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Binary Numbers 1s_complement 2s_complement Binary Subtraction Binary Sub. Ex's Sign_magnitude SignM EX Gray Coding BCD coding Digital gates NAND NOR & XNOR Theorems Boolean Functions BFunc Examples Minterm Maxterm Sum of Minterms Prdt of Maxterms 2 var K-map 3 var K-map 4 var K-map 5 var K-map Prime Implicant PI example K-map Ex's KMap minimization 2 var EX

3 variable K-map, Example -4

Minimize following

 

F(x,y,z) =     (0,1,2,3,4,5,6,7)

 

Above is a common format of representing the K-map problems.

The numbers 0, 1, 2, 3, 4,   5, 6, 7 are the location of cells in the 3-var k-map table.

3 variable K– map with 1 and 0 values assigned to cells.

00

01

4

5

11

10

7

6

 

x’y’z’ = 1

 

 

x’y’z = 1

 

 

x’yz = 1

 

 

x’yz’ = 1

 

 

xy’z’ = 1

 

 

xy’z = 1

 

 

xyz = 1

 

 

xyz’ = 1

 

0

1

x

yz

Interview Questions. Main, FPGA, Digital Fundamentals
The K-map for 3 variables is plotted above. You will notice the column for 11 and 10 is inter-changed. This is done to allow only one variable to change across adjacent cells. This adjustment in columns allows in minimization of logic mapped into tables.    

Any adjacent 1, 2, 4 or 8 cells can be grouped to find a minimized logic value. Following plot will show grouping of adjacent cells.
The two step minimization equation is shown below.
With reference to the table above the cells under the dotted box’s can be combined to come up with following reduced  equation.

00

01

4

5

11

10

7

6

 

x’y’z’ = 1

 

x’y’z = 1

 

 

x’yz = 1

     

 

x’yz’ = 1

 

 

xy’z’ = 1

 

 

xy’z = 1

 

 

xyz = 1

 

 

xyz’ = 1

 

0

1

x

yz

x’y’z’
x’y’z
x’yz
x’yz’
xy’z’
xy’z
xyz
xyz’
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.
Kmap 4var.
2 var EX.

F = x’y’z’ + x’y’z + x’yz + x’yz’ + xy’z’ + xy’z + xyz + xyz’

F = 1  ... Final Answer.