CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 CE 100 Intro to Logic Design Tracy Larrabee...
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CMPE100 – Logic Design CMPE100 – Logic Design acy Larrabee – Winter ‘08 acy Larrabee – Winter ‘08 CE 100 CE 100 Intro to Logic Design 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])
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Transcript of CMPE100 – Logic Design Tracy Larrabee – Winter ‘08 CE 100 Intro to Logic Design Tracy Larrabee...
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
CE 100CE 100Intro to Logic DesignIntro 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])
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
When will sections be?When will sections be?
•Section 1: MW 6-8
•Section 2: TTh 6-8
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
Truth tables…Truth tables…
How big are they?
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
0 0 00 0 10 1 00 1 11 0 01 0 11 1 01 1 1
x y z f=xy+yz
Converting non-canonical to Converting non-canonical to canonicalcanonical
=xy(z+z)+(x+x)yz
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
Figure 2.26. Truth table for a three-way light control.
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
f
f
x1
x3 x2
x3
x1 x2
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
MinimizationMinimization
• Algebraic manipulation• Karnaugh maps• Tabular methods (Quine-McCluskey)• Use a program
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy 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 4 00 01 11 10
1 1
1 1
1 1
1 1
00
01
11
10
1
f 1
x 1 x 2 x 3 x 4 00 01 11 10
1 1
1 1
1 1 1
1 1
00
01
11
10
f 2
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
Karnaugh mapsKarnaugh maps
• Prime implicants, essential prime implicants
1. Find all PIs2. Find all essential PIs3. Add enough else to cover all
• Don’t cares• Multiple output minimization
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
00 01 11 10
0
1
00 01 11 10
0
1
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
00 01 11 10
00
01
11
10
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
01 11
00
01
11
x 3 x 4 00 01 11
00
01
11
10
00 01 11 10
00
01
11
10
00 01 11 10
00
01
11
10
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
11= x 5 x 6 10= x 5 x 6
00 01 11 10
00
01
11
10
00 01 11 10
00
01
11
10
00 01 11 10
00
01
11
10
00 01 11 10
00
01
11
10
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
7 inputs
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
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 10 0 0 1 00 0 1 0 00 0 1 1 00 1 0 0 10 1 0 1 00 1 1 0 00 1 1 1 01 0 0 0 11 0 0 1 01 0 1 0 11 0 1 1 11 1 0 0 11 1 0 1 11 1 1 0 01 1 1 1 1
00 01 11 10
00
01
11
10
xyzw
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
x 1 x 2 x 3 x 4 00 01 11 10
1
1 1 1 1
1
00
01
11
10
x 1 x 2 x 4
1
1
x 3 x 4
x 1 x 2 x 4
x 1 x 2 x 3
x 1 x 2 x 3
x 1 x 3 x 4
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
0 0 0 0 0
0 1 0 0 1 0 0 0
1 0 1 0 1 1 0 0
1 0 1 1 1 1 0 1
1 1 1 1
4 8
1012
1113
15
0,4 0 - 0 0 - 0 0 0
1 0 - 0 - 1 0 0 1 - 0 0
1 0 1 - 1 1 0 -
1 1 - 1
0,8
8,104,128,12
10,11 12,13
13,15 1 - 1 1 11,15
0,4,8,12 - - 0 0
List 1 List 2 List 3
The function f ( x,y,z,w) = m(0, 4, 8, 10, 11, 12, 13, 15).
CMPE100 – Logic DesignCMPE100 – Logic DesignTracy Larrabee – Winter ‘08Tracy Larrabee – Winter ‘08
1 0 - 0
1 0 1 -
1 1 0 -
1 1 - 1
1 - 1 1
p 1
p 2
p 3
p 4
p 5
p 6 - - 0 0
Prime implicant
Minterm 0 4 8 10 11 12 13 15
p 1
p 2
p 3
p 4
p 5
Prime implicant
Minterm 10 11 13 15
p 2
p 4
p 5
Prime implicant
Minterm 10 11 13 15
