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