7/27/2019 5 Analysis Combinational Circuit

1/9

9/23/13

1

Analysis Combinational Circuit

Dr.LeDungHanoi University of Science and Technology

Dr. Le Dung Hanoi University of Science and Technology

Fromagivencombina2onalcircuit

toanalysis

Itsfunc2on(Truthtable,Expressionforms)

Timingdiagram(Testvectors,Delay,Hazard/Glitch)

7/27/2019 5 Analysis Combinational Circuit

2/9

9/23/13

2

Dr. Le Dung Hanoi University of Science and Technology

Anexample(1)

to4Decoder

A0

A1

m0

m1

m

m3

4to1MUX

S1S0

D0

D1

D

D3

Y

a

b

cd

f(a,b,c,d)?

Analysisthiscombina2onalcircuit

Dr. Le Dung Hanoi University of Science and Technology

Anexample()

4to1MUX

S1S0

D0

D1

D

D3

Y

Modularunderstanding

to4Decoder

A0

A1

m0

m1

m

m3

A1

A0

m0

m1

m2

m3

0 0 1 0 0 0

0 1 0 1 0 0

1 0 0 0 1 0

1 1 0 0 0 1

S1

S0

Y

0 0 D0

0 1 D1

1 0 D

1 1 D3

7/27/2019 5 Analysis Combinational Circuit

3/9

9/23/13

3

Dr. Le Dung Hanoi University of Science and Technology

Anexample(3)TruthtableExpressionforms

c d a b f

0 0 0 0 1

f=Y=D00 0 0 1 0

0 0 1 0 0

0 0 1 1 0

0 1 0 0 0

f=Y=D1

0 1 0 1 1

0 1 1 0 0

0 1 1 1 0

1 0 0 0 0

f=Y=D1 0 0 1 0

1 0 1 0 1

1 0 1 1 0

1 1 0 0 0

f=Y=D31 1 0 1 0

1 1 1 0 0

1 1 1 1 1

f=(0,5,10,15)=(0,5,10,15)cdab abcd

f=abcd+abcd+abcd+abcd

Dr. Le Dung Hanoi University of Science and Technology

Anexample(4)Expressionforms

=abcd+abcd+abcd+abcd

c

d

F=Y=

0 0 D0=m0=ab

0 1 D1=m1=ab

1 0 D=m=ab

1 1 D3=m3=ab

f=m0.cd+m1.cd+m.cd+m3.cd

=(ac)(bd) =(a+c)+(b+d)

7/27/2019 5 Analysis Combinational Circuit

4/9

9/23/13

4

Dr. Le Dung Hanoi University of Science and Technology

Anexample(5)Timingdiagramwithnodelay

a

b

d

c

ff=(ac)(bd)

Testvectors:abcd=000010001010111011110111010101000000

Dr. Le Dung Hanoi University of Science and Technology

Anexample(6)Timingdiagramwithdelay

a

b

d

c

f

m1=D1

m0=D0

Testvectors:abcd=00000100011001000101

7/27/2019 5 Analysis Combinational Circuit

5/9

9/23/13

5

Dr. Le Dung Hanoi University of Science and Technology

Sta2cHazard/Glitch

Hazardcondi2on:Asinglevariablechangecausesamomentary output change when no output change

shouldoccur.

Glitch:Themomentaryoutputchange=unwantedtransientpulse

+Sta2c1-hazard=glitch 101(inSOP)+Sta2c0-hazard=glitch 010(onPOS)

Cause:differentdelayintwopaths(seeExample)

Solu2on:Addingredundantterms(producttermsorsumterms)

Dr. Le Dung Hanoi University of Science and Technology

Anexampleofsta2c1-hazarda

c

b

A

B

A

B

Y X1

Y X

A

BY=f

c

AND

OR

AND

INV

a=b=1

c

X

X1

fSta2c1-hazard=glitch

7/27/2019 5 Analysis Combinational Circuit

6/9

9/23/13

6

Dr. Le Dung Hanoi University of Science and Technology

Removingsta2c1-hazardA

B

A

B

A

B

A

B

C

Y X1

Y X

Y X3

a

c

b

Y f

A

AND

ANDA

OR3

AND

Redundantterm=consensusterm

Sta2c

hazard

free

Dr. Le Dung Hanoi University of Science and Technology

Dynamichazard

DynamicHazardon01 DynamicHazardon10

Adynamichazardisthepossibilityofanoutputchangingmorethanonceasaresultofasingleinputchange

Cause:differentdelayinmul2plepaths

Anycircuitthatissta2chazardfreeisalsodynamichazardfree

Anycircuitdynamichazardfree

7/27/2019 5 Analysis Combinational Circuit

7/9

9/23/13

7

Dr. Le Dung Hanoi University of Science and Technology

Anexampleofdynamichazard(1)

Dr. Le Dung Hanoi University of Science and Technology

Anexampleofdynamichazard()

7/27/2019 5 Analysis Combinational Circuit

8/9

9/23/13

8

Dr. Le Dung Hanoi University of Science and Technology

Anexampleofdynamichazard(3)

Dr. Le Dung Hanoi University of Science and Technology

Func2onhazard

Func2on hazards are non-solvable hazards which occurswhenmorethanoneinputvariablechangesatthesame2me.

Func2onhazardscannotbelogicallyeliminatedwithactualspecifica2onofthecircuit.Theonlyrealwaytoavoidsuch

problemsistorestrictthechangingofinputvariablessothatonlyoneinputshouldchangeatanygiven2me.

7/27/2019 5 Analysis Combinational Circuit

9/9

9/23/13

9

Dr. Le Dung Hanoi University of Science and Technology

Hazard-freedesign

Hazardsarehardtodetectbyhand:importanceofsimula2on

Thedangerforhazardsincreaseswhenrise2mesandfall2mesarenotequal

Arehazardsaproblem?Forsynchronouscircuits,theyarenotUnlesstheycontroltheclockofamemoryelementForasynchronouscircuits,theyalwaysareaproblem