CSC 133 Practice Problems: Karnaugh Map Simplification

Determine minimal circuits based on these Karnaugh maps:

Write out the minimal expressions and draw the circuits.

Q R

P


0 0


0 1


1 1


1 0

0

1

 

 

 

1

1

 

 

 


Q R

P


0 0


0 1


1 1


1 0

0

1

1

1

1

1

 

 

 

 


Q R

P


0 0


0 1


1 1


1 0

0

1

 

 

1

1

1

 

 

1


Q R

P


0 0


0 1


1 1


1 0

0

1

1

 

 

1

 

 

1

1


w z

x y


0 0


0 1


1 1


1 0

0 0

1

1

1

1

0 1

 

1

1

 

1 1

1

 

 

1

1 0

 

 

 

 


w z

x y


0 0


0 1


1 1


1 0

0 0

1

 

 

1

0 1

 

1

1

 

1 1

 

1

1

 

1 0

1

 

 

1


w z

x y


0 0


0 1


1 1


1 0

0 0

1

1

 

 

0 1

1

1

1

1

1 1

 

1

1

 

1 0

 

 

 

 

Minimize the expression

((x Ú ~y) ® z) Ú (~x Ù ~y Ù ~z)

by first expanding it to disjunctive normal form, then using a Karnaugh map to simplify:

Solution: ~x Ú z.