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The total number of prime implicants of the function $f(w, x, y, z) = \sum (0, 2, 4, 5, 6, 10)$ is __________
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Best answer
64 votes
64 votes

As you can see that there is  one $4$ -set and two $2$ -set that are covering the star marked $1's$ (i.e. the ones that are not covered by any other combinations).

So, the answer is $3$.

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10 votes
10 votes

(Can be solved using K-Map also. )

Place all minterms that evaluate to one in a minterm table.

Input (first column for no. of 1's)

m0 0000
1 m2
m4
0010
0100
2 m5
m6
m10
0101
0110
1010

Combine minterms with other minterms. If two terms vary by only a single digit changing, that digit can be replaced with a dash indicating that the digit doesn't matter. Terms that can't be combined any more are marked with a "*". When going from Size 2 to Size 4, treat '-' as a third bit value. For instance, -110 and -100 or -11- can be combined, but -110 and 011- cannot. (Trick: Match up the '-' first.)


First Comparison

0 (2, 0)
(4, 0)
00-0
0-00
1 (6, 2)
(10, 2)
(5, 4)
(6, 4)
0-10
-010
010-
01-0

Second Comparison

0 (6, 4, 2, 0) 0--0

Prime Implicants

(6, 4, 2, 0) 0--0
(10, 2)
(5, 4)
-010
010-

Answer: Total number of prime implicants 3


Source: Finding prime implicants - Quine-McCluskey algorithm - Wikipedia

7 votes
7 votes

all the min terms can only be covered by three diffrernt color so there is only three prime imlecants

3 votes
3 votes

I think this is bit easier to understand.
The hint here is that we try to find the minimum number of groups(octa(eight 1's) ,quad (four 1's),dual(two 1's) that can be formed and that represents the minimum number of implicants that covers F which is Prime Implicant.

Here, we can form 1 quad and 2 duets.3 prime implicants.

 

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