Thiết kế mạch bằng máy tính part 9 potx

~~
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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

du\'·
thl,rC
hi¢n
dl,l'a
V~IO
cac
hQ
gl{\
Iri Ihu
nghi¢m
phat hi¢n l6i. d d,ly vi¢c phat
bl~n
C[IC
lui Ihiet
ke
co
the
th~fC
hi~n
tren
cac
m6
hinh
bi~u
dien bimg cac
ng6n
ngu·
m6
hinh
!loa phan dmg.

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

1,.10
b()
gI<'t
Iri Ihu nghi¢m
cho
cac
1l1i).ch
tel
hqp. Doi voi nhiJng
111'.ICh
tw.ln
It.l",
do
eu
che '
ho

~t
d(mg
pink
t".IP
cua
chullg
nen \'i¢c ph,it hi¢n loi
c!trq·c
11H.((;
hi¢n
dua
trell nhling
phuong

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

duqc
thkt
ke
thl,l'c
hi~n
dU<;1C
cac
chuc
nang
da de
ra.
D~
gii.li
qUYCI
bai
tOtin
nay
ehung
ta
can
phili
X<l.y
dl}"ng
ma
hlnh
cua
m~Kh
logic
nhu
mQI

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

10i li
1l1i lch
dL!<l
vao
hm~t
d(mg clla
chung,
eac
nwch
l6gic
dU(jc
chia
thanh thanh
d.c
m,~eh
to
hqp
va
cae
m,~ch
tU

11l
11,1'.
N1Hf
ta
uJ.
Ihi.ly
trong cae ml!c tru6c.
tren

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

cac
u[iu
\'~\o
tai
cung
m()1
th0i di6m.
Nc~u
xe\
t)"ei1
quan
diem
diu
Irue, trong cac
mi lch
to
h(."ip
hoan
toan
khong
chua
cac
vong tin
hi~u
phi.ln
hoi. Neu xet Iren
khia
c<.mh
pIliit hi¢n l6i,
ca.c

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

true,
ellC
nweh
nay
con
chua
cae
\long
phan
h6i.
Dieu
do lam
cho
\'i¢c phat
hi~n
loi
trong
de
m,!-ch
luan
It.!
la
mot
bili
Io<in
v6
eung
phuc
ti).p.
Ck

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

chung.
dc
Ill'.ICh
Illty
kh(lI1g
Ih~
x":·p
\"ao
nh6m c,ie
111<.lch
lu:in
Iy
Vrfi
nhCl"tlg
d:ll"
diem kh;tc
hi~t
nlHr
\'(1)'
\'l'i
crlu
truc
\,;1
h~U1h
\'i.
\'i~c
pil,l\
hil'l1
Ibi
ch'ij

\'(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

ph;ip chung
ell:
ph;i\
hi~'1l
!<;i
Imng
dc
m',tch 16gic.
De
co Ih6
Ihy-c
hien
dUCK
cr)!l,!!
\'i~'c
d6
lit
dn
ph,l]
lUi!
chon
GtC
phl!o'ng ph,ip ph,i!
l1ien
I(li
linb
tefi
de
d~\c
Int"ng

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

tra e;lc
111i,lch
lllgic
pln"t"c
lap. ehelllg la
lju;m
",at
de
tIll hicll Ih(mg qua
C<lC
dicm nul bcn Irnng ell;l
Ill,lCh.
KIll
merc
d()
11ch
ho'p ella
111;.1cl1
1,-mg
knl{Si
Jllu'e
nlll( lrung
de
Ill;.lch
LSI. \'i¢c
(t(ll
1111":'1
hi
\"'l(:m
tra

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

\,(l
dlllg kh()
kh[\I1
\'tl
Ilhi~u
kllJ
kh(mg the
Ihll'l'
hl¢n
n(~!.
:.JIm
\'~Iy.
pIllIon!,'.
ph:lp
ph:11
hi¢n
Itli
d(ii
\'6i
nhCmg
1ll<,ICh
LSI
chi
dut,1'e
"it'
dUllg
c;ic eh:m
\';10
\';1
eh:1ll

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

Ellll
e!.to
h~li
10:ln ph;il hiell
101
d(ii
\'()"i
nhLrng
111.,lel1
VLSI
!rl)'
n":n
phCl"e
lilp
ho'll
lllticll
:-'0
\'r1'i
\"~'e
ph;11
hicn
It)]
eho
CitC
Ill,teh LSI. Vice t;lnt!
lllere
d()
11cl1
h(fp
ell,\

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.

Vil'l'
tlill
r,\
de
phuong ph'lp gi:li
lIlIy":·t
bi:li
loan ph,il
hi":n
loi
I~I
cilia
f.cho;i
cllO
\ ll'e
Ih~rc hi~ll
d,c
mach
VLSI
\'~l
d611g
\'ai
trl)
H)
cllllg quail
tf(.lllg
l!'Ung
thtli
d:'li
ella

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

Ii:I
cal'
It'll
16g1C.
eic
J()]
I()gie bic'lI
lu~n
,inh hu'bng
eua
c,ie
16i
\'(11
I)'
len h;mh \'i ella
de
h~
Ihong
c1lfriC
m(l
hlnh h6a.
VI
trong qua trlnh
llH'l
hinh h6a cae ph:in
Ill'
mach chung
1<1
I,ieh hi¢t Gic
chue

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

anh
hUllng
t6i d()
tre
tin
hi~u
eli
qU'I
ph:in
Ill'.
Cac
j{l[
10<,11
n;IY
sc
;'mh
hU<1'ng
16i
Ih(Ji
gJan linh to.tn clla
ph;Ul
Ilf
\';\ do
LIt)
cling tlnh hUlmg
k~i
W;:11l
m'.H.:h.
Kill
\<1

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

I)'. Dit'll n:l)' lilln
dl)
phCre
tilP
ella
h~1l
Imin gl;im
\'1
nhlcLl
j(li
\',-Jt
I}
kh,te nhau
co
Ihe:
du'c:)"c
mo hlnh h6a hilng cling m(ll I\\i
IllgJC
ThCf
hal
1;:1
m<)1
,,6
I(li
Illgic
I["('f
nell
khllllg
phu
thUllC

\';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

khi
(6
s~r
Ihay
(bl
\'e
eong
ngh¢.
Thlr ha
Iii
cae
b()
gi<.t
tr\
thLi'
nghicm dc'
ph<.il
hien ei\c
16i
16glC
c6 the
(hrl)'C
sif (h.lIlg d6i \'6i
d.e
10)
V{lt
ly
co
h:mh
\'1

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

tu'('H1~
minh
dc
(tjnh m6t kh()ng gian
It)i,
[r(Jng
d{l
ILlng
lc'li
dw:c
xcie
djnh dQc
1(lp,
\'i:\
do
(k,
loi
SC
phfll1
lich
co
the dU\ie
X(IC
djnh
m()1
deh
tLfo'ng
minh. Tren tiurc
Ie'
ml1

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

Chl)ll
e:tc loi
IU)'
theo
mClc
d(l
quan
[,till
Cilll
ycu
lhl)ng
qu,1
c(tc
tinh
chill clla ehling.
~(yu
cho
tnr{J"c
16i
IO~iC
vit
m(J
hlnh mach,
vc
n~uycn
l~'.
Chlltlg
la
~;:
x(le

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.

Tuy theo
Il1l1
hinh
1l1;.leh
CitC
Itli
logic
C(')
the
dUl.~C
chia
.so
hl) Ihimh
de
loai salt:
C

ic
I(,i
ehrq'c
xac djnh gan lien
vl-)i
1l1()
hlnh
cril'
trllC ehrnc
gO!
Iii
Ule
Itli

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

1ll'.lcil
duoc
g(.)j
1:\
c(le It,i
chCrc
nfl11g.
Vi
elL.1.
,'mil
hu('mg ella
c(lC
!6i
clnk
2 l5
nimg
c6
the lam Ihay
deli
hang ehun
Iy
cua
thanh
philn
mi Ich
hO~IC
dan
t6'i
vi¢c
cam

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

Xi.lc
suat
cua
chung.
l\'hO"ng
dO"
li~u
nay can thlet de
Xi.lc
d!nh
s6
l[in
kiem
If a
mQt
deh
dqc
I~p
can
I~p
L.li
de"
cl,fc
d~\i
hoa
)i.ae
suilt phat
hi~n
nhO"ng
loi chi

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

nhUt
Iii.
sti
<.iI;lllg
dc
phuang
phiip kiem ngl1J¢m
In;J."c
tuyen. Tmng. glao
trlnh nay
chung
ta chi nghien
cCru
16i
cac
h,i
thuimg
tl""l!c.
Neu
khang
duqc
nhk
16i
m(lt
cach
lLro'ng
minh,
chung
ta giii thiet dIng
t".li

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

chi(/II flwc
1.:/£"111
'Fa
r/II(/f/lg xI/yell. Chien IWlc
kitm
tra thuimg
xuyen
co
the"
duqe
phat hicu
nhU
sau:
chung
ta
can
kie:m tra h¢ Ih6ng m()t
each
tilliang
xuycn
sao
cho
xac suat xual hi¢n nhieu
han
mOl
loi
giCi"a
hai
Hin
kiclll tra lien tiep

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

ki~m
Ira tlmong
xuycn
khong
du
de
ngan
ch~1l
twong
hqp
trong m'.lch
Cll
thc
xuat
hi~n
nhieu
loi
m9t
hic.
NhO"ng
truong
hqp
e6
Ihe:
xuAt
hi¢n
nhieu
hern
HH)t
loi trong

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.

Dicu
nay
c6
khu mlng
x<1.y
ra
16n
cloi
veii
nhOng
mi.lCh
co
d(>
tfch hqp
cao
trong
do
nhieu
loi \';)t
Iy
c6
Ih~
.lnh
huang
toi he
1l1~lt
tinh the tren do
e6
1119t
so

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

plli.it
hi¢1l
(loi
,1n).
Nhfrng loi an nay, khi
xu,Yt
hi¢n nhfrllg loi
dO'n
Ie
thu
hai giua hai
IiIn
ki~m
tra, sc
I<;tO
fa
nhieu
I<.\i
kcp trong
1l1i.lch.
Tuy
\,~ly.
mi~e
du
lrong
1l1i.lch
e6
the xuat hi¢n nhicu
16i
dtlng thai,

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

truang
hqp. nllll)lg hJi
Up
("()
the>"
(iI(I("
plllft
hifll
klli kit"rn
IIg!ti~;m
!Hillg
nhifng b(j
gici
tri tJllt
nghi¢m
thie
l
!
ki"
clIO
vi?'("
phdt hi¢1I lIill7ng
IrSr
dan
{c'IWp
tlulnh
//ii
kc'p
I/()i
frhl.

~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()]

c1~c
trtfng do
dc
duang
ket noi
t<).o
nen
thuang
lu:
ngan
m<;lch
ho{!C
he)'
mach.
Cae
lOi
ngcln
mfJeh
(
ch~p
m<).ch
) la nhfrng
16i
xual hil'n klli
nhung
duang
truyen khong
duqc
phep lien ket
bj

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

16i
logic
tuang
ung vai si!
Ch~IP
mi.~ch
sc bao
g6m
nhCi"ng
tin
hi¢u
nh,~n
nhung
gia tfj
e6
dinh \·E{O.l
f.
Nhung
16i
nay
dmyc
goi
Iii.
nhling loi
hang
so
va
(1trqc
ky'
hi¢u

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

bil.C
d.u
AND
va
16i
bac
Ci."iu
OR.
Cae
LOi
IIllJch hir la ket
qua
CLla
si! dlit
dc
ket noi.
Trang
nhieu
eang
~
~~~:nLJ
'I
d,e
dU"<!ng
lin ,
hleu
b,
nghel1~,
nghe
n

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

se lam
eho
dUC1ng
tin
hi~u
'laO do trd thanh
bj
ngat
vii
nh(m
IllOt
gia
tr~
logic
eo
djnh
(
nhu
lren hlnh
8.la
) va do
d6
Iren
duang
tin hi¢u
nay
xuat
hi¢n mot loi hung
so
.\'-(1-1'.

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

duqc
hai
tn1C1ng
hqp noi Iren.
Nhu
v~y
chung ta th:iy rang,
mot
loi
logic
dan
Ie.
VI
dl,l
nhu
loi htmg
so
nh~n
gii.l
tr! a E
{O,
I)
tren
dul':mg
tin hi¢u i
co
the:
bieu dien cae loi
v~t
Iy

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

i
I~l
dau fa
va
16i
nay lam
eho
duemg tin hi¢u i luon
giG'
gia trj bang
(I.
247
Su
11(\
lll'.lcl1lfcn
m{)t
dlf(l'Ilg
lin
hl\'U
c6
rc
nh<inh
co
lile
~inh
ra
nJlI~lI
161
llang
,()

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

dw\ng
1In
hi\'u laeh
bi~1
\,t'J'i
](ll
uen
llh,inh ehinh.
Kili
1:\
Ilwe
Ill~ll
mil hillil
l](l,i
lll',lch lil-:o
ILl'llg
hU(l'c
ph:'lll
c,Yp.
mell
Ih;mil
ph;'ul
mach
.,,0
dlH/C
hicu
tiil.'ll
Ihc()
c[le
lllt1

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

IIl'1
de
dlr(\ng
],;0'1
nt)!
gala
de
pll,ln
ILf
d().
: JIll!
\,(Iy
chung
la
'>c
]';hllllS
XCIl1
\l'l
etc
loi
xU,ll
hl~ll
b':n IlOng c,\c Ih;lnh
ph,'l1l
ll1;,lch
m;1
chi
gJ()'i
h:,ln
\'lCC

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!

c1:1Y
elll'l1lg
1.1
XClll
XcI
1l1l)1

6
\'1
dl,l
\'C
:lIlh hu('jug ella
dc
d
•.
lng
16i
n()i
Iren
dC:Jl
ehLre
J],-lIlg
]()gle ella
de
lll',leh.
Trollg
c<ie
lll:.lCh
j()gic. kli h;\ng
S()

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

S(l
yil
I Ull
ello gi,i
Iri
I
III
hicu e(i
d!I1h
h;'lJl),!
k
1111
It'>i
J1;l~
'>0
dL(,l"C
glH
1:'1
I(\i
h:"IJlg
sli
gi,i
II"!
k
\';\
dU\K'
hi'::u
dlCIl
Irl'll
~()'

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:

-
-/
(\\' r
1'1
- .r +
\'
- - .
.II
,

_ -
Tmng
IfUlf!lg
hqp
c()
Ibl
h~lllg
s6,' :/0
Ih]
h;Ull
ra
s0
h;\ng:
~
==.(jll'

cy)
==.1
+
-"

+ 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,

Nhu
I["ong
\,(
dy In:n.
IrCIl
c1ulmg
lin
hi~ll
g
XU<t"1
hicn
il)!
g/f), \':m
d~
d:,ll
]';11:1
Ibl
\li\\'
c6
,'tnh
hu'('mg
l6'i
dui\ng lin hi¢u k kh()ng,
Trong
mt)1
"0 Inrcmg hq'p.
nCLl
chi
:\~II()'i
C"IC

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

qUilL
chung
la
dn
ph:li
gl<l
t[u0"1
rtmg
[(\1,' ;/0
vii
k/IJ
lil
nillrng It)i
Kh.IC
nhau, Nhu v,)y, Irong Inri:ing
IH,1]1
IrOll!;
mach
'd.l:I't
hlcn
161
k/I),
h~\ln
ra
'>(:
cho
gi,i
Iq
::
biing:

::=/;",(\\',.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:

c~li
Itli
nilY
l2t
I[q)
h(JP
clla hai It'll
g/()
vii
k/()
l\11ll'
\',:IY
chLlllg
ta
thClY
c()
sv
ph,11l
nh<.lnh
\':1
Ian Iruy(!n [/)i Ih.:o c,ie dl((\ng lin hi¢u lien
KC"L.
Tr'1m
L.li.
t hi
c(l
,,~j'
phfl11
nhilnh
du'('mg

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

c6
the
dlfl,ie
coi
Iii
llhCl"Ilg
dlflYilg
IIIl
hi~u
kluic
nh<lu,
hO~lc
tAl
cii nhtlng (h[,\ng tin
hlCU
hcn
J d
nii
llhau
e6
Ihe
duU"c
coi
!iI
ellllg
!l1t)t
dui:mg:.
f3i"IY
gl{)
ChLlIlg

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'

h\i
eh')[1
m<'lch
I'.H)
llC'1l
nht:rng
h\i
bflc
dill
V~I
dUnc
d~lc
Inrllg
h('jl
\'i¢c thue hlen
dlc
11:1111
[(\glc
A0JD
h()~le
OR.
Khl
IrOIl);
m'.lch
dl
sl.l"
ch,\p hal
dU(\Il)l
tin
hl¢U

<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

1,\
Al\D(a-h). OR(iI-b). Ta
h:IY
X~I
\"I
du
mach
IrCIl
hillh X,2.
nClI
dlf(\ng lin hi0u
("
va
II
b!
eh:'!) "il sinh
ra
[(Ii
dl,:IP
Ill'.ICh
htIC
du
AND( c-d
).
hi\ll1
ra
,,;:
ell
lL.ll1g
nhu

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

[(lgie
c(l
Ih~
ph"\ll
{Inh
cae
[()j \'{II I)'
xu.11
hi~'n
lrong
cie
mach
\'6i d() trullg tlure
1l~IO.
-Dc
U) I
l
lC
nhi~n
tlwJc
Slf
Ilfong
uHg
m(ll
deh
kh.ich
quan
\'l)'i
dc
l(\i

\"(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

dLIllf!
de
ph;11
111cn
[ill
Irii
2 1-9
ncn phuc tap
han
nhi~u.
Doi v6i m(lt so m6 hlnh
It'll
logic nhu mo hinh
16i
h:lIlg so, vi¢c tao
d.c
h¢
gii
tr, thu
nghi~m
de
phat
hi~n
16i
wong
d6i dan
gian. Them vdo do m¢t diem yeu ella m6 hlnh loi hang so
lit
m6 hinh
16i

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:

de
m;;teh
16
hqp va
d.e
m<.lch
tuan ttl
d~ra
theo hanh
vi
hm.tt
d(lllg clla
m'.lCh.
Ci.c
1m.1i
m,~ch
nay co diem khiic bi¢t d
Sl!
ton
li.ll
eua
bQ
nho
va vong phan h6i. Do d6 cae phuong phap
li.to
de
bQ
gia Iri
tht'r
nghi¢m d6i v6i hai

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

m~ch
to hlJp
a. Bai
toan
ph at
hi~n
U)i
Cho
Z(x)
Ii!
ham logic clla
mi.lch
16
hqp N v6i x la v-:cw gia
tr!
dfill
\,~IO
hAl
ky
vA
Z(x)
bieu
Jien
anh
Xi.llhy.'c
hi¢n h6i
m~\eh
N.
V6i m(ll
vce\(1

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

lit
vec10.
Neu
trang
mi.leh
xuat hi¢n
10iI,
mi.lch
N se chuycn
th~mh
I1li,1ch
Nt.
Ta gia
Ihiet r:mg
m;.lch
N
j
c(jng
lit
lm~eh
t6 hqp
"oi
ham ehuc
n~\I1g
Z/x).
Mach
dU'<;1e
kie'm nghi¢m btlllg each d(lt day T
eu.a
cac veetlJ gia

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

Ie.
Chung la
dua
ra
dinh nghia nhu sau: vceta gia
tf!
kiem
nghi~m
t duqc gqi
lit
phat hi¢n
16i
f neu:
Zj(t)
1:-
Z(t).
Khi
ap
d~mg
dinh nghia trcn, chung la phai
chu
y nhi1ng diem dutii day:
250
Ciie
veeta
gia
tfj ki6m
nghi¢m
trung
day

Teo
th6
dUtJ'e
su:
dl;!ng
kh6ng
plW lhut)e
'laO
trlnh tl!
ap
dL.mg,
doi
voi IlWeh
16
hqp
N,
day
T dU(;iC
gQi
la
I~p
hqp
cae
vccto' gia tr!
h~'m
nghi¢m.
Djnh
nghla
11;'Y
kh6ng

ap
dyng
duqc
neu
m,!-eh
ehua
16i
N,
trl11htHlh
mach
tufln
t~r.
Trang
djnh
nghii.l
I1llY
ehung
ta gi,\
thiet
n'ing vi¢e ki6m
tm
loi b,\ng
each
d~lt
cae
gi<.1
Iq
Ihu
nghi¢m
va

thu
nh~Hl
cae
kc"!
qmt th(mg
qua
de
eh~1Il
clla ph

tn
tu
Va
so
siinh hoilll
toan
eua
de
ket
l}lt<i
nh~n
du·qe.
Chung
la
xac
djnh
h~lill:
F,(t}
==
F/x"x!

x,) =
Z(x/.x
2
•.••
x,,,)
EB
Zrr/,X:"",xl/)
t\'lm v('y, neu
Z(t)
-:;t;
2
1
(t)
ta sc
eo
F/(t)
nh(U1
gi[L
tr!
'I
';
con
neu %(t) = 2
1
(t)
b511g
nhau,
lue
IiI

F/f}
nh~n
gia Ir!
'0',
la noi rUng veeW
giil.
trj
thtl."
llghi~m
t
kh6ng
ph~t
hi¢l~
duqe
loi f
Ham
F/t)
eon
duqe
gQi
la
ham
khoJ.ng
each
10i.
Veeta
gia
Ir!
dau
vao 1 =

(X
I
'X
2
• •
x,,)
lam
eho
F/t)
=1
de
phat
hi¢n
duqe
loil
va
gQi
Ia
vceta
gia
Irj
kiem
nghi¢m
plutt
hi~n
lc\if
Ncu
trang
111<.,\ch
co

p
16i
viI
ncu
1',//),
FAt) ,

, FI'(t) la
de
ham
khmlng
deh
WOJlg
lrng \'6i
tung
loi, khi do
de
\'ecW
gi,i
Irj
hem
nghi¢m de
pllL!t
hl¢n nhil"ng Ill!
do
duqc
1,.10
thanh
t(lp hqp:
,-,

T(lp hqp
BtlY
g9i
Iii.
h~p
cac
gi[l Irj
kiem
nghi¢m
de
phat
hi¢n
16i.
Ta
hay
xct
ll1<)t
\'i
dl;!,
trC:n
m~.lch
hinh 8.4 xuilt hi¢n Il)ij"El
10i
bAe
c:iu
OR
Z
0<
"
Z,

,
1
Hinh
SA
Vi
du Inrollg
lKJp
101
biic
cau )(jgic OR.
gilra hai
du6ng
tin
hi~u
'\"/V~I
x
2
,
Loi
hAc
C,ill
n;IY
dua
de
ham
ra
ri.ti
ZI
va
1:2

tny thanh:
ZI,=
x/
+ X
2
(Ihay
eha
L/ =
X/X
2
)
L2/=
(XI
+x
2
}x(
(thay
choZ
1
=X
2
.\"3)
Veeta
gia
tr~
di.l.u
va~
t =
"011"
ello·

phep
phat
hi¢n loi
nay
VI
vceta
gia trj d:iu fa kili
mach
khCmg
16i
bitng
1:(011
)=01
trang
kill
do
khi XU;}t
hi¢11
16i
l
Z,(OII)=
II,
Nhu
V(IY,
la
co
Z(
I)
-:t:-
Z/

t)
viI
F,
(t)
=
1.
251
'~' 1
I G2 I
L-f l
',~ l
G3~
~_~
G5
Z
G4

Ilinh
1t5
Vi till
\'~
](li
hillll"
,(l
1',/1)
Ta
:\0t tl10m
vi
dL,1
\'C

CC\c
[tSl
him,S
~l-i
dlii
\'(ii
lll<,ICIl
tr0n
hl11h
~
5,
M'.ICh
n:\v
tln,re
hi~n
h:lI11
16gll":
Z=(.I.+,r,J.I, +
·1'11':
(Ii;\
t[Het
rClng
trung
mach
:,\Uil't
hi0lJ
I,\i
lI/lIlg
~(i
r

!;!I<ltri
'0'
.\"u-()
tn~n
dU'(\11g
<10.\

(
\(ll
_ljO
).
V(i'i
"V
.'\ll~lt
hi0n
ella
[(li
"Ij(),
t.1
IU(')ll
d)
1",
\~
= I
\'~\
h:ll11
fa 1
•.
11
ltLl(~IIg.

: Ira'
Ih;1Ilh:
ZJ
= (
r:
+
Xi
).1
1
_
DICU
) 1~ll
ph,it lli0n
Itll
Nllu
"[IY
mOl
\'ceW
gi.i
In
dCILl
v;\o c6 x'
\'J.
x Iho.\
111;111
(ti\5u
kll':'n
In':'1)
-
ILK

.
~.
" .
Ll
.1'1
=
()
v;\
.r.
i
=
1,
1:1
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gi;i
tq
kicll1
nghi~m
ph;!1
11101\
I()i
.I,m.
Suy
ra
"Celo' ,gitl
II!
kicmnghi01ll ph(tt
hi~ll
[OJ
x)O

ctllhc
b m()1 trung
11hCrng
\'l'ClO'
sau:!
OIiIlUIOI
UIIIII,
01
I
I),
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"
"
o
o
1
Gl
-r'~
G2
0/1
G3
-,
0
G4
0/1
G5
0/1
,
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quail

"at
11;\1111
vi
clla
m.Kh
1J'llllg
tnr(l'llg
hop
)"'hll!l,l!
c(i
Ill!
\'::1
U'l
Ill[
C()
lImh
.\
u-l
[ren d:iu
ra
ella
ph:lll
III
(;,.
1'1'011
I1lllh
I'e
dll'a
]''1 gi;i
Ir!

lin
hll:U
Irl:ll
eic
dUll'llg
lin
hi~'Ll
Imllt:'-
h,li
IrlnJ-llg
hop kh(Jllg
I(li
\'~\
c6 Ii)i dU(ii
dang
l'i1'I' IIOllg
dl')
\'
1::1
nhi:illt:'-
gi-i
II'l
ItHing
(l'Il~
\'(ii Inl'(\ng
hop
kh(mg
Ihi
\':1
I',

-
((1
I/)j
iJli
dll\ic ph;il
111\'11
Ill:n
d,'ltl
ra gi,i
11'\
\'=()
-I
\', = 1.
Vi dlt
In'n
Ill1n11
h()~l
hal
kh;ii
11~1ll
C(i
~l'i
lroll~
kll
\O;ln ph;il 1l1l'n kll
ella
ell'
Ill,.ICh
\()gll':
Vccto

gl~i
Ir!
kiem nghicll1 f dLlllg de ph;ll Iw:n
l()i
r dJ
J icllllO'_11
](ll
I
Irllng
'IU~1
Irlnll
m()
pllong. ( c{)]}
e6
Illc n6i
Et
J I[('ji
1'.10
I(\i
hO;lC Ll(l
Ili.:u
l'lll,!!
l\li
) b;\ng c.ieb lao ra nllll'llg gl;l In
J h;lC
llhau
\',
"I Ir':ll
de
dU(J'ng

(In
Incu tinh
Ill'
\'1
Irl kll.
VCC\(i
gl.i
II'!
kicll1
nghiclll t
Iniy~n
1()lflCii
drlU
rall'.
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Lun
eho
Ll'l
CI
nht:fng
c1u(mg
IIll
hicll Iren
il
nll:ll
1l1()\
du(\ng
lL\n
glLl"a
\'1 Irf

b1
lUI
\-:1
d:iu
fa
11
ph,u c6
nhCfng
gi.i Iq
\'
d
\','
J IHic
nllall. Trong
\'1
Lit!
IrCll
hlllh
8.6.
kll
dW,ie
Inly~n
Ihl'o
dLfiing
qua
de
ph,-tn
II'r
(
(;~,

(;-1'
(;~),
DLrlHlg
IrllY~ll
h1
\'ccLo'
gi.i
Ir!
J IClll
nghi~l1l
t Ihay (kil gi,i Iq klli \u:II hien
Illi
f lrong
Ill.,lell
gm
EI
m.ln C,\Il1 \'()-i
kH.I
qua
\'LClll'
J IClll
Ilghl~l1l
t
Dtri)ll,!!
ci.\n
c1uqe
1,10
h('ii
nlllIng
dLr(\ng

m,lll
dll11
,~
dune goi
1:1
du'img
lUll
m.\n
elm,
)lh,-ill
IU
[(lgic
c6
d:lll ra
m[1l1
dlln
\'6i I(\i.l
,;:
e6
il nh:il m(ll
d Ill
\':IU
CC11lg
du'(ye
blll
eho
m:lll
C,-I1l\
\{ii
]i)i

/'
eic
gi.i
Ir!
d,m
I',
\';1
gi.i
Ir!
d[~Ll
J hicll
\',
nu
pll:in Ill'
\()gJC
t\I\D,
OR,
~A~[),
:-';01{
C(')
[hl: dWfl' Ihe
hl~'ll
nlltf
""\ll:
(il,i In d:lll \ilo
du\1"l'
g~)i
b gi,i
11"i
dll:U killen

\'
ne'll
gi,]
Iii
d6
"IC
dPlh ltiU m ella
p!J:lll
ILr
kh{lllg
]111l.1
l!Jll(JC
\':10
e.ic
d:lU
\';\0 kll,ic.
(;i{l
tr,
(11.10
)',:
C~Il'
phclll til' 16gic
And.
Or,
l\and.
~or
nlu:lIl
(:.1(:
gi~i
tr,

d~io
1',
vil
gici
tri
dieu
khicn
I',
nhu
trong
InIB:":
sau:
" "
\'
\'
And
Or
II
l'\;md
()
Nor
tkjj
y(,'j
de
ph:in
11'[
(()gil'
CO'
han
1£1

And,
Or,
,'\and,
Nor,
gl:l
tri
d:'lt.
ra
dul,l'C
tinh
theo
e.l<:
gi:l
tri
d,IO
\';.
g;i:i
tri
di(;u khil"n
,a
h;'lllg
",
8j
""
1\1lll'
\'(ly,
111(,)[
ph~ill
ll'l'
l(lglC

\'('ii
:;
d:lu
do
"'0
c6
Ciic
J h(ii
CO'
'i('i
nlHr
~all:
\
8j
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, ,
\'
CD
\'
, ,
.\.
X
\'
\'
8)
\'
, ,
\'
\'
\'

CD
\'
, ,
V('ii
deh
bicll dlen Ih(lllg qua
Cite
gl,\
Ir!
\,
\'~t
\'"
lll~llh
de
\,(;
Illlh 1lI:111
cam \,()'i
]()i
ella e.ie pll:'inlLr logic
c(ilhe
dliq'e ph;ll
hlCll
nllu sau:
iVlcnh
dc
YC
tinh man cam
Illi
Cho G
la

ph,in
tLr
logic
w'1i
gia
Irj
nghjch
d,IO
\',
vii
gia
Ir!
clieu
kluen I c6
d<.tll
ra nlwy
cUm
\'('1i
101
I (lUang ung vai vecla gia
tri,
kic'm
nglli~m
t phal
hi~n
loi), la c6:
Tdl d cdc driu vao ella G
man
dm
voi

loi.f
sc nh(tn cung
m9t
g!a
Irj
(VI
du
iii a).
Ttlt eil nhO'ng d

lu
dlO
eLla
G kh6ng
m;.'tn
dm
v6i
16i
f (n2'u it nhiit m()t
diu
vao
ll~iO
do)
se
nh~n
gia
td
v"
Dilu
ra

ella G
se
nh[m
"ia
tri
(/
EB
\'
.
. c . ,
Cluing
minh
m~nll
de
vc
tinlt man cam Ibi.
,
-
Chung
ta cllling minh
m¢nh
de
phuang
phap phan
ehCrng
nlllr sau:
254
lllnh
R.7
Plulnllr NAND

Gdl thie! rung
e6
hai (![iu
V~IO
nil;\)'
cim
voi
16i
trang
ph~in
lit G
Iii
J,:,
, .
Cie
cHill
\':lO
nay
nh(lIl
de
gi{l
Iri
kh,ic
nhau
vii
gi,-'t
SLr
drill
vao
J,:

nh~n
gia
tri
c1icu
kllien ella
phfill
lu:
\'"
Khi Iren ph[in
Ill'
XUiYt
hi¢n
16il;
hai
dUll'ng
tin
hi~u
k va I Ihay
d{}l
g);l
Iri
vii
dU'ong I nh,)n gi,i tr!
dicu
khi(;n. Nhung
dicu
nay e6
IlghT<l
1:1
pilun

ILr
G
v;'in
nh,)n gia Iri eil,
dQe
1(lp
vai
~I!
xu[!!
hicn ella
161
r Biell
nuy
muu Ihuttn voi giil thiet
dau
ra
ella G
phAi
m;'in
dill
\'6i
10]
-
ICre
I~I
ph:li Ihay d()i
giti
Irj
khi
lrang

mi leh
xutil
hi~n
10]
f.
Nhu'
\,~Iy.
I,'l!
C'I
nhu'Jlg d:iu
\,~IO
mtll1
d!n
ella G
dn
ph;ii nh(trl cung 1119t gi,i tfj ( vi
d~l
la
(l
).
B:iu
ra
ella
(i
kh(mg Ihe thay d()j khi
xu,Yt
hi~n
loilncu
mQt
trang cae

d~iu
\,;10
kh6ng
nh' Iy
cam
\'o-i
loi f nh,)n gi;j
II"!
\',;
do
do
lat
e<"1
de
cUu
V~IO
eLw
G
khong
nlWY
dm
\'6i
Jili
f ( neu
:0
)
dn
ph,'l1
nh[m gi,i
trj \','

Nc'u
u =
\'"
d,-Iu
ra
eLla
pldn
tu:
16gie
nh~1ll
gia
Ir)
btmg
I',
EB
I',.
:"i~'u
(/
=
\',
'
I[it
d cae d[iu
V;'IO
eua G
: 0
nh,)n gia Iri
I',
va do
d6

driu ra
eua.pllau
Ilf
siS
nh~Hl
gia Iri bang
I',
EB
I',.
Nhu
V(ly,
trong
d hai
trLr('J'ng
hQ'p
d:iu ra ella
ph,-IIl
tu
16gie G dell llh,)n gia
tr~
bAng
a
EB
1'/.
Gi,i tr!
I',
gQi
la
gi<i
tri kfch

hm,lt
vi n6
eho
ph~p
d.c
16i
Ian truycn qua
phAn
tu
tai
d,-lu
nl. Tren
hLnh
8.7, dua
fa
vi
eh.1
ve
ph~in
tir
NA: ID
thoa
man
m~nh
de
Hen.
Ph,-In
IU:
NA; JD
nay se

c6
tAt
d
cae
d,lu vao
nh(11l
gia
Irj
'I'
ho,k
l[l(
d nhiIng duu vao
n1<1.n
cam
nh(m
gi,i
Irj
'0'
Y~I
nhO"l1g
dau elm
1'.li
duqc
d~lt
gia trj
'I'.
I\'CL!
t<-l
,ip dl,lng
phein

:3
ella
m~nh
de tren I,)p
h,li
nhicu
Ifin,
chung
ta sc
nh(ul
dtfQe
he
qu,-i
saL!
\'6
UIC
dLf('-mg
dJn
m,ln
dm
v6i
16i:
H~qml
Gii.l
thic"t
duang
tin
hi¢uj
man
dm

\'61
16i
hb.ng
so
gi,i lrj
I'
S-(I-I'f(tLwng
Lrng
vai
vcctO'
gi,i trj
kiem
nghi¢m t phat
hi~n
16i
) va p
Iii.
gia tfj ngh!ch
(Lto
eLIa
duang
man
dun
loi giG'afva,;.
Klli
d6 gia trj
eua)
lrong
veeta
t

Iii.
l'
GJ
p.
Ne"u
co
m()t
s6
(hl'ong tin
hi~u
nhi;lY
dm
giila f
\,~l
J Ihl
IAI
d C,-lc
duong
do
(h~lI
cllilg nh,)n
gii.l
tr! nghjeh
(h-to
p.
c.
Kha nang phat
hj~n
lui
Do

de
di~m
quan
sal chi gi6i lwn
(,.ti
d.e
(tiu
vao
\'a
driu ra (
co
nghTa
I~I
vi~e
kic'm tra chi duqe thlfc
hi¢11
Iheo gia
Ir!
ella
ham
fa ) nen
ec1
the x,iy ra
Iruling
IHJp
co
llh[C!1g
16i
kh6ng phat
hi~n

duqe ho;)c ell nh[Ing Illi khtlllg
ph,tn
bi~t
duqc. M9t
J6ilduqc
gQi
IA
e6
th~
phat
hi~n
duqe
nc"u
ton
t'-,Ii
\'eeto'
gi:i trj
him
nghi¢m t
ph,-it
hi¢n
dUQ'c
f
Trong
lruo-ng
hqp
IlgUQ'C
I<;l-i,
16i
I

duqc
COl
Iii
khlmg
tilt
phal
hi~n
dU<;1e.
Nhung
16i
f kll6ng the phat hi¢n
dLf<;1e
la nhGng
16i
lam
eho
gi,i tr!
hi"tm
fa
khong
thay dbi so sanll
y6'i
tmong
hQ'P
trong
nwch
khong
co
loi.
Nhu

Y(ly
ta
co
L"/
t ) =
2(
t
),
hay
e6
the n6i
c<ich
khac
I)
t ) =
O.
Khi
d6
kh6ng
the
co
\'ccto' gi,i
tr~
kicll1nghi~m
!liIO
co
the kich
hm,lt
qUii
trlnh lruycn

(6ifv~\
(!ling
thO'i
lao fa du(mg
dan
man
cam
voi loi r
den
d,l.u
ra chfnh ella m'.leh.
Nhu'lll,!
loi
kh6ng
the phiit hi¢n
duqe
gQi
la nhilng lui du
fhim
v,1
nhO"ng
mi,leh
tl;
h9'P
ehLJi.l
nhung
16i
hang
so
dLf

thua duve duqe
gQi
la
lll::,Ich
du fhl'm.
255
A~~~
, j
I-L
__
J
,
jLJ-
,I
J,
DO
I
r_
1
C
"1""1
I
)-'
Ilillh
1'i.1'i.
\llIlil
lin,!
Inrim12
ho'p
kh()l\g

ph.d
hlL'1l
dU'ljl'
Ill! iii! tron);!
Illalll.
Vi
tll.1.
\'6i
m<.lch
tfen
hlnh
~~.
lili
himg s(i
Iren
dlftmg lill
hlC"u
(1.1'-
(/-}
(/11
1;1
liil
~hhng
IhC:
ph,il bien
dlfP'C.
Nhung I(\i
~h()IlS
ph'll
hi~n

duoe
n{ll
Irell
u\
IhC:
hr')
qua \,'1 Chlillg
~h(lllg
!:till Iha\' (kil
l'llLk'
Jl,~ll1g
IClt!lC
etta
mach
nlumg
s~r
c6
m,H
clla
de
I()i
ll~ty
C()
Ih~
ph:i v
c:ia
Ihk,'t
n~
dicu
~il'll

Imllg
111'.ICh
chi
c6
m()1
161
\'~l
e6
Ihe:
dtlll
tkn
nllLfng
~l'l
lIlt,\ \ai. I\e'u
d~r<l
Hen
chIC·'n
lu(/c
~iC:1ll
tr;]
(1ll1tmg
XUyCll.
e6
Ih~
gi,i
thi0'l
r:lIlg Chl!llg la
: ':
ph"11
!lIen

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VI
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vitO
con

Ii.li
cua rhfin
IU
khi
m(lilrong
cac
eMu
vao
ella
ph~in
ttl
hi
loi
vii
nhf\l1
gi,i
tri
D
IllnIJ
X.17.
'll1l1
IliC
c1IUYCIl
[)
qlla
c;ic
pJdm
Itf logic
co
b;lli.

110i)e
/5,
sao cho gia trj n
(ho~c
i5)
dLI0c
Iruy':n nguyen
vt;n
16i
drill
ra
ella
ph{in
ttl'.
Tr6n hlnh 8.17,
ta
th[IY
doi \'oi cae ph,ln
tll'
AND
\';1
NA:'-JD,
phcp
Iruyen
D
Ja
thiet
1~IP
tren nhiIng
d~iu

vito
khong
bj
16i
nilting
gi{\
Ir\
hung'
1';
cl6i
\'ui
de
phfill
tu
OR
viI
NOR - lhiet
Ii)p
gia trj
'0';
lrang khi do d6i
vO'i
phtin
IU
XOR, phcp lruycn D
lL10ng
ung
v0i
vi¢c
(hie't

I{lp
Iren
cUu
\'~\o
con
le.li
gia
Irj
bill
ky trong
ti)p
hqp I
0,
1 J .Chung
ta
nh~U1
Ihay d(ii \'oi
doc
plli,ln
llr
NAND,
NOR, XOR,
gia
tri
tn~n
d<lu
ra
bi
(hio
I<,i:

V > D,
D >V
Dlya
Il"l~ll
kilai
ni<;m
kJ/()'i-D.
cae phuong
ph{lp
1'-,10
\'ecto gia
Irj
kiJm
nghi¢m pilat hi¢n
dc
loi
hAng
so
dlPl
Ircl1
s~['
kieh
ho' It
dU'i)ng
truycn lin hi¢u
\il Ihi0'tl,)p
<luong
diln man
cam
vO'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

xi.le
dinh cae gia
Ir!
tlIml man
kJ/(J'i-D
do
( thu
tl}C
,hie'l
h)p
D
).
K~I
qua
eua
blrC)'e
nay
IiI
xac djnh
dU0c
cae gia
Ir!
deiu
vao Iren ph:in
IU
Irl!c
tic"p
chju
,-lnh
Inro-ng

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

XU<ll
hi¢n nhieu duong
d,-tn
mall cam v6i
loi
(
1l1{)1
IrLIo-ng
hQ'p
de
tililY
kili
c<ic
phfin
tlr
logic co tile c6 nhi6u hon hai
d[iu
vao
).
3.
XCie
d~nh
e~ie
gi;i Irj ctlu
\';10
tlfO'ng
thieh
Vlii
de
gi:i

tq
'0'
\,~I
'I'
nh;)n dUne 1rollg
qu<i
Irlnh
Ihi":'l
I;'\p
D
\':1
trllycn
D.
Cic
hlrl1e 2
vi\
blrO'e
:;
dU9'e 1hue
hien
dll'a
v;\n
nhiIng
Ihao
t;ic
l'hinh
nhu
>;:lU:
Thao
t(le

IntY~Il-n.
Phcp
suy
dien.
Phcp
qU'ly lui.
Phcp
suy
chen c.i.n Ihi2't
de
<Ie
djnh gi,i
Ir!
tren
nhiIng
chl'tJ"ng
1ruycn
tin
hi¢u
111,)1
e:ich
tiuy
nh:il
Iheo
gi.i trj
tren
nhiJ'ng
dm\ng
till
ll1~ll

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

Yu
gi:i Iri
li.li
dll"(\lIg
lin
hi¢u
f (hl\K thie't
\;~p
b.\ng
'0'
Ihl
suy
ra
gii
Iq
Ir':n dl\'(\ng
Ii

"it g
cung
duO'e
thiC't \;lph
htmg
'0'.
Then
ehuc
nfmg
cua
ph:in
Ill'
AKD.
nC\1
(hrc1"ng
g du\'l"l'
Ihie;t
li~p
h,c
mg
'0'.
Suy
ra
(hrong i
: 0
tlm)'e Ihie't
1;1[1
hflllg
'0'.
t\'L)t

kh.ic
(1 :'
thie'l \;lp tlm)'e (hrO'llg f
gi~i
trj
'()'.
gi:i
In
Irell
dU(1"llg
II
\"i:t
('
eh,k
chtm ph'll
htmg
'0'.
Ui.i tr! 1r':n cluo-ng
('
htmg
'0'
sc
suy
ra
dlfong
h ph;li
nh(11l
gi.i
Iq
'I'.

Ta
c6 Ihe
t(~llg
kct
qu;.\.
trlnh
>;uy
dien
trcn
nhu
sau:
f =
0:::::::.
h =
(),
g:
=
(1,
Po
=
0:::::::.
i = 0:
r =
0:::::::.
a =
0.
c =
i,l:
"
::::

0
:=;>
b = !.
Ph~p
quay
lui
1~1
phcp
to.in thie't \')p
&1;1
Il"]lr':n
de
d<.lu
V:IO
ella
mach
sao
cho
kh6ng
(() tn.lll Ihu.ln
\'oi
dc
gi,i
tl'!
[<Ii
de
c1uO'ng
truyen
trong
nweh.

Ph':p
lo<.ln
n;IY
kh~ic
\'6i
ph':p
Suy
di~n
noi
tren
I~I
kc't
qUit
(()
Ihe' kh()ng
duy
nhS\.
Vi
cll.l
nhu
1ren
hinh
S.16. nc'tl
dU'lJ"lIg.i
nh(lIl
gii
Ir!
btlng
'0'
Ihl

[heo
ph~Jl
quay
lui
ta
Ihic't
l~lp
Iren
(hrong
II
\';1
('
Clie
t()
hop
e6
[h~
e6
1;1
(
LO
).
(
O.
1
).
l L I
).
Vi¢e
Iva

chqll
de
gi:i tr! phll
IH/P
phu
thu,:'}C
V;IO tlfOg
IrLl'll'llg
l19'p
Cl.l
IhJ
\,~l
dl.ra
V~IO
de
111.~1
iL.ra
eh9n.
Cie
lU;)1
hfa
eh(~n
c6
thJ
c6
llhung
(k)c diem
nhu
SilU:
Cae

lu;)t
iL.ra
eh91l
eo
th~
Iii
nhung
IUi)lnhu
S<lU:
• Chql1 dUll'Jlg
tin
hi¢u g[ln
\'(~i
d:ill
\'(10
nh:il;
•
Trong
trlfong
hqp
gi.i
1r!
lin
hi~'ll
tx\ng
'I',
ilya
chon
du6ng
Iruy"::n

ehlra
ph:in
Ill'
OR:
• Trong: truo-llg:
h9"P
giu trj
tin
hi~u
b.\ng
'0'.
!Ira
chqll
chl'(\ng
trlly~n
chua
ph:in til A'KO.
Vi¢c
dU''-1
cal'
lu(1t
I~ra
chQn
d.n
thiet
ngay
c

t doi
v6i

qua
Irinll Irllycn
D.
Trollg: trlfo-ng
hQ'p
!lCU
0 d:ill ra Clta ph[in ttl'
eo
riS
nh,inh
Ihl
~0
khung
dllY nhi.lt
[wng
\'i¢c
ehqn
duong.
Trong
nhicu
trlfong
I19'p
kinh
nghi¢m
clio
Ih:ty
nen
chqll
duong
tin

hicll
g ill
(t:ill ra nh;'\\.
267