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DON’T CARE CONTIONDON’T CARE CONTION
RULE:-RULE:-
• Karnaugh map usingKarnaugh map using• Encircle the actual 1s on the karnaugh Encircle the actual 1s on the karnaugh
mapin largest grops that we can fint the mapin largest grops that we can fint the by also treating the don’t care as 1s ,by also treating the don’t care as 1s ,
• 1s have been including grops,don’t care 1s have been including grops,don’t care by visualizing them as 0s.by visualizing them as 0s.
• Example:-Example:-
F(w,x,y,z)=F(w,x,y,z)=£( 1,3,7,11,15)£( 1,3,7,11,15)
Has the don’t care contion:-Has the don’t care contion:-
d(w,x,y,z)=d(w,x,y,z)=£(0,2,5)£(0,2,5)
Karnaugh map:-Karnaugh map:-
0100010001X0X11X
Yz Yz Yz Yz
WX
WX
WX
WX
F(w,x,y,z)=YZ+WZ
SUM OF PRODUCT SUM OF PRODUCT &PRODUCT OF SUM&PRODUCT OF SUM
• PRODUCT TERM PRODUCT TERM
• SUMTERMSUMTERM
• SUM OF PRODUCTS EXPRESSIONSUM OF PRODUCTS EXPRESSION Example:-Example:- (1) Y= ((B.C).(B.C))(1) Y= ((B.C).(B.C))
• PRODUCT OF SUM EXPRESSIONPRODUCT OF SUM EXPRESSION
Example:-Example:- y=(B+C).(B+C)y=(B+C).(B+C)
• TRUTH TABLE:-TRUTH TABLE:-
00110010
0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1
O/P YA B C
SOP DIAGRAM:-SOP DIAGRAM:-
A A B B C CA A B B C C Y= ((B.C).(B.C))Y= ((B.C).(B.C))
POS DIAGRAM:-
A A B B C C y=(B+C).(B+C)y=(B+C).(B+C)
BCD ADDER:-BCD ADDER:-8+7=158+7=15 1000+01111000+0111 (8)(4)(2)(1)(8)(4)(2)(1)
1 0 0 01 0 0 0 + 0 1 1 1+ 0 1 1 1 1 1 1 11 1 1 1 ILLEGAL CODEILLEGAL CODE + 0 1 1 0+ 0 1 1 0 ADD 6ADD 6 1 0 1 0 11 0 1 0 1 =5PERMITED CODE=5PERMITED CODE
WITH A CARRY GENARATEDWITH A CARRY GENARATED
MULTIPLEXERS:-MULTIPLEXERS:-
M control signals
n inputsSignal multiplexer 1
o/psignal
• TRUTH TABLE:-TRUTH TABLE:-
I0
I1
I2
I3
Y0101
0011
S0S1
DIAGRAM:-
I3
I2
I1
I0
S1S0
DEMULTIPLEXER:-DEMULTIPLEXER:-
M control signals
n out putsSignal Demultiplexer 1
i/psignal
• Truth tableTruth table
1 0 0 00 1 0 00 1 0 00 0 0 1
0 0 0 1 0 0 0 1
0 0 0 0
OUT PUTD0 D1 D2 D3
I/PA B
ENABLEE
D0=ABE
D1=ABE
D2=ABE
D3=ABE
• Diagram:-Diagram:-
E A B
D0
D1
D2
D3
