The document discusses the don't care condition rule for Karnaugh maps. It states that don't cares should be treated as 1s and included in the largest groups when minimizing logic expressions. An example problem with a Karnaugh map is given showing don't cares treated as 1s and the minimized sum of products expression. Truth tables, logic diagrams, multiplexers, demultiplexers and binary coded decimal adders are also briefly discussed.

1. DON’T CARE CONTION RULE:- Karnaugh map using Encircle the actual 1s on the karnaugh mapin largest grops that we can fint the by also treating the don’t care as 1s , 1s have been including grops,don’t care by visualizing them as 0s.

2. Example:- F(w,x,y,z)= £( 1,3,7,11,15) Has the don’t care contion:- d(w,x,y,z)= £(0,2,5)

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. SUM OF PRODUCT &PRODUCT OF SUM PRODUCT TERM SUMTERM SUM OF PRODUCTS EXPRESSION Example:- (1) Y= ((B.C).(B.C))

5. PRODUCT OF SUM EXPRESSION Example:- y=(B+C).(B+C)

6. TRUTH TABLE:- 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. SOP DIAGRAM:- A A B B C C Y= ((B.C).(B.C))

8. POS DIAGRAM:- A A B B C C y=(B+C).(B+C)

9. BCD ADDER:- 8+7=15 1000+0111 (8)(4)(2)(1) 1 0 0 0 + 0 1 1 1 1 1 1 1 ILLEGAL CODE + 0 1 1 0 ADD 6 1 0 1 0 1 =5PERMITED CODE WITH A CARRY GENARATED

10. MULTIPLEXERS:- M control signals n inputs Signal multiplexer 1 o/p signal

11. TRUTH TABLE:- 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. DEMULTIPLEXER:- M control signals n out puts Signal Demultiplexer 1 i/p signal

13. Truth table 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. Diagram:- E A B D0 D1 D2 D3