~~
z
CHUONG VIII.
CAC
PHUONG
PHAP
KIEM
TRA
LOI
M~CH
LOGIC
Trong
chuang
nay
chung
t6i trinll bay
I11QI
,6
phuong
phap
phat hl¢n cac
lui
cua
cac
m~ch
lOgic.
Vi~c
phal
hi~n
loi

Dl(~U
nay
dong
tn(lt
viii
tro
quan
h·9ng
trnng
qua
trlnh
s,ln xu[it va l;un
gl<.llll
dLfC:K
chi phi
ki~111
Ira. Trong chuc1ng
nilY
cilling loi
trIp
Irung
Chll
yeu vilo
de
phuo·ng
phap
pil{).1
hi~n
llli
\,:1

ph,ip
pht."l"c
1~.lr
han
doi v6i
de
m<'.lch
t6
heyp
\";1
"Un1
ra ngn:li khu6n kho cuon sach nay.
§8.1. C,ic
1116
hinh
liii logic
mli
to{\ll
ph,-!I
hi9n
1l1J
Irong eac
l1li.\cb
lOgic
Iii
bai
toan
xac d)nh so
do
logic

d6i
tuqng
kie'm Ira, sau do xfty
dl,l'ng
phuong phap phat hi¢n loi
V~I
cuoi
cung
la
xuy dl!ng
m6
hll1h loi
(eo
nghitl la
chi
ra
dU<jc
cac
d~c
trung
cua
loi
).
Ta
da
thfty rang
thea
'luan
diem
phan

quan
dic'm
ve
hOi.~1
d9ng,
cae
m'.lch
If)
h0P duqc the' hi¢n
(}
eh6
t1"<;lng.
thai clla
dc
duu ra d
1119i
tho-i
diem
Ihai
gian
dU(jc
xac
djnh
hoan
toan
bing
de
tn.lI1g
thai
cua

I11~ch
t6
hQ"p
lit
nhiJng doi tuqng nghien
euu
kha
dem
gi~\.n.
N6u xci
tre:n
quan
diem hanh vi, lrong
hm~t
c1Qng
cua
cac
lTH.lch
turin
It.!
xual
hi~i1
cac
tr<;lng
Ihai ben trong;
con
xel tren
quan
diem
c[iu

h<)
I1h6·
\'a
d.c
b<)
vi
xu
ly
ve
ly
thuyc~1
cling Ihu¢e
nhc5m
cae
1l1<.lch
lufin tl!,
nhung
VI
so
lU<jng
de
tn~ng
Ihai trong
CUi.1
chung
n1"t
16n,
do
d6, n6i
243

\'(1'1
ciie
h(l
nh6'
\'~l
hr)
vi
XLt"
I~'
c,ln phili tinh den
dc
d,k
lnrng
n"la
chung
\'(~
]ll,~ll
cau
Ink
\'~l
h~l1lh
\'i,
I\hu
\';)y
chLing
ta !hfly dmg
kh(lI1g
Ihc
cr'l
plut"rmg

ella
m,.tch.
M()I
hil.l
loan quan Irqng. xual Illen klli
X\ly
clL.rng
de
pl1urmg.
ph(lp
ph:11
hi~'1]
[('\i
!i"1
il,ra
chon
di~1l1
(1.)1
eho
de
lin hi¢u Ihll nghicill
\'~I
d,c
dicm quan
,,;il
Ibfch hqp.
Tnt'()'c
d{IY.
khi
kicill

de
llUt
ben lrong
1ll<,le[J
Ir(')'
Ill'n
phll"C
I'.lp
llO'll
nhicll,
Dil:U
d6
L:lln
"htl \'ll'l'
d'.ll
\';l
quan
",;il
de
tin Ju¢u
Ihtl"
nghl¢m
t:.,11
nlllIng
dicm hill
k~'
Cll,1
m;'\L"h
In')"
nen

ra eua mach.
Khi
Lll)
tich hop ella
ll1ill"h
limg
Ill"
LSI
den VLSI.
Iy
l~
gILt',\
-;6
Iw.mg
eh:ln
hCII
IIgo;li
eLla
1ll;.lch
\';1
",6
IUr1ng
plwll
Ill'
Irell tlllh Ihe
h;11I
(l:tn
~':J;'lnl.
<-lICU
d6

m;,lcll
elw
phl~]1
:,\,'\y
dl,rng
nhCrIlf!,
mach
co
chel"e
nang
phC!'e
1',lp.
\'1
ell.1
niH!'
Ciic
jl()
\'1
Xl]'
I~'.
dil:lI11;IY
1~1l11
t,-l1lg
cit)
pllll'c
t;.I]1
clla
h~\J
to,in phill hien
k)i.

de
m.,leh
VLSI
VI
1ll:.H,:h
dn
c1l1\iC
klC:1ll
tra
1;\
m',leh h'lgie, nen la gl,l thie'l dlllg khi trong
m;.teh
c6
161.
maeh vttn
Ihl,J'c
11l¢n
de
ehuc
n(mg
nhu
m(':l!
mach
j(lgJC,
Cic
lr'lJ
thoa lllail dicll ki¢n
n~ly
dCli
dune gqi

Il;tng logic
vi\
hi\nh
vi
Ihi)'i
gian. eho nell
\<1
si:
ph{m
ellia
dc
I()i
Ihi:lIlh
de
nh61ll loi sall:
NhOIl1
cac
I(ii
.lnh
hUtI'llg
tti"i
c1nl'c
n,ln~
lliglc
O'liI
ph ill
Ill':
i'<hl)l1l
dc
\(')i

m()
1,1
dc
16i
\',~I
I~'
nlHf
elic
i6i
logic. la sc dunc
llil(il1g
Iu-i
diem
niH!"
sall:
Thlr
nll[l\
lao
hili
10,\.n
ph[11J
lich Ibi IHlth;:ll1h
hill
10(111
l(lglC
110'11
Iii
hi\i
tmlll
\,[11

\';10
Clll1g
llgh~
Iheo
nghla: Ct:lllg
Im)1
lllO hlnh
k,i
dl
Ihd su'
dung
trong
nhicll c{mg
ngh¢ khac nhau. Do d6
dc
phuong philp kicm Ira \'i:1
ehu;in
dual]
(hfl.K x{\y
d~fng
eho
molmo
I1lnh
loi
sc
khlmg
thay
dOl
nga:,-"'
ce'l

tmill'. maeh Child
hO;1ll
lnilll
elLfO'c
hieu
ro
hO(lC
qu.\,
piJCl'e
1' lp
de
e6 the ph,ln lich.
Mc)t
1110
hlnh
!oi
eo
th~
Iii
11111
hlnh
fin
hoi.le
ml)
hll1l1
\U'(lng
I11mh.
;\1()
hlnh
lbi

hlnh
!t)1
1Lro-ng
111illh
Cll
the
clLnJC
1110'
rlm):!
Illy
nllJ(:~n
ph,'li
(him h.lo
du'Oc
kfeh tlur6e ella kh()\lg
gian
101
killing
qUit
16'11.
1\16
hlnh
h\i
an
xfly (hrng khong gian loi btlllg
(('tcll
;(i\c
dinh
c{l
IVa

djnh
dUl.iC
chCfC
nang
logic ella
ll1Hch
\'6i sv ton
t,li
cLla
Illi
nily lrong lllach.
l\lnr
\'(Iy,
qu,\.
lrlnh
ml)
h!nh
ho.1
l(li
lien quan
1l1,~1
11110.':'1
16i
loa I
Ill\'l
hinh
1l1',lCh
dang
slr
(h.mg.

e[tll
Irue
.•
;\nh
lllf6ng ella e,ic
16i
du
truc
let
1~\Ill
1I1~ly
(k)!
"lX
lien
kc't
"ilia
de
111;lnh
philil
mi.lch.
Cll
III
I duq'c
X,-IC
djllh
gtm
lien \'6i
1Il()
hlllh Clllk nfmg
eLla

cae
phep toan tren thanh ghi.
;-"1i~e
du cae loi
ngau
[lhien
h04C
loi
cJc)1
hi~n
co
mi~1
tllLJOng
xuyen
trong
mi H.:h,
\'i¢c
ma
hlah
hoa
nhfrng
li'li
do yeu
cau
cae dfr li¢u Ihong ke
\'~
s,!
xUil1
hicn
thea

xU<lt
hi¢n
viii
Ian trang
111".lch
v6i nhOng gia tri tht'r
nghi¢Jl1.
Thong
thuang
chung
ta kh6ng
c6
dfiy dll
nhung
thong
lin
vc
m~lI
thong ke.
do
cJ6
doi vai
nhO"ng
cJ(>1
bi6n hm)e
xuAt
hien
kh6ng
thu'ang xuycn.
lot

mot
thai
ditm
thai gian, trong
m<'.lch
chi
c6
nhieu nhal
lu
nH)[
16i.
VI¢C
Iillll
dan
gian hoa
bili
to{lI1
pld!
hi¢n
16i
hang
gi::i
thiet
ve
1M
dun
Ie
dw1C
bi¢n minh
bai

lu
du nh6.
Do
do
neu khoi.lng thai gian
hO'!t
d¢ng
eua
m,.teh
cang
l6"n,
ta sc
co
nhieu khu nang
g~p
tru'ong
hqp
xuat hi¢n nhicu
16i
trong
nwch
mot
lue. Tren
thI!C
te
van
XUi.lt
hi en nhung IrLiang
hqp
ma chien luvc

mi lch
co
the
iiI:
Cac lai
\,(It
Iy
c6
the:
XU;!I
hi¢n
tmng
llwch
giil"a
hat
][in
kicm
Ira
Et.
Trong
nhfrng loi
v~tt
15'
do,
m(H
saloi
c6
tht
tuong (rng vai nhicu loi
logic.

cac thanh ph[lll nwch.
Trong
nhO"ng
mqeh
mai
duqc san mii't, thl trong nhung Ian thlr diiu
nhCi"ng
loi kcp
e6
the xuat
hi~n.
Trong
tlUang
hqp
nhO"ng
phep
IlIti
khong
phat hi¢n duqc het nhOng
Uii
don Ie, tai bat
ky
hie nuo,
n1,!-eh
co
tM
chua
nhung loi
chua
duvc

nilU"ng
nhCi"ng
h9 gia trj thti nghi¢m
dung
de
phat
hi~n
cae loi
don
JC
e6
the
dung
de'
246
tim
nhung
16i
kep.
Sa
dl
co
the'
thl!C
hien duqc
nhu
v~y
Iii.
do Irong ph:ill [6n
d.c

~6i
chung.
cdc nUl Mllh
irS!
("(Ill
{nie
giu
thie!
rc1n;.;:
("{II-
rliiillir
pli,/'n
khollg
("()
J/ii
WI
eM
co
nl1l711g
dlf(llIg
kh
n6i
ellling
/d
("()
the"
("(J
/r~I.
Cic
I()]

ch(lp.
Vi
duo
lrang nhicll
cong
ngh~.
si! ngan
m<;lch
giua
day
dat
ho~e
ngu6n
voi cae
dUll"ng
lin
hi~u
e6
the lam
eho
dUC1ng
tin hi¢u bj
ch~lp
c6
muc di¢n
the
eo
dinh.
Khi
do

Iii.
S-(/-\'.
Sl! ch(lp nweh
giLra
iwi
dUC1llg
till hi¢u
thuang
sinh ra nhfrng ham 16gic
mai
vu
dltq"C
goi
I~I
d.e
Ibi
bac
d1,u.
Tuang
ung vai
nhung
ham
logic
dUQ'c
sinh ra
do
ch~p
mi.lch, chung ta phan
bi~t
16i

nhanh
r ,
.,
Innh
ttl.
Loi
ho-
mach:
a)
16i
her
ml.lch
ddn;
b)
16i
her
mach
kep.
ngh~.
s\!
h6
m~ch
tfcn nhGng
(hrCing
lin
hi~u
mot ehieu \'oi
nx)1
nhanh phan
ky

Nhling loi nay
cung
co
th~
la
ket
qUii
clla nhung
16i
Vi.}t
I)'
ben trong
phan
tt! dieu khien
duang
tin
hi~u.
Neu chung ta kh6ng
ki~m
tra
gii.l
tr! trcll hai
duu
cua
duong
tin hi¢u thl
khong
the
ph{\ll
bi¢t

hoan toan
kh.:ic
nhau:
16i
do
duong
tin hi¢u i bi ngat:
16i
do
duang
tin
hi~u
i
bj
ch~p
voi ngu()n
ho~c
dal; bat
ky
mOl
16i
V~lt
Iy
ben trong
phan
IU
e6
dUC1ng
tin
hi~u

lr~ll
de
nh<inh
Illanll phiin
(\'i
d~l
nilLr
Ircn hll1h X,I h), t\'Cli
ell!
gi6i
h;,lll
nglucil
eCru
lll(l hinh
16i
klng
s(}
ehm
le. ebling, I'l
pli,'u
XI.!Ill
xcI
JllO!
J()J
h,-lllg
,Il
d(in k Ircn e;ie
nll<inll
rC'
eLLa

Jdnh c;fu Inle ])':n
Iron,:!
ella
ehLlng. Tuy
Ilhj~ll.
nc'u
C<Ie
Ihi'lllh
r,\],\ll
m;.lCh
dUl.1C
kicm
Ira
d{lC
l<:lP
Inn'rc
kill
clll'lJlg dU\K
bp
r;ip.
klli
ell)
eheing la chi
dn
IhlC'1
].;iemlra
c<'le
Ihi
,'l11il
ilUCillg

kh:lO
"'[11
de
ll\i
gt!!J
\,{ri
de
eh:1Il
\';IO!ra
eLl,[
Ih;mh
ph{in.
lil,i Ihicl
n:'
gil)'j
han
etc
j()i
1;.li
Ch:1l1
\";'IO/ra
g(.ll
1:\
/11(1
lIillll
!tIl
I~/;
(Jlilll
nio/w.
Sal!

1;.161
hay
g'~lp.
Kill
IrCil
m()1
dlJ'(\ng tin
~
-c
(.r
I·
\
)+1I'+(.\"-;
y) =x
1.\
'-II'
Inuh
KZ
Vi
du
'-0
dll
m,ldl
1().~1L"
l1i\'Ll
(/
XU:!I
hi¢1l
It'll
h<'lllg

d6
In'.ldl
LI
(ill. T.l
h~ly
X~I
\"i
eh.!
m;.leh
Ir~n
hlllll
S.l.
\'':'-u
lrong m'.lch c61(\i htlng
s6
d/l
Ih]
d~iu
ra
~
sC'
b!
Ihay d6i
Y;'l
It;'ull
ra
Cll.!
1ll;'Ieh
,>0
h;\ng:

+ II'
Ilillh
KZ
Vi
du
lil.lch
lllgK.
t\·.:'u
c.ie
16i
h[l1lg
'>(1
XU,t'l
hien Irell
c1ucmg
lin
bicu (()
rc
nh:ulh.
la
dn
clui
5'
xcI
;lllh hu/mg
lall nhau ella ute loi Iren Gic
rh~11l
nh:lllh
eLLa
dUlfIlg lin hi¢u,

lien
k0"1
giG'a
dlc
c1u'ong
lin hi¢u
IhI111()t
deh
IV
nhiC'n,
[(li
Sj()
"e,;
g.\y ra
[(}i
k(():
nhung ne'u xci Ircn
quan
c1iem
\'[11
Iy
Ihl di':u
d6
Kh(lll~
eh~\c
chtlil N(li
chung.
de
(tim
bao Iinh 16ng

::=/;",(\\',.I",y)=
\\'
.rr*(1i
Trong
lnri:l'llg
hor
nil)"
h:l111
ra
Kh<.lc
\"(')'i
trlfimg
h<.1'p
I(\i
gj().
Tr{lng Irl((\ng
hop
lrollg
1ll',ICh
xUllt hlcn
\(')i
ej()
.
m(ll
ccich
[ll"
nhiC'IL
dLli1g ta
ct'i
[hC:

lin
hl~lI.
eilling
la
c:ln
ehu
)'
[l)'i
nhu-ng
khi\ n:lllg phal sinh
16i
[ren
C"IC
nh[lI1h
"il
l hei
n,-Illg
xCI
c;ie
c1u'(\ng
lin
hieu
phil]}
nh;jnh: Ule
clu'bng
tin
hi~'u n~lln
sall diem
rc
nh<.lnh

1<1
xCt
UIC
j()i
c11;)p
mach. t\hlf Iren
dJ
dc
qp
({"Ii.
11'011:;
x 0 k
\f>
,~~~£p-'-I
llillh
N,.'
Ul[
Il.lL'
l';lll
\:'-l1)1
l'-d
I
;"lI~\l
Ill":[lllll[):;
1Il:ldllll'nliillh::-;
2.
nhiC:u
tru'('jng
hop
Ceil'

<I
\':1
II \'il
'-;lIlh
ra
CiIl'
h\1
hell'
C~lU.
lLrU"llg
Cfll,:'-
\'(\'j
de
h~\lll
\('lgic
m;1
ChLlIlg
Ihe hlcn
[;\
AND
!JO;IC
OR.
dlc
h\i
n;IY
s0
dune
k~'
111cu
\Uung ling

S;IU:
f"\"iJ/,.,,/II"

r,yJ
~.I"
+ .\y +
II"
Y +
.1"
\\'
r-,.·1(ll
Irong
nhCrng
hili
to{Ul
co"
b,'lll
g:~n
licn
\'(')'i
m()
111nll
It,i [(lgie
[il
11','\
[(\i
C,'ILI
h()i:
m{l hinh
[{li

\"(11
I~',
ch(ing (,hI ph.ii
Ilghi011
etill m(ll
sCi
!u\mg kill
e,le
mo
hinh
it'll
[()gil'. Nhung Ull
d(").
m(ll
kh(")
kh,-m
g~lp
ph,li
1;1
dlCLI
n;\y
1:1111
elm
de
Ihll.lt lo.ill
t<'IO
ciic
bt'l
giii In Ihlf
nghiC'1ll

nay kh6ng phan unh m(lt each day
du.
cac
dij.c
t[nh clla cac loi
\,\It
\)'.
§8.2. Bili tmin
phat
hi~n
l<"Ii
Trang
ml.lc
nay chung ta
dLIa
ra
mQt
so khai ni¢m ve
hili
Imin
ma
hlnh
hO<.i
l6i va phal hi¢n
16i
trang
dc
nwch logic. Vi chung ta chi a cac
mi teh
logic lam hai nhom:

Im~i
mi.~ch
noi tl'en cung c6 nhiIng
ditm
khi.tc
bi¢t. Chung
ta sc xet ricng tung
10<;1i
m~ch;
mqt so phuong phap su
dy.ng
eho cae lmwh
tel
hqp
ding
co the phal tricn sang tru'ong hqp
de
mi.tell
tuAn
t~l'
veli
nhung
slJ'a
doi Ihich hqp.
1.
Pilat
hi~n
loi
trung
cae

gi[l
tl'!
dfiu
VilO
ql
the t = ( x
t
,x
2
,

,x
l1
),
ta se c6
Z(t)
la
dip
ling
dta
m,:!eh
N doi \'oi
vceta
t. Doi \'6i nhiIng
mi.lch
co nhieu
d[iu
ra,
Z(t)
cling

tl'j
thu nghi('m t
1
,t
2
,

,t,,,
len
c:.i.e
d~iu V~tO
eua
m,;lCh
va so sunil nhli'ng gia
Il'i
thu duq'c tl'en .Hu ra theo
Iy
thuyet eua nweh N tuang ling v6i nhling vceW
dfiu
"ao
do:
Z(lj)'
Z(t2)'"''
Z(t",) v6i
nhO'ng
giil.
tf!
thu
dUQ'e
lren thl!e

Teo
th6
dUtJ'e
su:
dl;!ng
kh6ng
plW lhut)e
'laO
trlnh tl!
ap
dL.mg,
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phuong
phap
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tong
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e

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ta
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AND
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D
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0,
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ta
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doc
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NAND,
NOR, XOR,
gia
tri
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ra
bi
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I<,i:

[oi
dLIqc
thl-!'e
hi¢n qua
ba
giai do"n:
266
1.
D(:ij
\'O'i
nhling lui
hAng
sO'
tren
lllQl
dLIong
lin hi¢u x,ic dinil. chelng la
lhiet
1~IP
kJ/()'i-D
tren phan
tlr
nh<:l11
duong
lIn
hi¢ll
l~l!ll
(hlu
\'ilo
\'~I

eua loi.
2.
Gia lrj ella kl/(ii'-D
dLI0c
dlla ra dtiu ra eua toan
mi.\eh
btlllg lhu
Il.IC
Ifuycn D.
Ke't
qu,\ cua buac nay
Ja
xac djnh
dLIqc
dllong diln man
dm
v6i
loi
de
truyen
gi<.l
tr~
D taj
d,-lu
ra. Trong
mQl
so
Illi,lch
co
Ih0

tq
'0'
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D.
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hlrl1e 2
vi\
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:;
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hien
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v;\n
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t;ic
l'hinh
nhu
>;:lU:
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t(le

khae.
Dicli
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co
the
c1U\.K·
minh
hO;.lixlng
VI
dl.11r":n
hinh
S.16, n

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lin
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II
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h ph;li
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:=;>
b = !.
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1~1
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mach
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cho
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(() tn.lll Ihu.ln
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dc
gi,i
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de
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truyen
trong
nweh.

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ph~Jl
quay
lui
ta
Ihic't
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(hrong
II
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t()
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(
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lu;)t
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tin
hi¢u g[ln
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d:ill
\'(10
nh:il;
•
Trong
trlfong
hqp
gi.i
1r!
lin
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chon
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qua
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D.
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~0
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duong.
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nhicu
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I19'p
kinh
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tin