Simplification Using Karnaugh-Map (K-Map) - New …bai/EGC220/4-Simiplication Using K-Map.pdfEGC220...
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EGC220 Digital Logic Fundamentals 9/20/2017 Simplification Using K-Map 1 EGC220 Digital Logic Fundamentals Simplification Using Karnaugh-Map (K-Map) Baback Izadi Division of Engineering Programs [email protected] SUNY – New Paltz Elect. & Comp. Eng. Test 1: Closed book and notes, no calculator Number systems Convert any base to any base Quick conversion between base 2, 4, 8, and 16 Add, subtract, multiply in any base Logic gate implementation of a Boolean function Boolean properties and laws Simplification of Boolean algebra using Boolean laws Representing Boolean functions in terms of Sum of min-terms, product of max-terms, standard sum of products, standard product of sums, minimum sum of products, minimum product of sums Representing Boolean functions using all NAND or NOR gates.
Transcript of Simplification Using Karnaugh-Map (K-Map) - New …bai/EGC220/4-Simiplication Using K-Map.pdfEGC220...
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 1
EGC220
Digital Logic Fundamentals
Simplification Using Karnaugh-Map(K-Map)
Baback IzadiDivision of Engineering [email protected]
SUNY – New PaltzElect. & Comp. Eng.
Test 1: Closed book and notes, no calculator Number systems Convert any base to any base Quick conversion between base 2, 4, 8, and 16 Add, subtract, multiply in any base
Logic gate implementation of a Boolean function
Boolean properties and laws
Simplification of Boolean algebra using Boolean laws
Representing Boolean functions in terms of Sum of min-terms, product of max-terms, standard sum of
products, standard product of sums, minimum sum of products, minimum product of sums
Representing Boolean functions using all NAND or NOR gates.
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 2
SUNY – New PaltzElect. & Comp. Eng.
Two Variables K-Map
SUNY – New PaltzElect. & Comp. Eng.
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 3
SUNY – New PaltzElect. & Comp. Eng.
Two Variables K-Map
SUNY – New PaltzElect. & Comp. Eng.
Two Variables K-Map
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 4
SUNY – New PaltzElect. & Comp. Eng.
Two Variables K-Map
SUNY – New PaltzElect. & Comp. Eng.
Three Variables K-Map
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 5
SUNY – New PaltzElect. & Comp. Eng.
F(x, y, z) = Σm(2, 3, 4, 5)
SUNY – New PaltzElect. & Comp. Eng.
F(x, y, z) = Σm(0, 2, 4, 5, 6)
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 6
SUNY – New PaltzElect. & Comp. Eng.
F(x, y, z) = Σm(3, 4, 6, 7)
SUNY – New PaltzElect. & Comp. Eng.
F=A’C + A’B + AB’C + BC
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 7
SUNY – New PaltzElect. & Comp. Eng.
Four Variables K-Map
SUNY – New PaltzElect. & Comp. Eng.
K-Map folding patterns
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 8
SUNY – New PaltzElect. & Comp. Eng.
F(A,B,C,D) = Σm(0,5,10,11,12,13,15)
SUNY – New PaltzElect. & Comp. Eng.
F(w, x, y, z) = Σm(0, 1, 2, 4, 5, 6, 8, 9, 12, 13, 14)
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 9
SUNY – New PaltzElect. & Comp. Eng.
Essential versus non-essential groups
SUNY – New PaltzElect. & Comp. Eng.
F=A’B’C’ + B’CD’ + A’BCD’ + AB’C’
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 10
SUNY – New PaltzElect. & Comp. Eng.
F(A, B, C, D) = Σm(0, 1, 2, 5, 8, 9, 10)
SUNY – New PaltzElect. & Comp. Eng.
Gate implementations of the function
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 11
SUNY – New PaltzElect. & Comp. Eng.
Example with Don’t Care Conditions
SUNY – New PaltzElect. & Comp. Eng.
Prime Implicants Example
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 12
SUNY – New PaltzElect. & Comp. Eng.
F(A, B, C, D) = Σm(0, 2, 4, 8)+ d(10, 11, 12, 13 , 14, 15)
SUNY – New PaltzElect. & Comp. Eng.
Five Variables K-Map
EGC220Digital Logic Fundamentals
9/20/2017
Simplification Using K-Map 13
SUNY – New PaltzElect. & Comp. Eng.
F(A, B, C, D, E) = Σm(6, 9, 13, 14, 18, 19, 25, 27, 29, 30)+ d(2, 5, 10, 11, 20, 22, 26)
