chương 3 mach logic theo de cuong moi
DESCRIPTION
Mạch logicTRANSCRIPT
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Chng 3: Mch logic
TS. Phm Vn Thnh
1
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Ni dung
Cng OR, cng AND, cng NOT, cng NAND, cng NOR
Cng XOR Cc nh lut ca i s Boolean Xy dng hm logic t bng chn l Rt gn biu thc logic Phng php ba Karnaugh (Bi ging in t mn k thut s TS. Trung Kin)
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Cc cng logic c bn OR, AND, NOT
Trong phn ny, chng ta s tm hiu v i s Boolean (Boolean Algebra), c dng phn tch v thit k cc mch logic.
i s Boolean l mt cng c ton hc tng i n gin v n m t mi quan h gia cc li ra ca mch logic vi cc li vo di dng cc biu thc i s, hay cn gi l biu thc Boolean.
Cu thnh ca biu thc Boolean l cc ton t c bn NOT, AND, OR, NAND, NOR.
Biu thc Boolean khng phi cng c duy nht phn tch, thit k hay m t mch logic. Mt s cng c khc cng c dng kt hp l bng chn l (truth table), s nguyn l (schematic symbols), gin thi gian (timing diagram).
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Cc cng logic c bn OR, AND, NOT
i s Boolean khc bit vi i s thng thng v cc hng s v bin Boolean ch nhn hai gi tr l 0 v 1.
0 - in th t 0 n 0.8V, 1 - in th t 2V n 5V.
Cc hng s v bin Boolean (Constants and Variables)
Logic 0 Logic 1
False True
Off On
Low High
No Yes
Open switch Closed switch
Cc li vo ca mch logic trong cc biu thc Boolean c gi l cc bin Boolean. Cc ton t to nn biu thc gi l cc ton t logic (logic operations). 3 ton t c bn l NOT, AND, OR
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Cc cng logic c bn OR, AND, NOT
Bng chn l m t li ra ca mch logic theo cc trng thi c th c ca li vo.
Cc li vo c th c nhiu kiu k hiu khc nhau: A, B, C, D; x, y, z, v
Bng chn l (Truth Table)
S trng thi c th c ca li vo tun theo cng thc: s trng thi = 2n. Trong n l s li vo.
Cc li vo Cc li ra
Cc trng thi
c th c ca t
hp cc li vo
Kt qu cc li
ra
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Cc cng logic c bn OR, AND, NOT
Khi vit bng chn l, cn ch tnh ln lt ca cc li vo. V d mch in c 2 li vo th cn m t trng thi A=0, B=0 trc. Tip A=0, B=1. Ri l A=1, B=0, v A=1, B=1.
Bng chn l (Truth Table)
A B Y
0 0 1
0 1 0
1 0 1
1 1 0
2 li vo
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Cc cng logic c bn OR, AND, NOT
Bng chn l (Truth Table)
A B C Y
1 0 1
1 1 0
1 1 1
3 li vo
A B C D Y
0 0 0 0
0 0 0 1
0 0 1 0
0 0 1 1
0 1 0 0
0 1 0 1
0 1 1 0
0 1 1 1
1 0 0 0
1 0 0 1
4 li vo
A B C Y
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 0
1 0 1 0
1 1 0 1
1 1 1 0
3 li vo
A B C D Y
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
0 0 1 1 1
0 1 0 0 1
0 1 0 1 0
0 1 1 0 0
0 1 1 1 1
1 0 0 0 0
1 0 0 1 1
1 0 1 0 1
1 0 1 1 1
1 1 0 0 0
1 1 0 1 1
1 1 1 0 0
1 1 1 1 0
4 li vo
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Cc cng logic c bn OR, AND, NOT
Cng HOC OR gate
A B Y = A +B
0 0 0
0 1 1
1 0 1
1 1 1
Hm logic: Y = A + B
Bng chn l:
Biu tng trong mch in:
U1A
7432N
A
BY
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Cc cng logic c bn OR, AND, NOT
Cng HOC OR gate
c im lu : Li ra cng OR bng 1 nu c t nht mt trong cc li vo bng 1. Li ra cng OR bng 0 khi tt c cc li vo bng 0.
Ch l hm logic, bng chn l, biu tng v cng tng ng u c th pht trin ln cho nhiu li vo. Trong cc trng hp ny vn tun theo c im lu ca cng OR 2 li vo trn. Y = x1 + x2 + x3 + + xn
xny
x1
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Cc cng logic c bn OR, AND, NOT
Cng HOC OR gate
V d v ng dng cng OR trong iu khin cng nghip:
Bo ng s xy ra khi c bo ng v qu nhit hoc qu p sut trong mt qu trnh ha hc. Khi nhit vt qu mc cho php, th VT tng ng s ln hn th tham chiu VTR. Tng ng li ra khi so snh TH s cho ra mc 1. Tng t khi p sut vt qu mc cho php, th VP > th tham chiu VPR, lm cho li ra PH = 1. Hai li ra TH v PH c a vo cng OR. V th, ch cn mt trong hai trng hp trn xy ra, hoc gi l c hai trng hp xy ra th li ra cng OR s bt ln mc cao, lp tc bo ng c bt.
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Cc cng logic c bn OR, AND, NOT
Cng HOC OR gate
V d v ng dng cng OR trong iu khin cng nghip:
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Cc cng logic c bn OR, AND, NOT
Cng HOC OR gate
Cc cng logic thc t vn lun l cc mch in t thun ty, ch l chng c thit k lm vic trong nhng ch c bit.
y
D1
D2
x1
x2R1k
y
+Vcc
5V
x3
0V
x2
0V
x1
5V Q3NPN
Q2NPN
Q1NPN
R51k
+Vcc
5V
Dng diode Dng transistor
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Cc cng logic c bn OR, AND, NOT
Cng V AND gate
A B Y = A +B
0 0 0
0 1 0
1 0 0
1 1 1
Hm logic: Y = A . B
Bng chn l:
Biu tng trong mch in:
yx2
x1
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Cc cng logic c bn OR, AND, NOT
Cng V AND gate
c im lu : Li ra cng AND bng 0 nu c t nht mt trong cc li vo bng 0. Li ra cng AND ch bng 1 khi tt c cc li vo bng 1.
Ch l hm logic, bng chn l, biu tng v cng tng ng u c th pht trin ln cho nhiu li vo. Trong cc trng hp ny vn tun theo c im lu ca cng AND 2 li vo trn. Y = x1 . x2 . x3 . . xn
xn
yx1
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Cc cng logic c bn OR, AND, NOT
Cng V AND gate
Transistor AND gate
Diode AND gate
y
y
Q1PNP
Q2PNP
Q3PNP
x4
0V
x5
5V
x6
5V
+5V
D1
D2
x15V
x2
0V
+5V
R21k
R11k
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Cc cng logic c bn OR, AND, NOT
Cng O NOT gate
A
0 1
1 0
Hm logic:
Bng chn l:
Biu tng trong mch in:
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Cc cng logic c bn OR, AND, NOT
Vi 3 cng logic c bn trn, c th thit k nn bt c cng logic hay mch in t s phc tp no.
Tuy nhin, khi cc yu cu thit k ngy cng pht trin, s lng v chng loi cc IC s ngy cng nhiu, chuyn dng ngy cng cao. Cc linh kin in t ny li c th ni vi nhau thit k thnh cc mch in mong mun.
y = ?
y = ?
A
B
B
A
74LS32
74LS08
74LS32
74LS08
T hp ca cc cng c bn
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Cc cng logic c bn OR, AND, NOT
T hp ca cc cng c bn
A
B
C
D
U5
NOT
U6
AND3
U7
OR2
U8
NOT
U9
AND2
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Cc cng logic c bn OR, AND, NOT
T hp ca cc cng c bn
A
B
C
D
E
U10
OR2
U11
AND2
U12
NOT
U13
OR2 U14
AND2
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Cc cng logic c bn OR, AND, NOT
Cng KHNG HOC NOT-OR = NOR
A B
0 0 1
0 1 0
1 0 0
1 1 0
yQ
x
Hm logic:
Bng chn l:
Biu tng trong mch in:
-
Cc cng logic c bn OR, AND, NOT
Cng KHNG V NOT-AND = NAND
A B
0 0 1
0 1 0
1 0 0
1 1 0
Hm logic:
Bng chn l:
Biu tng trong mch in:
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Cc cng logic c bn OR, AND, NOT
BI TP
S5V
y0V
v5V
x0V
z5V
7400-C
7400-B
7400-A
7400-D
74LS20
Q
Vit hm logic v nu chc nng hot ng ca mch in sau.
Vai tr ca chn S l g?
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Cc cng logic c bn OR, AND, NOT
NAND IC h TTL 7400
Trong 7400 c 4 cng NAND 2 li vo
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Cc cng logic c bn OR, AND, NOT
Cc bng mch th
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Cc cng logic c bn
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Ni dung
Cng OR, cng AND, cng NOT, cng NAND, cng NOR
Cng XOR Cc nh lut ca i s Boolean Xy dng hm logic t bng chn l Rt gn biu thc logic Phng php ba Karnaugh (Bi ging in t mn k thut s TS. Trung Kin)
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Cng Hoc Tuyt i XOR eXclusive OR
A B
0 0 0
0 1 1
1 0 1
1 1 0
Hm logic:
Bng chn l:
Biu tng trong mch in:
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Cng Hoc Tuyt i XOR eXclusive OR
74LS86 l IC XOR c 4 cng XOR 2 li vo
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Cng Hoc Tuyt i XOR eXclusive OR
c im lu ca cng XOR:
Cng XOR khng phi l mt cng c bn v n c biu din qua t hp cc ton t AND, OR, NOT.
Vi XOR 2 li vo, u ra s bng 1 khi hai li vo khc nhau u ra bng 0 khi hai li vo ging nhau
Vi XOR nhiu li vo, u ra s bng 1 khi c s l li vo 1 u ra bng 0 khi c chn li vo 1
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Cng Hoc Tuyt i XOR eXclusive OR
Mt s mch to thnh cng XOR t nhng cng logic c bn
a)b)
y
x
y
x
Yu cu: Chng minh hm logic li ra l hm ca cng XOR
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Cng Hoc Tuyt i XOR eXclusive OR
Hm logic:
Bng chn l:
XOR 3 li vo
A B C Y
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 1
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Cng Hoc Tuyt i XOR eXclusive OR
XOR 3 li vo xy dng t XOR 2 li vo
3-in XOR
74LS136
74LS136
74LS136
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Cng Hoc Tuyt i XOR eXclusive OR
Mch to s b 1
S
0V
A40V
A30V
A2
0V
A1
0V
Q4
Q3
Q2
Q1
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Cng Hoc Tuyt i XOR eXclusive OR
To bt kim tra chn l
Theo phng php chn l, khi c l cc s 1 trong chui m, bt chn l s bng 1.
Rt may y ta thy nguyn tc hon ton ging tnh cht ca Hoc Tuyt i.
V th, c th dng cc ca Hoc Tuyt i thit k mch to bt chn l ny
D
5V
C
5V
B
5V
A
0V
-
Cng Hoc Tuyt i XOR eXclusive OR
Hm logic:
Bng chn l:
Ca Khng Hoc Tuyt i XNOR
A B
0 0 1
0 1 0
1 0 0
1 1 1
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Cng Hoc Tuyt i XOR eXclusive OR
Ca Khng Hoc Tuyt i XNOR
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Cng Hoc Tuyt i XOR eXclusive OR
Mch so snh 2 s nh phn
A4
0V
A3
0V
A2
0V
A1
0V
B4
0V
B3
0V
B1
0V
B20V Q
Khi tt c cc cp bt tng ng ging nhau, 4 li ra ca cc ca Khng Hoc Tuyt i s bng 1. Tng ng li ra ca AND 4 li vo s ch th 1. Tt c cc trng hp cn li, A khc B th li ra s bng 0
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Cng XOR
Kt lun tiu m un
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Ni dung
Cng OR, cng AND, cng NOT, cng NAND, cng NOR
Cng XOR Cc nh lut ca i s Boolean Xy dng hm logic t bng chn l Rt gn biu thc logic Phng php ba Karnaugh (Bi ging in t mn k thut s TS. Trung Kin)
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Cc nh lut ca i s Boolean
Gi s, cn xy dng mt mch in c hm logic sau:
Nu khng rt gn hm logic, s cn 1 cng OR 3 li vo, 3 cng AND 3 li
vo, 2 cng NOT. Nh vy, phi dng ti 3 IC (nu c).
Nhng nu bit rt gn:
Y = A(B+C)
Lc ny, ch cn 1 cng AND 2 li vo, 1 cng OR 2 li vo.
S lng linh kin gim i ng k, kch thc mch cng gim i rt nhiu,
li ch hn v mt kinh t.
ng c ca vic s dng i s Boolean
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Cc nh lut ca i s Boolean
Cc nh lut i s Boolean cho hm 1 bin
-
Cc nh lut ca i s Boolean
Cc nh lut i s Boolean cho hm 1 bin
A.A=0A
A.A=AA
A A
A+A=1A
A+A=AA
A A
A.1=A1
AA.0=00
A
A+1=11
AA+0=A
0
A
74LS0874LS08
74LS32 74LS32
74LS0874LS08
74LS3274LS32
A: l 1 bin hoc l 1 biu thc logic bt k
-
Cc nh lut ca i s Boolean
Cc nh lut i s Boolean cho hm nhiu bin
nh lut giao hon (commutative): x + y = y + x (9)
x . y = y . x (10)
nh lut kt hp (associative): x + (y + z) = (x + y) + z = x + y + z (11)
x(yz) = (xy)z = xyz (12)
nh lut phn phi (distributive): x(y + z) = xy + xz (13)
(w + x)(y + z) = wy + wz + xy + xz (14)
-
Cc nh lut ca i s Boolean
Minh ha cho i s Boolean
Php tnh logic
Php tnh OR tng ng h cng tc tip xc mc song song parallel switch contacts
-
Cc nh lut ca i s Boolean
Minh ha cho i s Boolean
Php tnh logic
Php tnh AND tng ng h cng tc tip xc mc ni tip serial switch contacts
-
Cc nh lut ca i s Boolean
Minh ha cho i s Boolean
Cc nh lut ca Boolean
Php tnh AND tng ng h cng tc tip xc mc ni tip A = relay contact
-
Cc nh lut ca i s Boolean
Minh ha cho i s Boolean
Cc nh lut ca Boolean
-
Cc nh lut ca i s Boolean
Cc nh lut i s Boolean cho hm nhiu bin
-
Cc nh lut ca i s Boolean
Cc nh lut i s Boolean cho hm nhiu bin
-
Cc nh lut ca i s Boolean
Cc nh lut i s Boolean cho hm nhiu bin
-
Cc nh lut ca i s Boolean
Mt s nh lut ngoi suy khc
BAACCABA
ABBAA
BABAA
BCACABA
ABAA
AABA
))((
)(
))((
)(Yu cu bin i v chng minh cc nh lut ny
-
Cc nh lut ca i s Boolean
Mt s nh lut ngoi suy khc
-
Cc nh lut ca i s Boolean
Cc nh lut Boolean cho XOR
-
Cc nh lut ca i s Boolean
2 nh lut De Morgan
Hai nh l quan trng trong i s Boolean c ng gp bi nh ton hc ni ting De Morgan. Hai nh l ny cc k quan trng trong vic n gin ha cc hm logic. C th l vic c th chuyn t tng thnh tch, v ngc li, tch thnh tng.
x v y u c th l cc biu thc logic phc tp khc
Ngoi ra, 2 nh l ny cn p dng cho nhiu bin
-
Cc nh lut ca i s Boolean
2 nh lut De Morgan
ngha ca nh lut De Morgan
Bin i php tnh t tng thnh tch
Chuyn t NOR thnh NOT + AND
A.B
B
A
A+BA+B
B
A
74LS04
74LS04
74LS0874LS0474LS32
74LS02
B.ABA
-
Cc nh lut ca i s Boolean
2 nh lut De Morgan
ngha ca nh lut De Morgan
A+BA.BA.B
B
A
B
A
74LS3274LS08
74LS04
74LS04
74LS04
7400
BAB.A
Bin i php tnh t tch thnh tng
Chuyn t NAND thnh NOT + OR
-
Cc nh lut ca i s Boolean
Tnh vn nng ca cng NAND v NOR
Tt c cc biu thc Boolean bao gm hng lot t hp khc
nhau ca cc ton t c bn AND, OR, NOT. V th, bt c biu
thc no cng u c th biu din thng qua cc ton t ny.
Trong cc cng hc trn, 2 cng NAND v NOR c im rt
c bit l c th to nn cc cng AND, OR, NOT. Chnh v th,
ch cn dng duy nht cng NAND, hoc duy nht cng NOR l
c th lp rp nn mch in
-
Cc nh lut ca i s Boolean
Tnh vn nng ca cng NAND v NOR
NADN gate produce OR
A+B
B
A
NADN gate produce AND
ABB
A
NADN gate produce NOT
A.A = AA
7400
7400
7400
74007400
7400
Tng t chng minh cho cng NOR cng to ra 3 cng c bn OR, AND, NOT
-
Cc nh lut ca i s Boolean
Tnh vn nng ca cng NAND v NOR
CBABAABCABy
BABABAy
DABCCDABy
))()((
))((
Ch : Hm ca cng XOR
Hm ca XNOR
S dng De Morgan, chng minh: =
-
Cc nh lut ca i s Boolean
V d v s dng De Morgan
Dng De Morgan n gin ha mch in sau:
-
Cc nh lut ca i s Boolean
V d v s dng De Morgan
Dng De Morgan n gin ha mch in sau:
-
Cc nh lut Boolean
Kt lun tiu m un
-
Ni dung
Cng OR, cng AND, cng NOT, cng NAND, cng NOR
Cng XOR Cc nh lut ca i s Boolean Xy dng hm logic t bng chn l Rt gn biu thc logic Phng php ba Karnaugh (Bi ging in t mn k thut s TS. Trung Kin)
-
Xy dng hm logic t bng chn l
Trong thit k mch in, cc nh thit k thng bt u bng bng chn l, cng c dng m t chnh xc hot ng ca mch in s. Nhim v ca vic thit k l t bng chn l tm ra mch in ph hp. Mun vy th cn xc nh c hm logic, tc l tm ra mi quan h ton t gia cc li vo.
-
Xy dng hm logic t bng chn l
Cc tch c bn (fundamental products)
Tch c bn l cch n gin nht m t s kt hp ca 2 tn hiu bng mt cng AND 2 li vo.
V d vi 2 tn hiu, s c 4 kh nng c th xy ra:
-
Xy dng hm logic t bng chn l
Cc tch c bn (fundamental products)
Khi li vo trng thi 0, ng tn hiu tng ng c biu din bng gi tr b ca n. Mi tch c bn ny c gi l mt Minterm mi
-
Xy dng hm logic t bng chn l
Cc tng c bn (fundamental summaries)
Khc vi tch c bn, y, khi li vo bng 1 th ng tn hiu tng ng c dng b
-
Xy dng hm logic t bng chn l
Cc tng c bn (fundamental summaries)
Mt s c im ca Minterm v Maxterm
Minterm v Maxterm ca cng mt ch s l b ca nhau:
Cng logic ca cc minterm = 1
Tch logic ca cc maxterm = 0
Hai minterm nhn vi nhau = 0
Cng ca hai maxterm = 1
(Yu cu SV chng minh)
-
Xy dng hm logic t bng chn l
Xy dng hm logic bng phng php Minterm (SOP Sum of Products)
Cho trc bng chn l, tm biu thc Boolean bng cch cng cc tch c bn ca cc u ra c gi tr 1
A B y
0 0 0
0 1 1 AB
1 0 1 AB
1 1 0
BA
-
Xy dng hm logic t bng chn l
Xy dng hm logic bng phng php Minterm
V d khc:
-
Xy dng hm logic t bng chn l
Xy dng hm logic bng phng php Minterm
V d khc:
Cu hi: Hm logic
v mch in hp l cha?
BC+AC+AB
-
Xy dng hm logic t bng chn l
Xy dng hm logic bng phng php Minterm
V d t phn trc: Chng minh:
x1 x2 x3 y
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 1
- Suy hm logic t bng chn l ca v phi - T , s dng i s Boolean v De Morgan khai trin v tri - So snh kt qu hai bn chng minh.
-
Xy dng hm logic t bng chn l
Xy dng hm logic bng phng php Maxterm
Hm logic l tch ca cc tng c bn ca cc li ra c gi tr 0
A B y
0 0 0 A+B
0 1 1
1 0 1
1 1 0 A+B
BA
-
Xy dng hm logic t bng chn l
POS chun
Ch , POS c th c cc dng khc:
Trong biu thc 1, c th c 3 li vo A, B, C. Nhng tha s th nht ch c A v B.
Trong biu thc 2, c 5 li vo A, B, C, D, E. Nhng trong tha s th nht thiu D, E, tha s th 2 thiu A, B, tha s th 3 thiu A, E.
Dng POS chun: l tch cc tng m trong c ht tt c cc bin.
-
Xy dng hm logic t bng chn l
POS chun
V d: Bin i biu thc Boolean sau v dng POS chun
Biu thc ny chng t c 4 li vo A, B, C, D.
Tha s th nht thiu D. V th n c bin i nh sau:
Tha s th 2 thiu A:
Tha s th 3 l dng POS chun. Vy, biu thc POS chun ca c biu thc s l:
-
Xy dng hm logic t bng chn l
Bin i t SOP sang dng POS chun
Cc bc thc hin nh sau:
Xc nh trng thi nh phn tng ng ca cc li vo ca cc tch c bn
Xc nh cc trng thi nh phn cn li khng thuc nhm lit k trn
Vit cc tng c bn ca cc trng thi va xc nh trong bc 2.
-
Xy dng hm logic t bng chn l
Bin i t SOP sang dng POS chun
V d:
Bin i biu thc SOP sau v dng POS chun:
Cc trng thi nh phn tng ng l:
000 + 010 + 011 + 101 + 111
Cc trng thi nh phn khng thuc nhm ny l:
001, 100, 110
Do , dng POS chun ca biu thc trn l:
-
Xy dng hm logic t bng chn l
T SOP thit lp bng chn l
Cho 1 biu thc SOP nh sau:
-
Xy dng hm logic t bng chn l
T POS thit lp bng chn l
Cho 1 biu thc POS nh sau:
-
Xy dng hm logic t bng chn l
So snh 2 phng php SOP v POS
Tm hm logic t phng php minterm SOP
Tm hm logic t phng php minterm POS
-
Xy dng hm logic t bng chn l
Kt lun tiu m un
-
Ni dung
Cng OR, cng AND, cng NOT, cng NAND, cng NOR
Cng XOR Cc nh lut ca i s Boolean Xy dng hm logic t bng chn l Rt gn biu thc logic Phng php ba Karnaugh (Bi ging in t mn k thut s TS. Trung Kin)
-
Rt gn hm logic
Chng ta ch yu s s dng cc nh lut ca i s Boolean rt gn cc
hm logic. phn sau s c thm cng c ba Karnaugh. Ch mt iu l
khng c mt cng c no kim tra xem hm rt gn l ti gin hay
cha. V th, ngi thit k cn phi da vo kinh nghim tm ra p n
cui cng.
Nhn chung, vic rt gn thng qua mt s bc chnh sau:
Bin i biu thc v dng tng ca cc tch c bn SOP (sum of
products). Vic ny c thc hin bng vic nhn cc tha s trong
ngoc v dng 2 nh lut De Morgan.
Nhm cc s hng (cc tch c bn) c th vi nhau. Khi ta c th gim
c cc bin.
-
Rt gn hm logic
Tr li mt mch in c suy ra t bng chn l bng phng php minterm, vi cu hi l mch ny v hm logic ca n thc s ti gin cha?
-
Rt gn hm logic
Chng ta th rt gn:
Hm y l dng SOP, v th ch cn tm xem c th c cc s hng no c th nhm li vi nhau
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Rt gn hm logic
RT GN MCH IN
Xt mt mch in sau:
rt gn mch, chng ta kh c th nhn cc cng logic on nhn. Thng thng, cn phi vit ra hm logic tng ng ca mch in ny. Sau , ti gin hm tm ra mch in ti gin
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Rt gn hm logic
RT GN MCH IN
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Rt gn hm logic
Hai mch in hon ton tng ng
y l mt hnh nh khc minh chng tnh cc k thit yu ca vic rt gn hm logic hay mch logic
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Rt gn hm logic
Mt bn sinh vin lp rp mt mch in nh trn. Bn cho mch in ny bao nhiu im (/10)?
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Rt gn hm logic
Rt gn cc hm logic sau:
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Rt gn hm logic
V d: Rt gn hm sau:
p dng De Morgan cho s hng u tin:
Tip tc De Morgan cho 2 tha s:
p dng nh lut phn phi:
Tip tc bin i
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Rt gn hm logic
Mch no trong s nhng mch sau tng ng:
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Rt gn hm logic
Tm mch in tng ng:
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Rt gn hm logic
Tm mch in tng ng:
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Rt gn hm logic
Kt lun tiu m un