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CE 100 Intro to Logic Design

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). When will sections be?. Section 1: MW 6-8 Section 2: TTh 6-8.

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CE 100 Intro to Logic Design

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  1. CE 100Intro 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. When will sections be? • Section 1: MW 6-8 • Section 2: TTh 6-8

  3. Truth tables… How big are they?

  4. Converting non-canonical to canonical =xy(z+z)+(x+x)yz x y z f=xy+yz 0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

  5. Perfect time to talk about Algebraic Identities….

  6. Figure 2.26. Truth table for a three-way light control.

  7. f x1 x2 x3 x3 x2 x1 f

  8. Minimization • Algebraic manipulation • Karnaugh maps • Tabular methods (Quine-McCluskey) • Use a program

  9. x x 1 2 x x 3 4 00 01 11 10 00 1 1 x 2 01 1 1 1 x 3 11 1 1 x 4 f 1 10 1 1 x 1 x 3 f 1 x 1 x x 1 2 x x x 3 3 4 00 01 11 10 f 2 x 2 00 1 1 x 3 01 1 1 x 4 11 1 1 1 10 1 1 f 2

  10. Karnaugh maps • Prime implicants, essential prime implicants • Find all PIs • Find all essential PIs • Add enough else to cover all • Don’t cares • Multiple output minimization

  11. 00 00 01 01 11 11 10 10 0 0 1 1

  12. 00 01 11 10 00 01 11 10

  13. 00 00 01 01 11 11 10 10 00 00 01 01 11 11 10 10 x x 3 4 01 11 00 01 11 00 00 01 01 11 11 10

  14. 00 00 00 00 01 01 01 01 11 11 11 11 10 10 10 10 00 00 00 00 01 01 01 01 11 11 11 11 10 10 10 10 x x = 11 x x = 10 5 6 5 6

  15. 7 inputs

  16. 00 01 11 10 00 01 11 10 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 xy zw

  17. The function f ( x,y,z,w) =  m(0, 4, 8, 10, 11, 12, 13, 15). List 1 List 2 List 3 0 0 0 0 0 - 0 0 - - 0 0 0 0,4 0,4,8,12 0,8 - 0 0 0 4 0 1 0 0 8,10 1 0 - 0 8 1 0 0 0 4,12 - 1 0 0 10 1 0 1 0 8,12 1 - 0 0 12 1 1 0 0 10,11 1 0 1 - 11 1 0 1 1 12,13 1 1 0 - 13 1 1 0 1 11,15 1 - 1 1 15 1 1 1 1 13,15 1 1 - 1

  18. Prime Minterm implicant 0 4 8 10 11 12 13 15 p 1 0 - 0 1 p 1 0 1 - 2 p 1 1 0 - 3 p 1 - 1 1 4 p 1 1 - 1 5 p - - 0 0 6 Prime Minterm Prime Minterm implicant 10 11 13 15 implicant 10 11 13 15 p 1 p p 2 2 p p 4 3 p p 5 4 p 5

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