Post on 07-Apr-2018
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LogicComponents&QMLogic
Minimization
Dr.A.Sahu
De t of Com . Sc. & En .
IndianInstituteofTechnologyGuwahati
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Outline
Karnaugh mapwith>=5variable
Stu yo ComponentsMultiplexor,Decoder
LogicImplementationUsing MUX&Decoder
4BitAdder
u ne c us ey og c n m zat on MoreExamples
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Manycircuitshavemorethanoneoutput
Cangiveeac aseparatecircuit,orcans aregates
Ex: F=ab +c, G=ab +bcab
a
c
F
c
F
GG
3
(a)
Option 1: Separate circuits Option 2: Shared gates
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Receptioncounter:Whenyoureacha
ReceptionistAsk:WhichDepttoGo?
ecep on s e rec you osome u ngaccordingtoyourAnswer.
: :
Ninput:2N output
MemoryAddressing
Addresstoaparticularlocation
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Decoder:Popularcombinationallogicbuilding,
Convertsinputbinarynumbertoonehighoutput
numbers
,binarynumber
i0
i1
d1
d21
1
0
0i0
i1
d1
d20
0
0
0 i0
i1
d1
d2
i0
i1
d1
d20
1
0
1
1
0
1
0
5
d3 1d3 0 d3 d30 0
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InternaldesignANDgateforeachoutputtodetectinputcombination
DecoderwithenableeOutputsall0ife=0,Regularbehaviorife=1
n nput eco er: outputsi0
i1
d0
d1
d21
1
0
0
0
d0 d3e 1
1
d1
d2
i1i0
i0
i1
d0
d1
d21
1
0
0
0d3i1i0
6
e d3 0
0i0i1
Minterms
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4to16Decoderusingtwo3to8
Decoders
D0toD7
D8toD15
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BooleanFunctionImplementation
usingDecoders
functionsofnvariablescanbeimplemented.
S(x,y,z)= (1,2,4,7), C(x,y,z)=(3,5,6,7) FunctionsSandCcanbeimplementedusinga
3to8decoderandtwo4inputORgates
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X
Z
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ConfigurableFunctionusingDecoder
&Memory
10
Decod
er
100
ab
11 AnyFunction canbe
8rowx1col memory FunctiondependonMemory
10
E ements,D rect
correspondencetoTruthTable
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Mux:Anotherpopularcombinationalbuildingblock
RoutesoneofitsNdatain utstoitsoneout ut basedon
binaryvalueofselectinputs 4inputmux needs2selectinputstoindicatewhichinputtoroute
throu h
8inputmux 3selectinputs
Ninputs log2
(N)selects
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d
i0
212121 i0 (1*i0=i0)
i01
i1d
i1d
i1d (0+i0=
i0)0
0
s1
s0
sa
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i0
i0
i1i1
i2
i3
di2
s1 s0 i3
4x1mux CoversAll
ss
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Muxes CommonlyTogether Nbit
Muxi0i1
2 1da3 Simplifying
s
i0i1
2 1d I0
4-bit2x1Aa2b2
4C44
i0
s0i1
2 1
ds0
I1B
a1
b1 c3
for
i0
s0i1
2 1d
s0a0b0
c2
c1
Ex:Two4bitinputs,A(a3a2a1a0),andB(b3b2b1b0)
s0 c
4bit2x1mux (justfour2x1muxes sharingaselectline)can
selectbetweenAorB
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HOUR MIN
HR1
HR2
MUX
7
Segment
4
4 7
DEMUXMIN1
eco er4
MIN2 4
15
2bitcounter
Ruuning AtKhZ
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ImplementinglogicFunctionusing
MUX
i0
i1
1
0
i2
i3
d1
0
, = m ,
s1 s0
A B
4x1mux
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