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2 variable K-map, Example

Interview Questions. Main, FPGA, Digital Fundamentals
1. F(x,y,z) =     (0,1,6,7) - Minimization, on this page.
2. F(x,y,z) =     (0,1,4,5,6,7) - Minimization from here.
3. F(x,y,z) =     (3,4,6,7) - Minimization from here.
4. F(x,y,z) =     (0,1,2,3,4,5,6,7) - Minimization from here.

A solved example of 2 variable k-map below.

F(x,y)=sum(0,2,3)

0

1

0

1

x

y

x’y’ =1

xy’ = 1
xy = 1

 

Minimization solution to above function.

 

= y’(x + x’) + xy + xy’ = y’ + x (y+y’) = y’ + x

 

K-map Trick : From the elements in enclosed box, we can minimize by only keeping the element which is not changing. In this example its y’ and x.