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Kernaugh Map solving to reduce the electronic circuits size


Kernaugh Map solving to reduce the electronic circuits size

Kernaugh map is the technique to reduce the design of an electronic circuit . Any electronic circuit is made of different different small circuits like Multiplexers . Multiplexers uses binary values as inputs and produce the output in the binary format also and then converts these digital values into analog signal to perform the desired output .

Let , we take a Truth table of a 2-input Multiplexer as below with A,B , S as Inputs and Y as output  -

SABY
0000
0010
0101
0111
1000
1011
1100
1111
To design the reduced circuit from the truth table of this circuit , we need only the the output as 1 ( We say the outputs  1 are Minterms of standered sum of products .) .

So the output function in the terms of minterms as -
Y =  Σ(2, 3, 5, 7)

Here we can reduce electronic circuit , using the boolean algebra rules but it becomes very hard to reduce the size of circuit , when circuit is too big and have Large number of inputs and then the Technique of Kernaugh Map comes into the picture to solve the circuit reducing problems .

Basically We use kernaugh map for 2 , 3 and 4 inputs and for more larger designs other techniques are also available .

Rules to draw and reduce the circuit design as -

1. Design the basic cells for the number of inputs like -
Kernaugh Map solving to reduce the electronic circuits size
K-Map for 2-Input Circuits
Kernaugh Map solving to reduce the electronic circuits size
K-Map for 3-Input Circuits
Kernaugh Map solving to reduce the electronic circuits size
K-Map for 4-Input Circuits


2. Each cell with a 1 must be included in at least one group.
3. Try to make the largest possible groups.
4. Try to end up with as few groups as possible.
5. We can create groups of only 2 elements or 4 elements or 8 elements or in the power of 2 ,
    elements  and may be square or rectangular only .
6. We can include wrap around elements of multiple groups at the grid edges .
7. Do not include diagonals or zig-zags to form a group.

To Reduce above Multiplexer using Kernaugh map is like below -

Kernaugh Map solving to reduce the electronic circuits size
Steps and Groups making in K-Map
Kernaugh Map solving to reduce the electronic circuits size
Reduced circuit generated by K-Map