1

1

Chng 4Mch logic

Th.S ng Ngc KhoaKhoa in - in T

2

Biu din bng biu thc i s

Mt hm logic n bin bt k lun c thbiu din di dng: Tng ca cc tch (Chun tc tuyn - CTT):

l dng tng ca nhiu thnh phn m mithnh phn l tch ca y n bin.

Tch ca cc tng (Chun tc hi CTH): ldng tch ca nhiu thnh phn m mithnh phn l tng ca y n bin.

2

3

Dng chun tc tuyn

F=ABC+ ABC + ABC + ABC

Dng chun tc hi

F = (A+B+C)(A+B+C)(A+B+C)(A+B+C)

Biu din bng biu thc i s

= )6,5,2,1(FA B C F

0

0

00

00

000 0

0

0

0

0

1

1

11

1

11

1

1

0

111

11

0

1

1

0

3

21

4

7

6

5

V tr

= )7,4,3,0(F

4

Biu din bng biu thc i s

X = 1 ghi XX = 1 ghi X

X = 0 ghi XX = 0 ghi X

Lu cc gi tr 0Lu cc gi tr 1

Tch ca cc tngTng ca cc tch

Chun tc hiChun tt tuyn

3

5

Rt gn mch logic

Lm cho biu thc logic n gin nht v do vy mch logic s dng t cng logic nht.

Hai mch sau y l tng ng nhau

6

Phng php rt gn

C hai phng php chnh rt gnmt biu thc logic. Phng php bin i i s: s dng

cc nh l v cc php bin i Boolean rt gn biu thc.

Phong php ba Karnaugh: s dng baKarnuagh rt gn biu thc logic

4

7

Phng php bin i i s

S dng cc nh l v cc php bin iBoolean rt gn biu thc.

V d:

BD(A+B)(A+B+D)DBC+AD(B+C)AC(ABD)+ABCD+ABCA(B+C)ABC+ABC+ABCA(B+C)ABC+AB(AC)

Rt gnBiu thc ban u

?

8

V d 4-1

Hy rt gn mch logic sau

5

9

Bi ton thit k

Hy thit k mt mch logic c: Ba ng vo Mt ng ra Ng ra mc cao ch khi a s ng vo

mc cao

10

Trnh t thit k

Bc 1: Thit lp bng chn tr.

11111011

110100011110

001001000000

xCBA

Mchlogic

ABC

x

6

11

Trnh t thit k

Bc 2: Thit lp phng trnh t bngchn tr.

1111

10111101

000111100010

01000000xCBA

A.B.C

A.B.C

A.B.CA.B.C

ABCCABCBABCAx +++=

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Trnh t thit k

Bc 3: Rt gn biu thc logic

ABACBCxABCCABABCCBAABCBCAx

ABCCABCBABCAx

++=+++++=

+++=

7

13

Trnh t thit k

Bc 4: V mch logic ng vi biu thclogic va rt gn

ABACBCx ++=

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V d 4-1

Hy thit k mt mch logic c 4 ng voA, B, C, D v mt ng ra. Ng ra ch mc cao khi in p (c miu t bi 4 bit nh phn ABCD) ln hn 6.

8

15

Kt qu

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V d 4-3

Thit k mch logic iu khin mch phunnhin liu trong mch t nh sau:

Cm bin c kh cn t

Cm bin ngn la gia A v B

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17

Ba Karnaugh

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Phng php ba Karnaugh

Ging nh bng chn tr, ba Karnaugh l mt cch th hin mi quan h gia cc mc logic ngvo v ng ra.

Ba Karnaugh l mt phng php c s dng n gin biu thc logic.

Phng php ny d thc hin hn phng phpi s.

Ba Karnaugh c th thc hin vi bt k s ngvo no, nhng trong chng trnh ch kho st sng vo nh hn 6.

10

19

nh dng ba Karnaugh

Mi mt trng hp trong bng chn trtng ng vi 1 trong ba Karnaugh

Cc trong ba Karnaugh c nh s saocho 2 k nhau ch khc nhau 1 gi tr.

Do cc k nhau ch khc nhau 1 gi trnn chng ta c th nhm chng li tomt thnh phn n gin hn dng tngcc tch.

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Bng chn tr K-map

Y

0101

Z

1011

X

0011

Gi tr 0 Gi tr 1 Gi tr 2 Gi tr 3

1

1

0

1

Mt v d tng ng gia bng chn tr vba Karnaugh

0

1

2

3

Y

Y

X XZ