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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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Presentation Transcript
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

slide8
f

x1

x2

x3

x3

x2

x1

f

minimization
Minimization
  • Algebraic manipulation
  • Karnaugh maps
  • Tabular methods (Quine-McCluskey)
  • Use a program
slide10
x

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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
slide13
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slide14
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slide15
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slide16
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the function f x y z w m 0 4 8 10 11 12 13 15
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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

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8,10

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4,12

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8,12

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10,11

1

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11

1

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12,13

1

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-

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11,15

1

-

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15

1

1

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13,15

1

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1

slide22
Prime

Minterm

implicant

0

4

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15

p

1

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p

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p

-

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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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