CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 CE 100 Intro to Logic Design Tracy Larrabee –3-37A E2 (9-3476) –http://soe.ucsc.edu/~larrabee/ce100.

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Presentation transcript:

CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 CE 100 Intro to Logic Design Tracy Larrabee –3-37A E2 (9-3476) – –2:00 Wednesdays and 1:00 Thursdays Alana Muldoon Kevin Nelson

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

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

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

CMPE100 – Logic Design Tracy Larrabee – Winter ‘08

CMPE100 – Logic Design Tracy Larrabee – Winter ‘08

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

CMPE100 – Logic Design Tracy Larrabee – Winter ‘08

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

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 f 1 x 1 x 2 x 3 x f 2

CMPE100 – Logic Design Tracy Larrabee – Winter ‘08

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

CMPE100 – Logic Design Tracy Larrabee – Winter ‘

CMPE100 – Logic Design Tracy Larrabee – Winter ‘

CMPE100 – Logic Design Tracy Larrabee – Winter ‘ x 3 x

CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 11= x 5 x 6 10= x 5 x

CMPE100 – Logic Design Tracy Larrabee – Winter ‘08

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

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 xy zw

CMPE100 – Logic Design Tracy Larrabee – Winter ‘08

CMPE100 – Logic Design Tracy Larrabee – Winter ‘ , ,8 8,10 4,12 8,12 10,11 12,13 13, ,15 0,4,8, List 1List 2List 3 The function f ( x,y,z,w) =  m(0, 4, 8, 10, 11, 12, 13, 15).

CMPE100 – Logic Design Tracy Larrabee – Winter ‘ p 1 p 2 p 3 p 4 p 5 p Prime implicant Minterm p 1 p 2 p 3 p 4 p 5 Prime implicant Minterm p 2 p 4 p 5 Prime implicant Minterm