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### digital

1. 1. DON’T CARE CONTION <ul><li>RULE:- </li></ul><ul><li>Karnaugh map using </li></ul><ul><li>Encircle the actual 1s on the karnaugh mapin largest grops that we can fint the by also treating the don’t care as 1s , </li></ul><ul><li>1s have been including grops,don’t care by visualizing them as 0s. </li></ul>
2. 2. <ul><li>Example:- </li></ul><ul><li>F(w,x,y,z)= £( 1,3,7,11,15) </li></ul><ul><li>Has the don’t care contion:- </li></ul><ul><li>d(w,x,y,z)= £(0,2,5) </li></ul>
3. 3. Karnaugh map:- Yz Yz Yz Yz WX WX WX WX F(w,x,y,z)=YZ+WZ 0 1 0 0 0 1 0 0 0 1 X 0 X 1 1 X
4. 4. SUM OF PRODUCT &PRODUCT OF SUM <ul><li>PRODUCT TERM </li></ul><ul><li>SUMTERM </li></ul><ul><li>SUM OF PRODUCTS EXPRESSION </li></ul><ul><li>Example:- </li></ul><ul><li>(1) Y= ((B.C).(B.C)) </li></ul>
5. 5. <ul><li>PRODUCT OF SUM EXPRESSION </li></ul><ul><li>Example:- </li></ul><ul><li>y=(B+C).(B+C) </li></ul>
6. 6. <ul><li>TRUTH TABLE:- </li></ul>0 0 1 1 0 0 1 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 O/P Y A B C
7. 7. SOP DIAGRAM:- <ul><li>A A B B C C </li></ul>Y= ((B.C).(B.C))
8. 8. POS DIAGRAM:- A A B B C C y=(B+C).(B+C)
9. 9. BCD ADDER:- <ul><li>8+7=15 1000+0111 </li></ul><ul><li>(8)(4)(2)(1) </li></ul><ul><li> 1 0 0 0 </li></ul><ul><li>+ 0 1 1 1 </li></ul><ul><li>1 1 1 1 ILLEGAL CODE </li></ul><ul><li>+ 0 1 1 0 ADD 6 </li></ul><ul><li>1 0 1 0 1 =5PERMITED CODE </li></ul><ul><li>WITH A CARRY GENARATED </li></ul>
10. 10. MULTIPLEXERS:- M control signals n inputs Signal multiplexer 1 o/p signal
11. 11. <ul><li>TRUTH TABLE:- </li></ul>DIAGRAM:- I 3 I 2 I 1 I 0 S1 S0 I 0 I 1 I 2 I 3 Y 0 1 0 1 0 0 1 1 S0 S1
12. 12. DEMULTIPLEXER:- M control signals n out puts Signal Demultiplexer 1 i/p signal
13. 13. <ul><li>Truth table </li></ul>D0=ABE D1=ABE D2=ABE D3=ABE 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 OUT PUT D0 D1 D2 D3 I/P A B ENABLE E
14. 14. <ul><li>Diagram:- </li></ul>E A B D0 D1 D2 D3
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