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3 variable K-

Minimize following

F(x,y,z) = (0,1,4,5,6,7)

Above is a common format of representing the K-

The numbers 0,1,4,5,6,7 are the location of cells in the 3-

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 = 0

x’yz’ = 0

xy’z’ = 1

xy’z = 1

xyz = 1

xyz’ = 1

0

1

x

yz

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.

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.

00

01

4

5

11

10

7

6

x’y’z’ = 1

x’y’z = 1

x’yz = 0

x’yz’ = 0

xy’z’ = 1

xy’z = 1

xyz = 1

xyz’ = 1

0

1

x

yz

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.

F = (x’y’z’+ x’y’z + xy’z’ + xy’z) + (xy’z’ + xy’z + xyz + xyz’)

F = (y’ + x)

... Final Answer.

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’y’z’+ x’y’z + xy’z’ + xy’z) + (xy’z’ + xy’z + xyz + xyz’)

F = (y’ + x)

... Final Answer.

Resources

Clock Domain Crossing Discussion with

rtl & testbench example.

Rate change (asynchronous) FIFO design and fifo depth calculation.

Half-adder , Full-adder , 4-bit binary adder , adder-subtractor circuit, overflow with rtl & testbench. Binary Multiplier, Parity error TT

Arithmetic, logical, shift micro-operations . Stack organization, LIFO, RPN discussion.

VHDL rtl - Synchronous flip-flop , latch, shim to improve timing and counter example

RTL coding guidelines. ICG cell, Assertions, $assertkill, levels.

Digital design Interview questions.

FPGA Interview. FPGA flow.

Graduate studies in US

Pipeline vs. Parallel processing.

Clock Domain Crossing Discussion with

rtl & testbench example.

Rate change (asynchronous) FIFO design and fifo depth calculation.

Half-

VHDL rtl -

Digital design Interview questions.

FPGA Interview. FPGA flow.

Graduate studies in US

Pipeline vs. Parallel processing.

x’y’z’

x’y’z

x’yz

x’yz’

xy’z’

xy’z

xyz

xyz’

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.