Alj a ba r B o olea -...
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1 n a e l o o B r a b a j l A x t a p a d r e t n a k l a s i M - n a d + : r e n i b r o t a r e p o a u D - . ’ : r e n u r o t a r e p o h a u b e S - B , + r o t r a e p o a d a p n a k i s i n i f e d i d g n a y n a n u p m i h : ’ n a d , - i r a d a d e b r e b g n a y n e m e l e a u d h a l a d a 1 n a d 0 B. l e p u T (B , + , ) ’ , t u b e s i d n a e l o o B r a b a j l a p a i t e s k u t n u a k i j a, b, c B u k a l r e b a m o i s k a - : t u k i r e b n o t g n i t n u H t a l u t s o p u a t a a m o i s k a . 1 e r u s o l C : ) i ( a + b B ) i i ( a b B : s a t i t n e d I . 2 ) i ( a = 0 + a ) i i ( a = 1 a : f i t a t u m o K . 3 ) i ( a + b = b + a ) i i ( a b = b . a : f i t u b i r t s i D . 4 i ( ) a (b + c ( = ) a b ( + ) a c) ) i i ( a ( + b c ( = ) a + b) (a + c) n e m e l p m o K . 5 1 : ) i ( a + a 1 = ’ ) i i ( a a 0 = ’
Transcript of Alj a ba r B o olea -...
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naelooB rabajlA
tapadret naklasiM - nad + :renib rotarepo auD - .’ :renu rotarepo haubeS - B ,+ rotraepo adap nakisinifedid gnay nanupmih : ’ nad , - irad adebreb gnay nemele aud halada 1 nad 0 B .
lepuT (B ,+ , )’ ,
tubesid naelooB rabajla paites kutnu akij a , b , c B ukalrebamoiska - :tukireb notgnitnuH talutsop uata amoiska
.1 erusolC : )i( a + b B
)ii( a b B
:satitnedI .2 )i( a = 0 + a )ii( a = 1 a
:fitatumoK .3 )i( a + b = b + a
)ii( a b = b . a
:fitubirtsiD .4 i( ) a (b + c ( = ) a b ( + ) a c) )ii( a ( + b c ( = ) a + b ) (a + c)
nemelpmoK .5 1: )i( a + a 1 = ’ )ii( a a 0 = ’
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surah ,naelooB rabajla haubes iaynupmem kutnU:naktahilrepid
.1 nemelE - nanupmih nemele B,
.2 rotarepo kutnu isarepo hadiaK ,renu rotarepo nad renib
.3 .notgnitnuH talutsop ihunemeM
auD naelooB rabajlA - ialiN
aud naelooB rabajlA - :ialin - B }1 ,0{ = - nad + ,renib rotarepo - ’ ,renu rotarepo - :renu rotarepo nad renib rotarepo kutnu hadiaK
a b a b a b a + b a a’ 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 1 1 1 1 1 1
:notgnitnuH talutsop ihunemem hakapa keC .1 erusolC ukalreb salej : .2 :awhab tahil atik tapad lebat irad anerak ukalreb salej :satitnedI
1 = 0 + 1 = 1 + 0 )i( 1 )ii( 0 = 0 0 = 1
.3 :fitatumoK rotarepo lebat irtemis tahilem nagned ukalreb salej.renib
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.4 )i( :fitubirtsiD a (b + c ( = ) a b ( + ) a c nakkujnutid tapad ) lebat kutnebmem nagned sata id renib rotarepo lebat irad raneb
:naranebek
a
b c b + c a (b + c) a b a c (a b) ( + a c)
0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1
fitubirtsid mukuH )ii( a ( + b c ( = ) a + b ) (a + c tapad )anebek lebat taubmem nagned raneb nakkujnutid nagned nar
.)i( itrepes amas gnay arac
.5 naktahilrepmem 3.7 lebaT anerak ukalreb salej :nemelpmoK:awhab
)i( a + a 1 = 0 + 1 =’1 + 1 nad 1 = 1 + 0 =’0 + 0 anerak ,1 = ‘ )ii( a a 0 anerak ,0 = 0 =’0 1 nad 0 = 1 1 = ’1 0 = 0
ilek aneraK awhab itkubret akam ,ihunepid notgnitnuH talutsop am
B amasreb }1 ,0{ = - nad + renib rotarepo nagned amas rotarepo .naelooB rabajla nakapurem ‘ nemelpmok
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naelooB iserpskE
( naklasiM B ,+ , utauS .naelooB rabajla haubes halada )’ ,naelooB iserpske ( malad B ,+ , :halada )’ ,
malad id nemele paites )i( B, ,habuep paites )ii(
akij )iii( e1 nad e2 akam ,naelooB iserpske halada e1 + e2 , e1 e2 , e1 naelooB iserpske halada ’
:hotnoC
0 1 a b c a + b a b a’ (b + c) a b + ’ a b c + ’ b ayniagabes nad ,’
naelooB iserpskE isaulavegneM
:hotnoC a’ (b + c)
akij a ,0 = b nad ,1 = c :iserpske isaulave lisah akam ,0 = ’0 1 = )0 + 1( 1 = 1
nakatakid naelooB iserpske auD nelavike nakgnabmalid(mem aynaudek akij )’=‘ nagned kutnu amas gnay ialin iaynup
ialin nairebmep paites - adapek ialin n .habuep :hotnoC
a (b + c ( = ) a . b ( + ) a c)
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.hotnoC awhab naktahilreP a + a’b = a + b . naiaseleyneP :
a b a’ a’b a + a’b a + b 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 1 1
( kitit adnat :naijnajreP nasilunep irad nakgnalihid tapad )
:nanakenep ada akij ilaucek ,naelooB iserpske
)i( a(b + c = ) ba + ca )ii( a + cb ( = a + b ( ) a + c) )iii( a 0a nakub , 0
satilauD pisnirP
naklasiM S ( naamasek halada ytitnedi rabajla malad id )
,+ rotarepo naktabilem gnay naelooB ,nemelpmok nad , naataynrep akij akam S itnaggnem arac nagned helorepid *
+ nagned nagned +
1 nagned 0 0 nagned 1
,aynada apa patet nemelpmok rotarepo nakraibmem nad naamasek akam S .raneb aguj * S iagabes tubesid * laud irad
S.
.hotnoC ( )i( a + 0()1 a aynlaud 0 = )’ (a 1( + )0 + a 1 = )’ )ii( a(a + ‘ b = ) ba aynlaud a + a‘b = a + b
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mukuH - naelooB rabajlA mukuh
.1 :satitnedi mukuH )i( a = 0 + a
)ii( a = 1 a
.2 :netopmedi mukuH )i( a + a = a
)ii( a a = a
.3 :nemelpmok mukuH )i( a + a 1 = ’
)ii( aa 0 = ’
.4 :isnanimod mukuH )i( a 0 = 0
)ii( a 1 = 1 +
.5 :isulovni mukuH )i( (a = ’)’ a
.6 :napareynep mukuH )i( a + ba = a
)ii( a(a + b = ) a
.7 tatumok mukuH :fi )i( a + b = b + a
)ii( ba = ab
.8 :fitaisosa mukuH )i( a ( + b + c ( = ) a + b + ) c
)ii( a (b c ( = ) a b ) c
.9 :fitubirtsid mukuH )i( a ( + b c ( = ) a + b ( ) a + c)
)ii( a (b + c = ) a b + a c
.01 :nagroM eD mukuH )i( (a + b = ’) a’b’
( )ii( ba = ’) a + ’ b’
.11 1/0 mukuH 1 = ’0 )i( 0 = ’1 )ii(
.3.7 hotnoC )i( nakitkuB a + a’b = a + b )ii( nad a(a + ’ b = ) ba naiaseleyneP :
)i( a + a’b ( = a + ba + ) a’b )napareyneP( = a ( + ba + a’b) )fitaisosA( = a ( + a + a )’ b )fitubirtsiD( = a 1 + b )nemelpmoK( = a + b satitnedI( )
)i( irad laud halada )ii(
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naelooB isgnuF naelooB isgnuF naatemep halada )renib isgnuf aguj tubesid(
irad Bn ek B aynnaksilunem atik ,naelooB iserpske iulalemiagabes
f : Bn B ini lah malad gnay Bn nakatoggnareb gnay nanupmih halada
adnag tururet nagnasap -n ( n deredro - elput haread malad id ) lasa B .
isgnuf nakapurem nial kadit naelooB iserpske paiteS
.naelooB halada naelooB isgnuf haubes naklasiM
f(x , y , z = ) zyx + x’y + y’z
isgnuF f ialin nakatemem - adnag tururet nagnasap ialin - 3 (x , y , z .}1 ,0{ nanupmih ek )
itrareb gnay )1 ,0 ,1( ,aynhotnoC x ,1 = y nad ,0 = z 1 = 1 = )1 ,0 ,1(f aggnihes 0 ’1 + 1 ’0 + 0 . 1 = 1 + 0 + 0 = 1
.hotnoC hotnoC - aelooB isgnuf hotnoc :nial gnay n .1 f(x = ) x .2 f(x , y = ) x’y + yx +’ y’ .3 f(x , y = ) x’ y’ .4 f(x , y ( = ) x + y ’) .5 f(x , y , z = ) zyx ’
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malad kusamret ,naelooB isgnuf malad id habuep paiteS tubesid ,aynnemelpmok kutneb laretil .
isgnuF :hotnoC h(x , y , z = ) zyx adap ’ iridret sata id hotnoc
utiay ,laretil haub 3 irad x nad ,y , z .’
.hotnoC naleooB isgnuf iuhatekiD f(x , y , z = ) z yx nakatayn ,’ h.naranebek lebat malad
naiaseleyneP :
x y z f(x , y , z = ) z yx ’ 0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1
0 0 0 0 0 0 1 0
isgnuF nemelpmoK .1 nagroM eD mukuh nakanuggnem :amatrep araC
,habuep haub aud kutnu nagroM eD mukuH x1 nad x2 halada ,
.hotnoC naklasiM f(x , y , z = ) x(y’z + ’ zy akam ,) f (’ x , y , z ( = ) x(y’z + ’ zy ’)) = x ( + ’ y’z + ’ zy ’) = x ( + ’ y’z ( ’)’ zy ’)
= x ( + ’ y + z ( ) y + ’ z )’
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.2 .satilaud pisnirp nakanuggnem :audek araC
nakisatneserperem gnay naelooB iserpske irad laud nakutneT f , malad id laretil paites naknemelpmok ulal .tubesret laud
.hotnoC naklasiM f(x , y , z = ) x(y’z + ’ zy akam ,)
irad laud f: x ( + y + ’ z ( )’ y + z)
:aynlaretil pait naknemelpmok x ( + ’ y + z ( ) y + ’ z = )’ f ’
,idaJ f (‘ x , y , z = ) x ( + ’ y + z () y + ’ z )’
kinonaK kutneB
:kinonak kutneb macam aud ada ,idaJ .1 ( ilak lisah irad nahalmujneP mus - fo - tcudorp )POS uata .2 ( halmuj lisah irad nailakreP tcudorp - fo - mus )SOP uata
.1 :hotnoC f(x , y , z = ) x’y’z + yx ’z + ’ zyx POS ( ukus paiteS mret tubesid ) mretnim
.2 g(x, y , z ( = ) x + y + z () x + y + ’ z () x + y + ’ z )’
(x + ’ y + z ()’ x + ’ y + ’ z ) SOP
( ukus paiteS mret tubesid ) mretxam
paiteS mretnim / mretxam pakgnel laretil gnudnagnem
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mretniM mretxaM x y ukuS gnabmaL ukuS gnabmaL 0 0 1 1
0 1 0 1
x’y’ x’y yx ’ y x
m0 m1 m2 m3
x + y x + y’ x + ’ y x + ’ y’
M0 M1 M2 M3
mretniM mretxaM x y z ukuS gnabmaL ukuS gnabmaL 0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1
x’y’z’ x’y’z x‘y z’ x’y z x y’z’
y x ’z x y z’
z y x
m0 m1 m2 m3 m4 m5 m6 m7
x + y + z x + y + z’ x + y +’ z x + y +’ z’ x +’ y + z x +’ y + z’ x +’ y +’ z x +’ y +’ z’
M0 M1 M2 M3 M4 M5 M6 M7
.01.7 hotnoC kutneb malad ini hawab id naranebek lebat nakatayN.SOP nad POS kinonak
01.7 lebaT x y z f(x , y ,
z) 0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1
0 1 0 0 1 0 0 1
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naiaseleyneP : )a( POS
ialin isanibmoK - isgnuf ialin naklisahgnem gnay habuep ialin isgnuf akam ,111 nad ,001 ,100 halada 1 nagned amas
halada POS kinonak kutneb malad aynnaelooB f(x , y , z = ) x’y’z + yx ’z + ’ zyx
kanuggnem nagned( uata gnabmal na mretnim ,)
f(x , y , z = ) m1 + m 4 + m7 = )7 ,4 ,1(
SOP )b(
ialin isanibmoK - isgnuf ialin naklisahgnem gnay habuep ialin akam ,011 nad ,101 ,110 ,010 ,000 halada 0 nagned amas
halada SOP kinonak kutneb malad aynnaelooB isgnuf f(x , y , z = ) (x + y + z () x + y +’ z () x + y +’ z )’
(x +’ y + z ()’ x +’ y +’ z)
,nial kutneb malad uata
f(x , y , z = ) M0 M2 M3 M5 M6 = )6 ,5 ,3 ,2 ,0(
.11.7 hotnoC naelooB isgnuf nakatayN f(x , y , z = ) x + y’z malad
kutneb .SOP nad POS kinonak naiaseleyneP :
POS )a( x = x(y + y )’ = yx + yx ’ = yx (z + z + )’ yx (’ z + z )’ = zyx + zyx + ’ yx ’z + yx ’z’
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y’z = y’z (x + x )’ z’y’x + z’yx = idaJ f(x , y , z = ) x + y’z = zyx + zyx + ’ yx ’z + yx ’z + ’ yx ’z + x’y’z = x’y’z + yx ’z + ’ yx ’z + zyx + ’ zyx
uata f(x , y , z = ) m1 + m 4 + m 5 + m 6 + m7 = )7,6,5,4,1(
SOP )b( f(x , y , z = ) x + y’z ( = x + y ()’ x + z) x + y = ’ x + y + ’ zz ’ ( = x + y + ’ z () x + y + ’ z )’ x + z = x + z + yy ’ ( = x + y + z () x + y + ’ z) ,idaJ f(x , y , z ( = ) x + y + ’ z () x + y + ’ z ()’ x + y + z () x + y + ’ z) ( = x + y + z () x + y + ’ z () x + y + ’ z )’ uata f(x , y , z = ) M0M2M3 = 2 ,0( )3 ,
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kinonaK kutneB ratnA isrevnoK
naklasiM f(x , y )z , = )7 ,6 ,5 ,4 ,1(
nad f irad nemelpmok isgnuf halada’ f,
f (’ x , y , z = ) = )3 ,2 ,0( m0 + m 2 + m3
helorepmem tapad atik ,nagroM eD mukuh nakanuggnem nagneD
isgnuf f :SOP kutneb malad
f (’ x , y , z ( = ) f (’ x , y , z ( = ’)) m0 + m 2 + m3 ’) = m0 . ’ m2 . ’ m3’
( = x’y’z ( ’)’ x’ ’z y ( ’) x’y z ’) ( = x + y + z ( ) x + y + ’ z ( ) x + y )’z + ’ = M0 M 2 M3 = )3,2,0(
J ,ida f(x , y = )z , = )7 ,6 ,5 ,4 ,1( .)3,2,0(
nalupmiseK : mj = ’ Mj
.hotnoC nakatayN f(x , y , z =) nad )5 ,4 ,2 ,0( g(w , x = )z ,y , )51 ,01 ,6 ,5 ,2 ,1(
.POS kutneb malad
naiaseleyneP : f(x , y )z , = )7 ,6 ,3 ,1(
g(w , x , y , z =) ,4 ,3 ,0( )41 ,31 ,21 ,11 ,9 ,8 ,7
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.hotnoC irad SOP nad POS kinonak kutneb haliraC f(x , y , z = ) y + ’yx + x ’zy’
naiaseleyneP : POS )a(
f(x , y = )z , y + ’ yx + x’ zy ’ = y ( ’ x + x ( )’ z + z + )’ yx (z + z + )’ x’ zy ’
( = yx + ’ x’y )’ (z + z + )’ zyx + zyx + ’ x’ zy ’ = yx ’z + yx ’z + ’ x’y’z + x’y’z + ’ zyx + zyx + ’ x’ zy ’
uata f(x , y = )z , m0 + m 1 + m2 + m4 + m5 + m6 + m7
SOP )b(
f(x , y = )z , M3 = x + y + ’ z’
ukaB kutneB
,aynhotnoC f(x, y , z = ) y + ’ yx + x’ zy POS ukab kutneb(
f(x , y , z = ) x(y + ’ z () x + ’ y + z )’ )SOP ukab kutneb(
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naelooB rabajlA isakilpA
.1 ( naralkasneP nagniraJ krowteN gnihctiwS )
nad akub :naadaek haub aud iaynupmem gnay kejbo halada ralkaS .putut
agiT :anahredes gnilap gnabreg kutneb
.1 a x b
tuptuO b akij aynah nad akij ada aynah x akubid x
.2 a x y b tuptuO b akij aynah nad akij ada aynah x nad y akubid yx
.3 a x c b y tuptuO c h akij aynah nad akij ada ayna x uata y akubid x + y
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:kirtsil naiakgnar adap naralkasnep naiakgnar hotnoC
ralkaS .1 DNA akigol :IRES nagnubuh malad upmaL B A
nagnaget rebmuS
kaS .2 ral RO akigol :LELARAP nagnubuh malad A upmaL B
nagnageT rebmuS
.hotnoC hawab id rabmag adap naralkasnep naiakgnar nakatayNnaelooB iserpske malad ini .
x’ y x’ x x y x y’ z z
bawaJ : x’y ( + x + ’ yx )z + x( y + y’ z + z)
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kinortkelE latigiD naiakgnaR .2
reG DNA gnab RO gnabreG ( TON gnabreG retrevni )
.hotnoC isgnuf nakatayN f(x , y , z = ) yx + x’y naiakgnar malad ek.akigol
bawaJ amatrep araC )a( :
audek araC )b(
agitek araC )b(
y
xyx
y
xy +x 'xx
'x
x
yyx
x
yy'x
y'x+yx
'x
yx
x y
y'x
y'x+yx
x'
xyxy
x'y
x x+y 'y
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nanurut gnabreG
DNAN gnabreG ROX gnabreG
nabreG RON g RONX gnabreG
x
y( yx ')
x
y( y+x ')
x
y+x y
x
y+(x y ')
x'
y'x'y' nagned nelavike x
y( y+x ')
x'
y'x + ' y' nagned nelavike
x
y( yx ')
x
y(x + y ') nagned nelavike x
y(x + y ')
x + y
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naelooB isgnuF naanahredeyneP
.hotnoC f(x , y = ) x’y + yx + ’ y ’
idajnem nakanahredesid f(x , y = ) x + ’ y’
:arac 3 nagned nakukalid tapad naelooB isgnuf naanahredeyneP
.1 rabajla araceS
.2 hguanraK ateP nakanuggneM
.3 )isalubaT edotem( yeksulC cM eniuQ edotem nakanuggneM
rabajlA araceS naanahredeyneP .1
hotnoC : .1 f(x , y = ) x + x’y
( = x + x ()’ x + y ) 1 = (x + y ) = x + y
.2 f(x , y , z = ) x’y’ z + x’ zy + yx ’ = x’z(y + ’ y + ) yx ’ = x’z + zx ’
.3 f(x , y , z = ) yx + x’ z + zy = yx + x’z + zy (x + x )’ = yx + x’z + zyx + x’ zy = yx + 1( z + ) x’z + 1( y = ) yx + x’z
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hguanraK ateP .2
.a habuep aud nagned hguanraK ateP y
1 0 m0 m1 x 0 x’y’ x’y m2 m3 1 yx ’ yx
.b agned ateP habuep agit n
zy
00 10
11
01
m0 m1 m3 m2 x 0 x’y’z’ x’y’z x’ zy x’ zy ’
m4 m5 m7 m6 1 yx ’z’ yx ’z zyx zyx ’
.hotnoC .hguanraK ateP nakrabmag ,naranebek lebat nakirebiD
x y z f(x , y , z) 0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1
zy 00
10
11
01
x 0 0 0 0 1
1 0 0 1 1
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b . habuep tapme nagned ateP
zy
00 10
11
01
m0 m1 m3 m2 xw 00 w’x’y’z’ w’x’y’z w’x’ zy w’x’ zy ’
m4 m5 m7 m6 10 w’ yx ’z’ w’ yx ’z w’ zyx w’ zyx ’
m 21 m 31 m 51 m 41 11 yxw ’z’ yxw ’z zyxw zyxw ’
m8 m9 m 11 m 01 01 xw ’y’z’ xw ’y’z xw ’ zy xw ’ zy ’
hotnoC .hguanraK ateP nakrabmag ,naranebek lebat nakirebiD .
w x y z f(w , x , y , z) 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0
zy 00
10
11
01
xw 00 0 1 0 1
10 0 0 1 1
11 0 0 0 1
10 0 0 0 0
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hguanraK ateP nagned naelooB isgnuF isasiminiM kinkeT
.1 nagnasaP aggnatetreb gnay 1 haub aud :
zy
00 10
11
10
xw 00 0 0 0 0
10 0 0 0 0
11 0 0 1 1
01 0 0 0 0
nakanahredesid mulebeS : f(w , x , y , z = ) zyxw + zyxw ’ edeyneP lisaH naanahr : f(w , x , y , z = ) yxw
:rabajla araces itkuB f(w , x , y , z = ) zyxw + zyxw ’ = yxw (z + z )’ = yxw )1( = yxw
.2 dauK aggnatetreb gnay 1 haub tapme :
zy 00
10
11
01
xw 00 0 0 0 0
10 0 0 0 0
11 1 1 1 1
01 0 0 0 0
nakanahredesid mulebeS : f(w , x , y , z = ) yxw ’z + ’ yxw ’z + zyxw + zyxw ’ naanahredeynep lisaH : f(w , x , y , z = ) xw
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:rabajla araces itkuB
f(w , x , y , z = ) yxw + ’ yxw = xw (z + ’ z) = xw )1( = xw
zy 00
10
11
01
xw 00 0 0 0 0
10 0 0 0 0
11 1 1 1 1
01 0 0 0 0
:nial hotnoC
zy 00
01
11
01
xw 00 0 0 0 0
10 0 0 0 0
11 1 1 0 0
10 1 1 0 0
:nakanahredesid mulebeS f(w , x , y , z = ) yxw ’z + ’ yxw ’z + xw ’y’z + ’ xw ’y z’ naanahredeynep lisaH : f(w , x , y , z = ) yw ’
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.3 tetkO aggnatetreb gnay 1 haub napaled :
zy 00
10
11
01
xw 00 0 0 0 0
10 0 0 0 0
11 1 1 1 1
10 1 1 1 1
nakanahredesid mulebeS : f(a , b , c , d = ) yxw ’z + ’ yxw ’z + zyxw + zyxw + ’ xw ’y’z + ’ xw ’y’z + xw ’ zy + wx’ zy ’
naanahredeynep lisaH : f(w , x , y , z = ) w
:rabajla araces itkuB
f(w , x , y , z = ) yw + ’ yw = w(y + ’ y) = w
zy 00
10
11
01
xw 00 0 0 0 0
10 0 0 0 0
11 1 1 1 1
01 1 1 1 1
52
.11.5 hotnoC gnuf nakanahredeS naelooB is f(x , y , z = ) x’ zy + yx ’z + ’ zyx +
zyx .’
bawaJ : :halada tubesret isgnuf kutnu hguanraK ateP
zy 00
10
11
01
x 0 1
1 1 1 1
:naanahredeynep lisaH f(x , y , z = ) zy + zx ’
.21.5 hotnoC t naranebek lebat utaus nakiadnA malad ek nakhamejretid hale anahredeses naiausesreb gnay naelooB isgnuf nakanahredeS .hguanraK ateP
.nikgnum
zy 00
10
11
01
xw 00 0 1 1 1
10 0 0 0 1
11 1 1 0 1
01 1 1 0 1
bawaJ )hguanraK ateP tahil( : f(w , x , y , z = ) yw + ’ zy + ’ w’x’z
62
.31.5 hotnoC ateP nagned naiausesreb gnay naelooB isgnuf isasiminiM.ini hawab id hguanraK
zy
00 10
11
01
xw 00 0 0 0 0
10 0 1 0 0
11 1 1 1 1
01 1 1 1 1
bawaJ )hguanraK ateP tahil( : f(w , x , y , z = ) w + yx ’z
hotnoC naiaseleynep akiJ :ini hawab id itrepes halada 31.5
zy 00
10
11
01
xw 00 0 0 0 0
10 0 1 0 0
11 1 1 1 1
01 1 1 1 1
halada naanahredeynep lisah naelooB isgnuf akam f(w , x , y , z = ) w + w’ yx ’z )5 = laretil halmuj(
nabid anahredes muleb hisam ataynret gnay nakgnid f(w , x , y , z = ) w + yx ’z .)4 = laretil halmuj(
72
.41.5 hotnoC /nagnuluggneP( gnillor gnay naelooB isgnuf nakanahredeS )
.ini hawab id hguanraK ateP nagned naiausesreb
zy 00
10
11
01
xw 00 0 0 0 0
10 1 0 0 1
11 1 0 0 1
01 0 0 0 0
bawaJ : f(w , x , y , z = ) yx ’z + ’ zyx anahredes muleb >== ’
:laminim hibel gnay naiaseleyneP
zy 00
10
11
10
xw 00 0 0 0 0
01 1 0 0 1
11 1 0 0 1
01 0 0 0 0 f(w , x , y , z = ) zx ’ anahredes hibel >===
82
51.5 hotnoC moleK( : gnay naelooB isgnuf nakanahredeS )nahibelreb kop
.ini hawab id hguanraK ateP nagned naiausesreb
zy 00
10
11
01
xw 00 0 0 0 0
10 0 1 0 0
11 0 1 1 0
01 0 0 1 0
bawaJ : f(w , x , y , z = ) yx ’z + zxw + zyw .anahredes muleb hisam
naiaseleyneP :laminim hibel gnay
zy 00
10
11
01
xw 00 0 0 0 0
10 0 1 0 0
11 0 1 1 0
01 0 0 1 0
f(w , x , y , z = ) yx ’ z + zyw anahredes hibel >===
92
.61.5 hotnoC ateP nagned naiausesreb gnay naelooB isgnuf nakanahredeS hawab id hguanraK .ini
dc
00 10
11
01
ba 00 0 0 0 0
10 0 0 1 0
11 1 1 1 1
01 0 1 1 1
bawaJ )sata id hguanraK ateP tahil( : f(a , b , c , d = ) ba + da + ca + dcb
.71.5 hotnoC naelooB isgnuf isasiminiM f(x , y , z = ) x’z + x’y + yx ’z + zy
bawaJ : z’x = x’z(y + y = )’ x’ zy + x’y’z
x’y = x’y(z + z = )’ x’ zy + x’ zy ’ zy = zy (x + x = )’ zyx + x’ zy
f(x , y , z = ) x’z + x’ y + yx ’z + zy = x’ zy + x’y’z + x’ zy + x’ zy + ’ yx ’z + zyx + x’ zy = x’ zy + x’y’z + x’ zy + ’ zyx + yx ’z
tubesret isgnuf kutnu hguanraK ateP :halada
zy 00
10
11
01
x 0 1 1 1
1 1 1
:naanahredeynep lisaH f(x , y , z = ) z + x’ zy ’
03
habuep amil kutnu hguanraK ateP
001 101 111 011 010 110 100 000 00 m0 m1 m3 m2 m6 m7 m5 m4
10 m8 m9 m 11 m 01 m 41 m 51 m13 m 21
11 m 42 m 52 m 72 m 62 m 03 m 13 m 92 m 82
01 m 61 m 71 m 91 m 81 m 22 m 32 m 12 m 02
nanimrecnep siraG
.12.5 hotnoC anahredes isgnuf haliraC )habuep 5 ateP naanuggnep hotnoC( irad f(v , w , x , y , z = ) 2 ,52 ,12 ,71 ,51 ,31 ,11 ,9 ,6 ,4 ,2 ,0( )13 ,92 ,7 bawaJ :
:halada tubesret isgnuf irad hguanraK ateP
zyx 00
0
00
1
10
1
10
0
11
0
11
1
01
1
010
wv 00
1
1
1
1
10
1
1
1
1
11
1
1
1
1
01
1
1
idaJ f(v , w , x , y , z = ) zw + v’w’z + ’ yv ’z
13
naadaeK eraC t’noD 61.5 lebaT
w x y z lamised 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
0 1 2 3 4 5 6 7 8 9
erac t’nod erac t’nod erac t’nod erac t’nod erac t’nod erac t’nod
.52.5 hotnoC isgnuf isasiminiM .71.5 lebaT nakirebiD f anahredeses.nikgnum
71.5 lebaT
a b c d f(a , b , c , d) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
1 0 0 1 1 1 0 1 X X X X X X X X
23
bawaJ :halada tubesret isgnuf irad hguanraK ateP :
dc 00
10
11
01
ba 00
1 0 1 0
10 1 1 1 0
11 X X X X
01 X 0 X X
:naanahredeynep lisaH f(a , b , c , d = ) db + c’d + ’ dc
.62.5 hotnoC naelooB isgnuf isasiminiM f(x , y , z = ) x’ zy + x’ zy + ’ yx ’z + ’yx ’z .aynakigol naiakgnar nakrabmaG .
bawaJ isgnuf akigol naiakgnaR : f(x , y , z halada nakisasiminimid mulebes ):ini hawab id itrepes
x y z
x' zy
x' zy '
yx 'z'
yx 'z
33
da hguanraK ateP nagned isasiminiM :tukireb iagabes hala
zy 00
10
11
01
x 0
1
1
1
1
1
halada isasiminim lisaH f(x , y , z = ) x’y + yx .’
.82.5 hotnoC edok nakanuggnem latigid metsis iagabreB dedoc yraniblamiced B isrevnok kutnu 91.5 lebaT nakirebiD .)DCB( edok ek DC ssecxE -
:tukireb iagabes 3
91.5 lebaT DCB nakusaM edok narauleK ssecxE -3 w x y z f1(w , x , y , z) f2(w , x , y,z) f3(w , x , y , z) f4(w , x , y , z)
0 1 2 3 4 5 6 7 8 9
0 0 0 0 0 0 0 0 1 1
0 0 0 0 1 1 1 1 0 0
0 0 1 1 0 0 1 1 0 0
0 1 0 1 0 1 0 1 0 1
0 0 0 0 0 1 1 1 1 1
0 1 1 1 1 0 0 0 0 1
1 0 0 1 1 0 0 1 1 0
1 0 1 0 1 0 1 0 1 0
x'y
x y
yx '
x' yx+y '
43
)a( f1(w , x , y , z)
zy 00
10
11
01
xw 00
10 1 1 1
11 X X X X
01 1 1 X X
f1(w , x , y , z = ) w + zx + yx = w + x(y + z) )b( f2(w , x , y , z)
zy 00
10
11
01
xw 00 1 1 1
10 1
11 X X X X
01 1 X X
f2(w , x , y , z = ) yx ’z + ’ x’z + x’y = yx ’z + ’ x (’ y + z) )c( f3(w , x , y , z)
zy 00
10
11
01
xw 00 1 1
10 1 1
11 X X X X
01 1 X X
f3(w , x , y , z = ) y’z + ’ zy
53
)d( f4(w , x , y , z)
zy 00
10
11
01
xw 00 1 1
10 1 1
11 X X X X
01 1 X X
f4(w , x , y , z = ) z’
x y zw
f3
f4
f2
f1
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