n~ly
c1lt'(.K
nha
thiet
I c'
(hl'a
ra
hO(lC
dunc
tong
hqp
tir
Ule
mo
hlnh
()·llllt'C
kic>'n
trlle.
Cic
thao
tac
0'
mlJoc
k'lgic
co
Ih~
khae
nhau
tU)'"

theo
tinh
ch,"l[
cLla
mach
(nhu
lll'.ICh
t()
hqp
hofle
111i,lch
turin
Il,r)
va
d'.lIlg
hieu
dicll ban
t1:iu
(biC:ll
d6
ehuyen
tn,mg Ihiii
hay
sa
do
l6gic).
va'n
de
toi uu
hOii

dong
\'ai tro
he'[
slk
quan
tr9llg.
N6
gflll
lien
voi qu,i trlllh
t6ng
hop
lrung
yi2c
,de
dillh
de
C:\U
truc
vi
mo
ctl<l
m' lch.
Ket
qua
cuoi
cung
clla
tong
IWp

('j
mu'c 16gic
El
hi~u
dlCI1
CtlLl
trllC
dfiy
uti.
VI
dl,l
n!ur
bang
cac
phan
tlf
logic
ca
h:1ll
\'il
kc:t
Mii
giu<l
nhlJ"ng
ph:in lir do.
Trang
VI
dL.1
tru6"e
cac

d<:mg
dCr
li~Ll
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dua
vc
hO
nila
va
dU'<jC
(1tt'a
lU
ht)
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t6i
ALU
va
bt.,'l
nhfm.
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o<)ng clla
b9
dicu
khien
du'(.l'C
bidu
(hen
hang
sa
do

cllUy~n
In.mg th,ii
va
so
do
logic.
15
ThllYI
ke'
\'(11
I}'
1<'1
qu<i.
Irlnh
lao
ra
~o'
d6
h6
lri
eLJa
('/iiI} dien
ILl'.
Ceil'
16"r
btl trf
m"Jch
luang
lIng \'6i
de

1ll,:11
n'.1
dung
lrong
qu,i Irlnh
ehe"
t:.IO
('Iill). ])0
ct6
c,k
116
tri hlllh hqe iii
nwe
IICU
euoi cung ella
Ihl2'1
kc"
ole
m,.teh
\'1
di~n
tu.
Cie
Ihao
I,ic
chlnh
Ircn
rh,ln
elm,lll
1l~IY

hI
b6
trlm'.leh, di
del)"
dinh
tllv(n.
Trotlg
eut'J1l
;;ieh
n~ly
chung:
1<1
khong
di
~[tll
\,~10
ph,-Ill
doan
ni:'y.
2. l'{ii un hna
m: teh
di~n
l1~li
lo<i.1I
t6i
Ull
Iio;.
me.leh
Iw:m
di

dOl
\'Cri
h(li locin tc'ing
hq'p
m,.tell,
T(\i
U'u
iW[1
m:,lch
f h6ng
nhO:ng
d~
(1;.\1
dU\K
()'
ll1u'L'
<16
eao
nil:11
n:: cltSt
IWl'J]g
nwch
mil
C(m
1',10
ra nhlrng llweh
e6
trnh
c.mh
ttanh

C,IO.
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\:U\
de
t6i
uu
hal d(l
do
eh,lt
Im mg
quan Ir9ng: di¢n tieh
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hO' lt
(h)ng
ell,.
mach.
l\g(}~li
ra
11l(lt
do
do
ehAI
IU'qng
qu,1ll
tn.mg !lila
I~I
kh,i
n,1ng
de
kiC:m

Ira
\-il
ph;'lt
hi¢n
Ibi
eua
Il1<)eh.
DiC:n
Ifeh
eLla
ll1'.Kh
dUq"e
x,ic
dinh
hill1g
t()ng di¢n tfeh ella
de
ph,in tll'
Im,ch.
Do
d{l
dJ¢n tteh
e6
tilt:
"[Ie
djnh
duqc
thcmg
qua
g6e d(l

du
true
nla
m'.leh
nc"u
ta
bie"t
di¢n
tich
ella
Ilrng
th~lIlh
ph:ln m'.Kh. Thclng Ilnrh'ng
de
ph;:in
tlf
ec1
b,in ella
m"ch
16gic
1:1
6e
ph:in
ILr
[clgie,
c.:ie
thanh
ghi,
de
pltan

h'l'
n~IY
c6
dl¢n tfeh
bie't
lnr{re
lu)'
tllll<)e
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lung
loai
Ihicl
kc",
Di¢Jl licll
dc
d,'IY
n6i
d{lng
\'ai trt)
4uan
trqIlg \'il
khong
the
h()
qUa.
C,k
th:ulh ph:in
di¢n
l!ch
Il~ly

c6 Ihe
X<.lc
djnh
IU
mo
hlnh
m'.leh tren g6e d(l
\',:11
I)' IH\le
u6"c
Im)"llg
tlf
,-"ie
rlH)
hlnh
111":0
g(~le
dt)
(;j"u
Iruc th :o
cae
phuong
phcip
Ihollg
kc.
l-liC:u
n{lI1g
ella m'.lch dlf(fe t6i U'u hoa til/a
IrCII
(h(\i gi'lll

tre.
Ihb'l
gldll
d(ing
h().
c,mh
tranh
Iren
ccie ph:in
IlJ',

Dc
Ifnil to,in
d()
d,)
ho'.11
cklIl)},
eua
Illi)eil
c:in
thic"1
ph,ii ph'ln
lieh
c'lu
Iruc
"il hanl]
\'J
cLla
mach,
V:Yn

d ::
nilY
kllelc nhau dui
\'rJ'i
dc
IO' li
mach
kll,ie
nhall.
,
HI¢u
n,-lI1g
eLla
de
m',lcll
10
h(JP
dU(,J"c
x,ic
dinh
th{ltIg
qua
thlji gldn tre
truY~1l
Ill'
lUU
\'ilo
den
dell!
nl.

TIt(lng
Ihui\ng
dl~
gr,illl dl) pln!c
I'n)
clla tlllll
IO[\ll, la lut)]] giil
thiet
rang
de
gi,i
tf!
d{iu
\'~10
Xll~ll
11I";ll
IrDlIg
dlllg
Ill()\
Ihi)i
dr(~ln
\,:1
hicll
m-lllg
ub
m',lell
dU\1e
tinh qua
Ihr'ii
gian

tn~
truYCII
tllLo lILt'ling
dO
Ii¢u dili
nhat.
Dt'Ji
\'6i
e<i.e
mi lell
tu,\n
t~f
dong
b<\
d(l
do
hi¢u nrlllg
c6
lh~
uuve x,ie djnh
Ihong
qua
thoi
giall
quay
yong
cua
llli.,leh. Tho'i
gian
n;l)'

IiI
chu
k)' dc)ng
b()
nhanh
nhJ"t
c6
the
et,H
\,~IO
tlweh.
Tel
nh,)n
IhAy
dll1g
tllb'i
giaD Ire lruycil ct'la
Iii
thitnh
ph::in
m'.leh t6 hqp
etta
rn'.lch
tu,i.n
~I!
Iil.
can
d116i
ell,1
thh'i

gian quay
vt'mg.
Khi la
:xct
m6 hlnh
trC'1l
111lTC
kicll true nhu
qp
h{)"p
d.e
phep
lo{m,
d{il
vll'i
de
m'.lch
tlHll1
t~t"
ddng
bi\
m¢t
trong
nlllrng
ci{)
do
hi('u
lHlng
li\
Ihi)i giml

dn
thiitt
tte'
tlll.TC
hi~n
d.c
phep to,in.
Th()'j
gian
nay co the
dU'0C
uo-e
Ilfong
Ih<'lllg
qua
d.c
chu ky thai gian. Tich ella thoi gian quay \'ong
vii
Ih(Ji
glan tlllrc
hit;n
eho
ta thi\i
gWIl
thl!e hien
tcing
e(lllg ella
111'.lch.
Thong
tlmi::mg

Ihi:J'i
gian
quay
\'(lI1g
\,ZI
thai
gi<1ll
tlllTC
hl~n
dlTOC
t6i
Ull
hoa
riC'Jlf;
r~
de'
don
gi"111
[10ii
qu{i
:rlllh
leli
u'U
\,;1
Ih(x!
man cae yell
([ill
(t)1 ra d6i v6i thict
kc".
eic

m;,leh
d60g
h6
c{)
the'
dune Ilnrc hicn day
dc
phcp toan theo
chl:"
dl)
d.\y
ehuYCll
~
pipdlll':
),
trong
dCllll' leh
se
tlll.fC
hi~n
c{le
phcp loan song song
tn:'lI
nhung
t~lp
hqp dll'
li~u
khJe nhau.
Nhu
\'~\y

hl~ll
n[lIlg
Cllil
m' lch
ellil e6
th~
dU(l'e
thc
hi~n
qua
kh,\
n:mg
XLI'
15'
def
liC'Lt,
luqng
tier
!t~u
m;\
llI'.leh
e{\
IhJ
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1\'.
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do
dt'i
eni
li\

th{llIg
lunllt'. ella lIldeh. Doi
\-(ii
nhG"nl!.
mach
kh{llll!.
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~_
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L
Ihvc
hi~n
qua
ky
IhU<)1
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chuy~n,
tIH'UIg
hrqng
hj
glll'i
h'.lll bni nglqch (j.\O
eLlCl
tfch giiIa th6i gian quay
\'i:mg
va
thll'i
gl:ln tlwc

hi~n.
K5'
Ihu(\t
(by
ChUYCll
cho phep
]\I'.LCh
t~ll1g
thong
111(l'Ilg
dCl'
liC'u
dll'{~'c
XLI'
15'
nrot
qua gl6i
h'.1lI
n6i trcII.
V6'i
nhG'ng
dQ
do n6i Ircn, tui
uu
hexi
hi~u
n:ll1g
ella
lIl' lch
bao

g()111
\'icc
gle\m
thicu
tlli:ri
gian (re
truy'?l1
lt6i \'6i
111'.ICI1
t6 hqp, Ihai gian quay
\'{'ll1g
\':1
(he)'j
gial}
Illl,TC
Iw:n
d6i v6i
111'.1Ch
tll<ln
1l/
d6ng
bel:
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Uing
t6i cb thong
IlTong
ella m'.lch d(ii
\<'ri
nhCmg:
mach tlulc

hi~lllhco
\ 5'
thu[lt d.\y chuyen.
Ngoi\i
nhu'l1g
h~li
100In
t6i
lTli
hoa
vc
kreh
tl1Ll'(k
\,~I
thai
gW!1
n61
In~lI,
hlCll
liang ella
ll1' lch
con lien qllan t6i
kh,-'l
ni"llIg
phal
hi~n
l()i
V:I
d]llh
V!

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16i
lrong
m:.Ich.
(-l,:'11
10:ln
x:ly
d~mg
nhCrng
m~lch
cho phcp
de
d:l1lg
Illll
It'll
c111ng
mot yai
lri'l
qllan trong trong
qUii
IrJllh
tllle"1
kc'
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t6i
lilt
ho,1
tnach.
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m'.lell de kicm tra cho phcp giam

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gian
Sll1h
Ci\c
b()
gla
Ir!
thl! nghi('lJl
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gl'-'lll1
s6
lu'{.mg
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gia In
IhlT
nghi~lll.
V[\n
de
(hlU
lien
dlH)'C
giai
qllyc-I
h~lllg
deh
It
III
ra nhling
thui.lt

to{m
tclng
hnp mach c6
hi~'u
qu,'t:
ctll1
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dc
tilL!"
hal hen quail
h'ri
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to,\])
tIm j()j nhanh
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thili glan
ph,-i!
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h(l
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kC'
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vc
ke'l
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hal
h~\i
10,111'
giall1
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di~n
lich
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k'
ella
lIl'.Ich

vi\
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ella
llli.lch
y(J'i
J h,\
ll{lllg
cao nhtlt e6 the c6.
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loan
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h'.111
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17
lmin
l(ii
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co
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c:lll
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c6 the
c()
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mc.teh
,,;:

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kl: l.!n lh:lnh !Illll kh(mg
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nilY
1;(,)/ b kh(Jllg
gl<lll
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il
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han cac
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nhu
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gian Ire. lhi)i
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thi)'i
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Ru
tmin
ll1i
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hoa
mach
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tmin lim kicm dicm
\<ie
d!llllirung
kh(lllg
gl<.ln
thic'l
k.::
"ao
l'l1O

cac
dlli
1Lfong:
dat
g,1J.
tri t6i uu.
'Jhu
"\y.
1j'()llg
ChUUllg
nilY
Chllllg la
dJ
nghicn u'rll
elc
hlJ'('j"C
Cit
b,111
l!\lllg
ljlH!
trillll thie't
k0
t(~lIg
hop nwch.
18
CHlJONG II.
CO
SO
ToAN
HQC

Trong chuong
nuy
chClllg
\()i
nh:-tc
1,.ti
nlt)1
sCi
vCin
de
loan hoc liull
co
_~(j
cho
C[IC
chu'ong
lier
Ih(;o.
Cell'
kien
there
10;111
Cllll
)eu
xoay
quanh
CO'
so'
X[IY
d~rng

d.c
mach
so
dna
trcn
cac
d',\llg
ci1Uan
lAc
ella cae biel! thue 16gic.
l\hD'ng vall
de
lien
quan
\(Ii
qua
trtnh
11m
\/:'i
!runt-'
dIe
Ill' lch
logIC liell
quan
loi
cae
plllwng ph,ip
ma
ho<i
vi:'

1~'
thuy6t
d6
Ill!_
Do
d6
ChUD'llg
n~IY
(\uoc
chia
lum
hal
phiin chinh, m(l\
phfin
lien
quail
tlij
v[l'lI
de
16i
thieu
I1mi
cae hl0u
lhCi'c
logic,
phfill
thLi
hai
lien
quan

I(:ii
I)'
Ihuyet
de;
til!
vii
rna
hoa.
L~;
thuy61
chlly~n
Im,\Ch
Iii co'
'>()"
Ihi(:',
ke
dIe
h¢ thling
so
hi¢n
(L,IL
L)'
thuye",
nilY
cI\ra
Ircn logic
ky
Il.r
do nha tmln
hQc

Bool s:ing li.\O nen.
Unh
\'~rc
[()gic
k~'
t\f
Iii
phil!
tritll
ella logic
hl.lc
khi ta
c1ua
\,~lO
cae
ky'
hi¢u hlnh lillie
vii
e,ie
thao
t,-Ie
d<;ll
s6
ilinh tillfe.
Hai
~6
Bool
dU(:il:
dPlh
nghla Iii m()t h¢

d~li
sci
Iho,llllan
he
de
lien
ck
H,nh nghla:
Doi
Hii
\,Jp
hop B
~
{
<.\,
h,

) vZlllili
1001.n
IV
'+'
vi\
' "
n(u
h6n
li('11
de
~all
lho<\
man

1111
he
Ih61l~
(t.11
sci
g9i
IiI
d'.li
s6 Bool:
1)
Va.
h E
B.
a + h:= b +
ii,
a . h =
h.
a:
Tfnh eh[it
giao
hmln:
(2.
1)
2)
Va,h.e
E
It
a + ( h . c )
::::;
(

<.l
+ b ) . ( a + e
).
a . ( b + e ) =
(a,
b)
+ ( a .
C):
Tfllh
ehtl! ph:ln
phcii:
(2.2)
J)
3
IE
13,
30
E::
B:
7<1
E B, a +
0:::
<I,
a.
1 = a: Ton
ti li
e,ic ph,ln
tlr
dO'll
q:

(2.3)
-

4) J
<lEB:liaEB,a+
a=La.
a=O:PldnhtL
C~A)
C{u:
djnh
I~'
ella
(h.li
s6
Bool:
\. a + a::: a:
2.
a,
a:::: a:
J.
a + I =
I:
(2.5)
(2.6)
(27)
19
c).
a.{),-O:
(2.~
)

5.
"
-u
C.9)
6.
(a.h).c=a.
( b . c
):
(2.111)
7.
( a -j- b ) + C = a + ( b + c
):
(2.11 )
~.
<I+<I.11=a:
C.12)
9. a . ( a + h ) = a:
(2.13)
10.
(/+h=a.h:
(2.1-+j
II.
(/,h
= u
• h :
(2
151
Vt'i'i
he
lien

de
ella dai
so
Boo1.
ta c6 the
chung
l1linh
de
djnh
l~'
{rell.
Cic
llplb
ly'
eua
d<.li
,,6
13001
c6
the
ctmK
tile
hi~ll
du6i
(h,lng-
l~'
thuyc't
t,~p
hop
n h

Lr
"~lll
(Ila
[hie'!
c61flP hl/P A.
xci
1(111
hlJP S
lZI
qp
cae
1{1[1
COil
eua
A.lX<i
\'ri'i
hal
phan
ttr
kit
k.~'
ell,t t;)p S :';:i\c d!llh phcp
hop
u
\'~\
phcp
giao
n.
Do
S iii

t'~[2
n'la Cjl'
1,:ljl
(.",'11
eua A
l1en
llC:U
[;Jr con
(/
E.S thl
ph<:in
bLI
ella a
11\'1l~
A
IiI
,I
Cllllg
thUl)C
S.
V(\'j
de
khJI niCIl1I(lp
!J(:P
A
\,ZI
S,
la
c()
the l\llnh

iH.la
c,le
Jl11h
\)
(tl.l
dc.li
s6
Boo!.
2.
Vai

6 chuycn
m;~{'h
\1()1
\ i
ell,l
Cl1<1
dal
S()
Bou[
h.hl
up
hop B = 10, [
I.
Kbl
d6 ta
c()
hl' llai
,,\')
B(lul

dun
gi,ln nh,IL
\Jm
!tcn
he
10'11-1:1
d:'l!
s6
Bool
nr'll
trcn
\'(ii
1)'
(Iluy':-'t
d{mg
m.!~-\l
mach
d1011
duoe
SIWlll1Ull
dUd
ra
do
ni1Q"ui.',
n,-ll1l
.:"i()
ClICI
Ih(: kv
20_
1

h>
L • _ • , •
(L.II
~ll
bao )!lim hdi ph'\1l1lf (0.
1)
Cllll
dl!\~l'
goi
1:1
eli.!1
S\-j
ehuycllll1ach.
Cae
lien
d~
\'~I
u\c
d!lIh
1.\
Cl1.l
dal
~(j
Ik)d]
h\l~\l1
to;'\l1
dlf(:'l'
<ip
dung
cho

dai s6
ellll\'l~n
lllach.
Dc
11l1et
1(1]1
mIll
wong
ql!<l11
glli,(
1)-
tllu)
c'l
d61lg ngiil
m,.tell
dl~l\
\'6i c.ic
lil'll
de
\':t dplil
1)'
ella
d,\]
Sll clluycl1
IUOlch.
1,\
dua
ra
de
sO'

Mi
llle.teh
dU\K
,<l\'
dung
Ill' nhCrng
~()'
dli
co'
Sl)'"
==
<l.h
a 0
()
20
Tron~
uie
~ll'
M;
mach do,
Inl11Q
Iluii d6m! lllaeh
Cltd
kho,i
Itr(jll~
li!le:
\(~~i
~_
, '
~

L,
• L
gia Iri
1:
\',1
1r<.ll1g
Ih;il ngat
mach
tHong
lrng
\'l1i
glei
In
O.
Theo
c,i.ch
quy
d!lIh
gi,i trj
IlhH
Irl:ll,
ph~p
tmin
tU)'(:1I
e6
Ih~
duq'c
hiC::u
dl\':n
nhu

doall m,lch tn.ie
~t1ng
,~()ng
cae
ki1O,[,
trong khi
d6
ph~p
toan
h()i
~e
tu'o'ng ling \'6'i
dO,lll
Ille.tell
mill' nt)i
ti(p
dc
kho,i.
Vl'"1i
«ic
qlly
Ul'"1C
d6. tien
d~
hai ella dai
~6
Boo]
C()
the:
dUne

bi~u
chcn thitnh
dc
me.tch
wong
dunng nilu "au:
aT
b.
c
(a+b),(a'
cJ
IIlnh .2.2
SCi
rl()
mach
dtlllg !lgal
1ll111h
hoa
dlO
linn
chXI ph:1Il plHil
S~r
tuong
dU'ung
gili'<l
hai
sO'
do
lmwh khmi
nilY

co
th~
duqc
kicl11
c!ll'rllg h,ing
cac h,ing chan
I)'
tuong ung.
Dl!<l
\,:\0
~~r
tlro'ug thlch
giCi'a
dc
bieu Ihuc
iClgie
\'01
dc
S0
(1<)
mach
khmi
ta
co
Ihe
t'.IO
ra
dc
m',lch khoa
tuong

duong
de
hiel!
thCre
\()glC
\'t1'i
nhlt'llg
dC)
rhll'c qlp kh,\c nhall dl/a
\"ilO
c[te
pher
hl(':'n
dC;i
trong m,.tcll
di~n,
I\-'lac
lItl
\,,~y
eo
m()t
so
1m,Ii
m'.leh kh(mg the
hi~u
dicn
dU"l,K
1!J;l11h
h,'t
hop

giCi'<l
de
t()
h(.ip
mach
~()ng
song
\'il
n6i li':p, troog nhu'ng
tIlJ'i'.ing
hnp
(kl
la ph,ii
x{ry
dtfll~
mach
dl,fa
theo
h,ing ch,tn
Iy
hm~e
su
dt.mg
pi1Llnng
rhiip
li.IO
t')\1
h(,1P
c[ic h('ll
kel.

Chllllg ta xci tnro-ng h0P m',lch
theo
lien
kcI
lll'll'h
crill:
de
(tLfl1!lg
(1i
Ill'
ph:in
phia
Ir,ii
111<,leh
"ang pilfin phla phiil
11l'.leh
bao g()1l1
uic
dtrong
(ab,
aed.
ecb. cd
\.Phll'(mg rh{tp
t'.IO
t~\P
hop
de
lien
ke't
the hi¢n nhu' "au: nell Ircn

bilt
e d
IIlnh
2.3
/l.t<1(11
du.
1<5'
du'o-og
di
IiI'
pll<i,n
ben
Ir[ii
maeh
du
, ,<log
philO
ben ph'l!
ta
dClng
I{II
cit
de
kho,i, kill
do
mach dien se U trall" thai
MJll!.!
ebn
.•
.

~
L'
trang
tru'o-ng
Iwp trcn
moi
duo'ng
C('l
it
nhAt
I11Qt
khOii
111(1
thl
11I' lch
s0
l1
t .
'l~
th,-ii
mil'.
Vi
d~L
ne'u trcn
ducil1g
(lcd ta dt'lllg
1:\1
c:t
de
khOii

a, c, d
m~lCh
se
d
tr~\llg
thai dl'lng.
Nhu
\'~\y
d6i \'6i
nli,leh
Irtn,
bieu
thCl'e
IClgic
tLfO'llg
c1uong
~C
Ia:
21
a.b+a.e
.d+c.e.
h+c.d
Khi
SlJ'
dl.m,!!
1~'
lhuy0'l chuyc'n mach Irong
hieL!
dien
die

hi~u
thClC
iClgic,
de
dinh
15'
ella
d, \i
,,6
chlly~n
mi tell
C()
th~
rut ra
ilf
elc
lien
de.
nguyen
\)'
d6i
ng:hl
etla
I)'
thuyc'\
mach
uj
\'<li
\r()
kllti quail

In~ng.
]\;<ru\'t'n
1\'
dlii
11(l~u:
JEW)'ell
1<'
d6i
ngilU
dua
Ircll cu
w'5
X[tV
dIm"
uk
'"'.
•
'"'
L •
L.
.,
_ c
bi~u
thCre
d6i
ng'\u.
D{)i
llg:1ll
eLla
llH)1

bi2u
th{t'c
di.1i
s6
Bool
1:1
IlH)t
hi2u lIllIe
](\gic
lrong
d6
de
b16n
u elta bic'u
thli'C
ban (Ull
duqc
thay
him,!!
(/"."J' lhay bimg
'(r,
'(i'
thay hllllg
'I'.
ph':p
tuy01l
chroe
lhay
btlllg
phcp

Il()!,
phcp
h(ll
lhH/C
Ihay
him,!!
pllcp
tuyen. Kill
th~l!lh
hlp bicll
thCre
d6i ngilu la
piJ.'ti
su'
dung
de
d:iu
ngo(1C
de
d.ltn
IXlO
Irat
II!
tinh
1O

in bieu
there.
Nguyen
15'

dui
ng{\ll:
gi;i
Lrj
eLla
1l1l)t
hieu
111l1-c
(h.1l
s6 Bool
bllllg
bll
ella gia
Ir!
bbieu
thlic doi ng,\u Wong
u'ng.
Ta
e6
lh~
chung
minh
nguyen
I)'
dCii
ngtIU
htlllg plu(o'ng phiip
quy
m,lp
tmin

hqc
va
Sli
ch;Jllg
cae
djnh
I)'
de
Morgan.
1.
('{u:
h:'U11
Wgic \:1 khlii
n-chieu
HilIl1
16gie
/I
bi~ll
throe djnh
nghTa
la anI! xa k.h6ng gian I/-cl!icu
B"
\'ao
II:
B"
>
II
il={O,l)
(2.16)
t<cu

x;
li\ phun Itt Ihu9C
B.
khi do
x=(x/"",xI/J
Iii
m91
\'ccto ella kh6ng gian
veeto'
/I
chicu
nil. Hum
logic
trell kh6ng gian n"
({j
Ihe duqe viet
dU'{l'j
dang
.J(r/

r"J.
KhCmg
gian veeto'
un
eh(ra
2/1
diem
\'a
m(lt
yceW

x Ihu(K kh6ng
glan
B"
chtQ'e
hieu
di~n
iii mot trang
s6
2"
diem
clla kh6ng gian 1/
ehi~ll
nil.
C{IC
diem
nay
e6
the'
dUQ'e
d~lt
{ltong
(rng
\'oi cae dinh
eua
llH)t
hlnh
kh6i
e6
2"
dinh trong kh6ng

gian
B".
HilIll
logie.!L\·/ .

x,,.!
SC
ct~lt
tuang
ling m6i dinh
clla
hlnh
kh6i
\'(.'~i
cae gia trj
()
hO(lc
I.
22
rrong
llu11
\,lfe
I111e'l
k~
clie
m'.Kh
~6
khllllg
nhil't
thle-L

ph' lI
cli,ll
~)_I' l
Ln
()
ho:)c J
eho
1:11
e<t
Cite
dinh ella khoi -
dIe
\"l'elO' x.
i\NI
dch
ehillh
de
IHin.
1121111
\(lglcj"dude
djnh
Ill:!hTa
Ul
,Inh).a eua t(tp
con
A
cLla
kh(lllg
t'lan
B"

\'ito
B.
r A
c;;
13"
+
B B={O,l)
(.~.17)
Khi la
x01
m(lt
1(lp
con
Ac
Bn
\;1
kim
f
ct'l
l111en
x,le dill!.
1;1
A.llhLl'Ill:!
diem
IhU(lC
W
\,;1
kh6ng thu(lc A l
XE
un \ A }

121
lilllh ta kh0ng quail
1~1111
L6i
\'il
h.~,
hi~u
121
l/inh-d;
Cite
dinh Ihu()e
,\
d.
IU'l~lIg
ling
\'('jl
de
gi<,i
Ifi
()
ho:1C
J
se JlIrrc gqi Ian
IUCft
lit
i/illlr-O
\,,\
d//lII-I. Vdi
Ciich
h.~'

Im;u
UIC
dlllh
ella
hinh
kh6i
2"
(tinh
nhu'
\'ZI)'.
lll()\
hill11
16giefsc
,inh
X'.I
de
di(:llltrOlII;
khll11g
glan
B"
\';\0
I~IP
h(,1"p
/().J.d)·
I(x)
:
il"->
(O.l.dl
121N)
'[\\?U

1l1l)1
dinh ella hinh kh6i II-ehieu bi':u
(hell
du6i
d~lllg
!lieu
thCre
I(ltlie.
la
nh(\I1
dLrqc
nn)1
bi':u
thCre
h()i.
VI
dl,l
trong khong gian 3-ehicll. dinh
Olls0
tlXong
Crng
\'(ii
bi':u
Ihl'rc
16gie
XI_\"_'X;,
Bi(:L1
thCfe
Il)glC
e6

Ihe
nh~11l
ctWK
ILl'
cae
dinh
cLld
hlllh kh6i
2"
cillCU
kll1g
deh
gbi
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llC'U
gi<.'t
Ir!
eua
10,.1
d()
thu-
i
wong
ling
1i\
. r
hO[le
x,
lle'u
gi,\

11'\
10,1
d(l
tlHi'
I
1:1
'if.
Bi~u
thtre
h()1
chi
nhtll1
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diem x du)'
J1h~it.
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10,.1
do-
ella
dinh
s0
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Ling
w1i
n1lit
phfin

ILl'
Irong
bi~u
Ihlk
h()j.
\'l()t
deh
I()ng qual
La
cllra
\,;\0
k.h,ii
nil:lll kh6'i
e,fp
III
nhl1
Sillt:
M(ll \'ccto' " chicu
C::
le/

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i't}.
c,.::{O.l.xf. "<II
dul,l"c
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III
~Y'Il.r
\-
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1;\
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III.
Vfdu:
(01
I)
!akh6ictlpO:
(Olx)-kh6ieiip
I:
Kh;ll
nl~'m
I.fili'j
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h'lng qual h6a
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klHii
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diuh
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III
ehlcLI
co ch(ra
2'"
lImh. Vi
d\1
kh6i
(0/.\)
ehtra hai
dmh
(O/())
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(OJ
j).
Noi m()t
deh
kh;ic
k~'
It!.r ('6 Ih':
nktn
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kh6i
ecip

rn
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ling
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1/-111
blCil.
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link
h(li
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e6 th':
nh:111
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nell ghi x, khi
gl;1
If!
Ililing trng
ella
19<1
d(l
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i
1;1
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khl
gi,i
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tqa d() d6
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l kh(lIlg clune
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1\,
t\
deh
kh;lc
ky
I~r
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c6
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r
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k.h6i
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lUring
dUO'll::;
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bi0'u
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bic'n
.
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k116i
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()
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nh{11
cua
kll6i II-ehicu, kh6i
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til
sc
bao
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kh6i
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o.
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cae khoi C
I
V~\
C
2
•
nc'u
I~p
hQ'p
dinh
0,\0
phll
1116i

kh6i Ihu(lc nhom
('
I
1~1
1(lp
con ella
ItlP
hop
!.tinh
hao phll
de
kh6i
eLla
C
2
,
khi d6
[a
nOI
r;'mg
C
2
bao phu C
I
•
2.
Cae
d~ng
chU<ln
tile

eua
ham
16gic
T\'cu
h;\111
i(lgie.l
khLing
ehCra
ll/o/l-d, khi do
dC:'
xae dinh ham la
din
dlra
ra
I<)p
h(.~p
de
d/II/I-I
V;'I
dilllr-O.
Do
kh6ng
ehu:a
cal' d/llh-d
ncn
1(lp
hop
dc
d/nh-I(\
"l{))

Y~I
!(Ip
hl)"P
dc
d/nh-O
(Vi!))
htl
nhau.
\'1(11
dinh
("
(kh6i
cAp
())
!Lru"llg
CfIlg
y(ri
m()t bieu
[hCre
hOI
F(cj.
khi
d6
h:ll11
.f(x)
sc
dU(iC
hi~u
(hen
lh6ng

qua
I(lp hop
de
dr'IIIi-1
\!
/f)
nhtl"
-;au:
H\)
= V
Pic)
(2.19)
P(c)
gqi
la
bi~u
thCre
h(li
ct.rc
tieu hay ng{m gqll
l~\
tfeh
eLfc
lieu.
Nlur
[r~n
oJ.
de
c)p
1(1i,

m()[
kh6i
eAp
m
d~\i
di~n
eho
2'"
dinh.
hiju
thCl"e
h(li
ct.re
li(:u
: i:
luang
(rng \'6i
-;6
Iwmg cuc li2u
de
dillh Iham gia
\,;)0
hi~u
Ih(rc h(li
V~I
st::
nh,}n
gi,i
Iri
1

1'.Ii
nhil'ng dinh
nay.
Ricu
thCre
(2.19)
IiI
hieu thu:c
tuyen
ella
de
hieu
Ihue
h(li
eve [iell
\"a
c!Lrq'e
gQi
Ja
d' mg
ehu,ln I,k luycn ella
hi0u
Ih(rc
logic.
Ta x5e dinh
hi:tnl
hCI
I(lgie (
goi
t<"11

I~I
ha111
Otl
)eu<l
m(l[
ham f
I~I
m(ll
hi:lln
nh,:111
gi<.l
Iri
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1<.li
nhung dillli
1l1~1
f nhtlll gi,i
Ir!
'I'
Y;I
nh,-}n
gia lri
'J'
I'.li
nl11.1ng
dinh
lll~lfllh,}n
gi5 tri '()';
h~\ln
nilY

chrqe
ky-
hi~u
h,\ng
I"
-
I 1\)
~
1 ffJ/lx)
12.20)
Ta
ell
the
nh,}n
dUQ'C
h;Ull
I neu
tlMY
V1(P(e) hitng
V1,(P(c»)
lrong
bi~u
therc
(2.19).
I(x)
= v P(c)
(2.21 )
TLf
do
ta co the nh,)n

dWJC
hietl
thefC
eua
J(x)
bflllg
d.ch
,ip
dl.lIlg
cong
1111.re:
I~
I .
j(.\)
=
/\
S(c)
(2.22)
eci
;,(,fJ
Oil'
bi2'u
thlre
S(c)
nh(1ll
dUQ'C
tu
pre) h,\ng lhay X
J
Ih~lIlh

x
J
'
x,
th;lllh \
\,;:1 thay
phcp
h(li
(/\)
thanh
phcp
tuyen
(v).
Ta nh(m
IhAy
S(C) sc tuung (rug
J'
-"