1. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 CE 100 Intro to Logic Design Tracy Larrabee (larrabee@soe.ucsc.edu) –3-37A E2 (9-3476) –http://soe.ucsc.edu/~larrabee/ce100 –2:00 Wednesdays and 1:00 Thursdays Alana Muldoon (newmoon@soe.ucsc.edu) Kevin Nelson (rknelson@ucsc.edu)

2. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 When will sections be? Section 1: MW 6-8 Section 2: TTh 6-8

3. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 Truth tables… How big are they?

4. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1 x y z f=xy+yz Converting non-canonical to canonical =xy(z+z)+(x+x)yz

5. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08

6. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08

7. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 Figure 2.26. Truth table for a three-way light control.

8. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08

9. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 Minimization Algebraic manipulation Karnaugh maps Tabular methods (Quine-McCluskey) Use a program

10. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 f 1 f 2 x 2 x 3 x 4 x 1 x 3 x 1 x 3 x 2 x 3 x 4 x 1 x 2 x 3 x 4 00011110 11 11 11 11 00 01 11 10 1 f 1 x 1 x 2 x 3 x 4 00011110 11 11 111 11 00 01 11 10 f 2

11. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08

12. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 Karnaugh maps Prime implicants, essential prime implicants 1.Find all PIs 2.Find all essential PIs 3.Add enough else to cover all Don’t cares Multiple output minimization

13. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 00011110 0 1 00011110 0 1

14. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 00011110 00 01 11 10

15. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 0111 00 01 11 x 3 x 4 000111 00 01 11 10 00011110 00 01 11 10 00011110 00 01 11 10

16. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 11= x 5 x 6 10= x 5 x 6 00011110 00 01 11 10 00011110 00 01 11 10 00011110 00 01 11 10 00011110 00 01 11 10

17. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08

18. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 7 inputs

19. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 The function f ( x,y,z,w) =  m(0, 4, 8, 10, 11, 12, 13, 15). x y z w f 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 00011110 00 01 11 10 xy zw

20. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08

21. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 0 0000 0100 1000 1010 1100 1011 1101 1111 4 8 10 12 11 13 15 0,4 0-00 -000 10-0 -100 1-00 101- 110- 11-1 0,8 8,10 4,12 8,12 10,11 12,13 13,15 1-1111,15 0,4,8,12 --00 List 1List 2List 3 The function f ( x,y,z,w) =  m(0, 4, 8, 10, 11, 12, 13, 15).

22. CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 10-0 101- 110- 11-1 1-11 p 1 p 2 p 3 p 4 p 5 p 6 --00 Prime implicant Minterm 0481011121315 p 1 p 2 p 3 p 4 p 5 Prime implicant Minterm 10111315 p 2 p 4 p 5 Prime implicant Minterm 10111315