# QUINE-Mccluskey (TABULAR) METHOD

The K-map method for obtaining simplified Boolean the expression is very effective for Sunction with less than or equal to four variables. For more than 4-variable logic espresso with less than t becomes any more difficult pumped to draw and solve the K-map. However, there are some general ones which are applicable to functions of ay number of variables. One such procedure was originally suggested by Quine and later modified by Mc Cluskey. The Quine-Mc Cluskey method approves so to minimize the Boolean function in the SOP and POS form. The tabular method is explained as follows.

## (1) Combination of minterms

(a) All the minterms given in the Boolean function are expressed in the binary representation.

(b) Now all the minterms are arranged in the increasing index. The index is nothing but the number of Is in the binary representation of a given minterm.

(c) After arranging all the minterms in various groups of indexes, the “n” index
minterms will be compared with all the minterms of (n + D) index. If two minterms differ by only one variable, then this variable will be eliminated and a dash (-) is placed in that position. Then again we compare (n 1D) hand (n + 2) index, groups. This the process is repeated until the comparison over with all the midterms.

(d) Now in the next stage, further elimination of variables is done from the combination
of two minterms to the combination of four minterms.

(e) This process is repeated untül further elimination is not possible.

(e) This process is repeated until further elimination is not possible.

## 2)  Selection of prime implicants

In the above step, all the possible combinations are grouped and marked with the check sign  Remaining unchecked minterms are called prime implicants. To make the table of prime implicants, all the prime implicants are arranged in the column and all the minterms in “a row”.

If they don’t care terms are given in the Boolean function, then these terms are not written in the row of the table of prime implicant. Now crosses are placed in the column of minterms which are associated with the prime implicants.

## (3) Selection of essential prime implicants

Now we will check the single cross in each column, with prime time implicants the cover minterm with a  single cross in each column is called the essential prime implicants. These are shown by a star marked over the prime implicants.

Now the sum of the essential prime implicants is written in the SOP form. If the midterms
are not covered by essential prime implicants, then we will consider another prime implicant which covers these midterms.