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Is there any method to find the prime implicants without using the tabular method (Quine-McCluskey method) . As an example

the prime implicant for the function F(w,x,y,z) = Σ( 1, 4,6,7,8,9,10,11,15 )  are  6 in numbers i.e.  x'y'z  ,  w'xz'  ,  w'xy   ,   xyz ,  wyz  ,   and  wx'   using Tabular method  (ref. Morris Mano / p.g. 107 )

However , using K-map the function F can be represented as F= x'y'z + w'xz' + xyz + wx'   gives only 4 prime implicants ( which doesn't include w'xy  and wyz  ) .  

Now the question is which will be the prime implicant of the given function 4 or 6 ....  If it is 6 then Is there any method other than Tabular method to find prime implicants of the function...

1 Answer

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it is 6 only by K-map also.

Prime implicants are biggest possible groups such that we get atleast one uncovered minterm is group. 

so you will get 

1) group (1,9) essential prime implicant.

2) group (4,6) essential prime implicant.

3) group (8,9,10.11) essential prime implicant.

Now two minterms are left and each can be cover in two groups of same size (pairs of 2)

1) Minterm 7 can be covered in group (6,7) or group (7,15)

2) Minterm 15 can be covered in group (7,15) or group (11,15)

Now we have 6 prime implicants (3 EPIs + 3 NEPIs)

By Tabular method, you will get 3 essential prime implicants and one extended essential prime implicant. 

By K-map method, you will get 3 essential prime implicants and choose best to cover remaining minterms from given choices from non-essentials to get minimal expression, that is, I think clear from choices. 

So by any method, minimized expression will have same solution.

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