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4 variable K-map, Example -2

Minimize following

F(x,y,w, z) =     (0,2,4,6,12,14)

Above is a common format of representing the K-map problems. The numbers 0, 2, 4, 6, 12, 14 are the location of cells in the 4-var k-map table. Discussed below is a 4 variable K– map with 1 and 0 values. assigned to cells.

Interview Questions. Main, FPGA, Digital Fundamentals
The 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.
F = x’w’ + yw’
Resources

Clock Domain Crossing Discussion with
rtl & testbench example.

Rate change (asynchronous) FIFO design and fifo depth calculation.
FPGA Interview. FPGA flow.
Solved Examples for 3 variable Kmaps
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.
MINIMIZATION USING FOUR VARIABLE KARNAUGH MAP

00

01

11

10

0

1

xy

zw

00

01

11

10

1

0

0

1

1

0

0

1

0

0

0

0

1

0

The K-map for 4 variables is plotted above. You will notice the column and rows for 11 and 10 are 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.