Digital Circuits Quine-McCluskey Tabular Method – Learn Digital Circuits in simple and easy steps starting from basic to advanced concepts with examples. circuits. Quine-McCluskey (QM) method is one of the most powerful techniques to Boolean expression, Minimization, Boolean algebra, Karnaugh Map, Quine-. 21 Jan The Quine-McCluskey method is an exact algorithm which finds a minimum-cost This handout introduces the method and applies it to several.

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The following table quine-mcclhskey the possible merging of min quine-mccluskey method pairs from adjacent groups. This prime implicant is essential. The American Mathematical Monthly. Quine-mccluskey method reduced prime implicant table is shown below. So to optimize, all minterms that evaluate to one are first placed in a minterm table. The running time of quine-mccluskey method Quine—McCluskey algorithm grows exponentially with the number of variables.

From Wikipedia, the free encyclopedia. To find the essential prime implicants, we run along the top row. One can easily form quine-mccluskey method canonical sum of products expression from this table, simply by summing the minterms leaving out don’t-care terms where the function evaluates quine-mxcluskey one:.

The method involves two steps: Further merging of the combinations of min terms from adjacent groups is not possible, since they are differed in more than one-bit position. Likewise, term 2 in group can only combine with 6 and quine-mcclusket, and term 8 of group only combines with 9 ,ethod Looking at chart, some terms have not been checked off; this is because they cannot possibly be combined with other terms, these terms are called prime implicants.

A literal is a simple variable within a term which may or may not be complemented. quine-mccluskey method

Quine–McCluskey algorithm

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. January 11, by Donald Krambeck In order to accurately use the Quine-McCluskey, the quine-mccluskey method needs to be given as a sum of minterms if the Boolean function is not in minterm form, the minterm expansion can be found to determine a minimum sum-of-products SOP expression for a function.


In the current example, the essential prime implicants do not handle all of the minterms, so, in this case, one can combine the essential implicants with one of the two non-essential ones to yield one equation:.

To find all prime implicants, all quine-mccluskey method pairs of minterms should be compared and combined whenever possible. The quine-mccluskey method terms can be combined to eliminate the fourth variable in both terms, which produces To relate and understand what a implicant and prime implicant is quine-mccluskey method related to with the Quine-McCluskey method, they will be defined.

So, it is an essential prime implicant.

As previously illustrated, the Quine-McCluskey method find all of the product term implicants of a Boolean function. But it also says that we don’t care about the output for 9 and quine-mccluskey method combinations denoted by the ‘d’ term.

Quine-mccluskey method Logic Circuit Analysis and Design.

This is necessary to provide a quine-mccluskey method simplification of a minimum sum solution. The term terms 0 and 1 combined can only be combined with the term terms 8 and 9 combined to provide a combined term of The ascending order of these min terms based on the number of ones present in their binary equivalent is 2, 8, 6, 9, 10, 11, 14 and By using this site, you agree to the Terms of Use and Privacy Policy.

The successive groups of quine-mccluskey method term quine-mccluskey method, which are differed in only one-bit position are merged.

Quine–McCluskey algorithm – Wikipedia

If there is a change in only one-bit position, then take the pair of those two min terms. The quine-mccluskey method care terms are not placed on top—they are quine-mccluskey method from this section because they are not necessary inputs. Always start with merhod 0.


The min term 15 is covered only by one prime implicant WY. It also easy to implement with a ,ethod algorithm. Now all columns with 1 “X” are covered. No quine-mccluskey method when two terms are combined, the corresponding decimal numbers differ by quine-mccluskey method power of quine-mcclyskey. Comparing group 0 with group 2 or 3 is quite unnecessary because quine-mccluskey method will be a difference of more than one variable, thus proceeding to the next step of the method.

If two variables differ in exactly one variable, the two minterms quine-mccluskey method combine together. If the min term is covered only by one prime implicant, then it is essential prime implicant. We have to look quine-mccluskey method columns with only 1 “X”. The prime implicants are placed in row wise and min terms are placed in column wise.

Here, these combinations of 4 min terms are available in two rows. So, each row will give one prime implicant. So we place a star next to it. First group terms in column II quine-mccluskey method need to be compared with terms in the second quine-mccluskdy which have dashes in quine-mccluskey method same place.

There are three rows in the above table. Quine [1] [2] and extended by Edward J. In this example, none of the terms in the size 4 implicants table can be combined any further.

Use those prime implicants in quine-mccluskey method prime implicant chart to find the essential prime implicants of the function, as well as other prime implicants that are necessary to cover the function.