cec 220 digital circuit design implicants wed, sept. 23 cec 220 digital circuit design slide 1 of 10
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Four Variable Karnaugh Maps Implicants and Prime Implicants Wed, Sept. 23 CEC 220 Digital Circuit Design Implicants A single 1 or group of 1’s which can be combined to form a simpler term is called an implicant AB CD Slide 3 of 10TRANSCRIPT
CEC 220 Digital Circuit DesignImplicants
Wed, Sept. 23 CEC 220 Digital Circuit Design Slide 1 of 10
Lecture Outline
Wed, Sept. 23 CEC 220 Digital Circuit Design
ImplicantsPrime ImplicantsEssential Prime Implicants
Slide 2 of 10
Four Variable Karnaugh MapsImplicants and Prime Implicants
Wed, Sept. 23 CEC 220 Digital Circuit Design
• Implicants A single 1 or group of 1’s which can be combined to form a
simpler term is called an implicant
ABCD 00 01 11 10
00 1 1 1
01 1 1
11 1
10 1 1
ABCD , ABC , ABC , ABC , ACD ,, AC ,BCD
Slide 3 of 10
Four Variable Karnaugh MapsImplicants and Prime Implicants
Wed, Sept. 23 CEC 220 Digital Circuit Design
• Prime Implicants An Implicant which can NOT be combined into another
block is called a prime implicant
ABCD 00 01 11 10
00 1 1 1
01 1 1
11 1
10 1 1
ABCD , ABC , ABC , ABC , ACD ,, AC ,BCD
Slide 4 of 10
ABCD , ABC , ABC
Four Variable Karnaugh MapsImplicants and Prime Implicants
Wed, Sept. 23 CEC 220 Digital Circuit Design
• Prime Implicants An Example
ABCD 00 01 11 10
00 1 1
01 1 1 1
11 1 1 1
10 1 1
, ACD , ABBCD , AC,BC, ABDAll Prime Implicants:
Min SOP Expression:
f AC BC ABD
Not all Prime Implicants are essential!!
Slide 5 of 10
Four Variable Karnaugh MapsImplicants and Prime Implicants
Wed, Sept. 23 CEC 220 Digital Circuit Design
• Essential Prime Implicants If a minterm is covered by only one prime implicant then
that prime implicant is an essential prime implicant. ABCD 00 01 11 10
00 1 1
01 1 1 1
11 1 1 1
10 1 1
, ACD , ABBCD , AC ,BC, ABDEssential Prime Implicants?
Min SOP Expression:
f AC BC ABD
BCD , ABD , ACD , AB
Essential Prime Implicants MUST be included in the min SOP expression
Slide 6 of 10
Karnaugh MapsFlowchart for Determining the min SOP Expression
Wed, Sept. 23 CEC 220 Digital Circuit Design
All uncovered 1’s checked?
Are the chosen 1 and its adjacent 1’sand X’s covered by a single term?
Find a minimum set of prime implicantswhich cover the remaining 1’s on the map.
That term is an essential prime implicant. Circle it.
Find all adjacent 1’s and X’s.
Choose a 1 which has not been covered.
yes
yes
no
no
Start
Slide 7 of 10
Karnaugh MapsFlowchart for determining the minimum SOP
Wed, Sept. 23 CEC 220 Digital Circuit Design
• An Example
1
1
1
Essential Prime Implicants:
BC
All uncovered 1’s checked?
Are the chosen 1 and its adjacent 1’sand X’s covered by a single term?
Find a minimum set of prime implicantswhich cover the remaining 1’s on the map.
That term is an essential prime implicant. Circle it.
Find all adjacent 1’s and X’s.
Choose a 1 which has not been covered.
yes
yes
no
no
Start
1
1
1
BD1 1
1
ACf BC BD AC
f
Slide 8 of 10
Karnaugh MapsFlowchart for determining the minimum SOP
Wed, Sept. 23 CEC 220 Digital Circuit Design
• An Example
1 1
1
1
All uncovered 1’s checked?
Are the chosen 1 and its adjacent 1’sand X’s covered by a single term?
Find a minimum set of prime implicantswhich cover the remaining 1’s on the map.
That term is an essential prime implicant. Circle it.
Find all adjacent 1’s and X’s.
Choose a 1 which has not been covered.
yes
yes
no
no
Start
Essential Prime Implicants:
AC
1
ABD1 1 1
ACDf AC ABD ACD
f
BCD ABD
Slide 9 of 10
Next Lecture
Wed, Sept. 23 CEC 220 Digital Circuit Design
Multi-Level Gate Circuits
Slide 10 of 10