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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 100 intro to logic design
CE 100Intro to Logic Design


When will sections be
When will sections be?

  • Section 1: MW 6-8

  • Section 2: TTh 6-8


Truth tables

Truth tables…

How big are they?


Converting non canonical to canonical
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




f

x1

x2

x3

x3

x2

x1

f


Minimization
Minimization

  • Algebraic manipulation

  • Karnaugh maps

  • Tabular methods (Quine-McCluskey)

  • Use a program


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


Karnaugh maps
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


  • 00

    00

    01

    01

    11

    11

    10

    10

    0

    0

    1

    1


    00

    01

    11

    10

    00

    01

    11

    10


    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


    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



    The function f x y z w m 0 4 8 10 11 12 13 15

    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


    The function f x y z w m 0 4 8 10 11 12 13 151
    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


    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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