Quine Mccluskey Method with Example

24 May

Quine-Mcclusky method for minimization of logic function:             

Question: minimize the following logic function using Quine Mcclusky method: Y(A,B,C,D)= ∑ m(0,1,3,7,8,9,11,15)

Solution:

Table 1:

Make a table of four columns. In first column we have to write group i.e. the number of ‘1’s present in given minterms. For example first group having zero times ‘1’s i.e. there is no ‘1’ in that row (see column of variables), where as in second group that is group having one time ‘1’ , there are two possible cases first is 1=0001 and second is 8=1000 in both cases ‘1’ is present only one time. Just follow it for all the given minterms. We will discuss remark column in second table.

quine mcclusky method 1

quine mcclusky method 1

Table 2:

Now here is second table. In second table we have to do the same thing only the difference is that, we have to refer first table. For first group i.e. group ‘0’ (0,1) and (0,8) have only one digit different (see third column of table1). So put ‘-’ in that place.(keep in mind that group ‘0’ means there should not any ‘1’ in that row). Similarly for group ‘1’ there should present ‘1’ only ones. Now check the remark column of first table. When we take (0,1) for first group, we have to fill remark column.

quine mcclusky method 2

quine mcclusky method 2

Table 3:

The same procedure is repeated here in third table. In this table there will be two ‘-’s. Fill the remark column of second table when you select minterms for next table.

quine mcclusky method 3

quine mcclusky method 3

Table of prime implicants (PI):

Finally, the following table is of prime implicants. If you observe last table (table 3) carefully, the minterms for each group are same only the position is different, for example for first group ‘0’ there are 0,1,8,9 which is nothing but 0,8,1,9. So we have to fill prime implicants with corresponding variables of third table. There is (-00-) it means B’C’ since A and D are absent. Similarly (-0-1) means B’D and so on.

quine mcclusky method 4

quine mcclusky method 4

Now in the final step we have to round those minterms which has single ‘X’ in its column. And here is our final answer i.e. corresponding PI terms which are (B’C’+CD).

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