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CE 100 Intro to Logic Design - PowerPoint PPT Presentation

CE 100 Intro to Logic Design. Tracy Larrabee ([email protected]) 3-37A E2 (9-3476) http://soe.ucsc.edu/~larrabee/ce100 2:00 Wednesdays and 1:00 Thursdays Alana Muldoon ([email protected]) Kevin Nelson ([email protected]). When will sections be?. Section 1: MW 6-8 Section 2: TTh 6-8.

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CE 100Intro to Logic Design

• Section 1: MW 6-8

• Section 2: TTh 6-8

Truth tables…

How big are they?

=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

x1

x2

x3

x3

x2

x1

f

• Algebraic manipulation

• Karnaugh maps

• Tabular methods (Quine-McCluskey)

• Use a program

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

• Prime implicants, essential prime implicants

• Find all PIs

• Find all essential PIs

• Add enough else to cover all

• Don’t cares

• Multiple output minimization

• 00

01

01

11

11

10

10

0

0

1

1

01

11

10

00

01

11

10

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

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

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

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

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