Digital Circuits Quine-McCluskey Tabular Method – Learn Digital Circuits in simple and easy steps starting from basic to advanced concepts with examples. Karnaugh map and Quine McCluskey (Q-M) method are the systematic approach for simplifying and manipulating Boolean expressions. In this paper a simpler. circuits. Quine-McCluskey (QM) method is one of the most powerful techniques to Boolean expression, Minimization, Boolean algebra, Karnaugh Map, Quine-.

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Quine Mccluskey Method with Example

The resulting terms are listed in the table below. The following table shows these min terms and their equivalent binary representations. The reduced table after removing the redundant rows is shown below.

When we take 0,1 for first group, we have to fill remark column. A literal is a simple variable within a term which may or may not be complemented. It is sometimes referred to as the tabulation method. And here is our final answer i.

One can easily form the canonical sum of products expression from this table, simply by summing the quine mccluskey method leaving out don’t-care terms where the function evaluates quine mccluskey method one:.

We will now finding quine mccluskey method prime implicants using Petrick’s method, simplifying The and terms can be combined to eliminate the fourth variable in both terms, which produces Don’t-care terms are also added into quine mccluskey method table, so they can be combined with minterms:.

So to optimize, all minterms that evaluate to one are first placed in a minterm table. In second table we have to do the same thing only the difference is that, we have to refer first table.


Use those prime implicants in a 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. Quine mccluskey method, term 2 in group can quien combine with 6 and 10, and term 8 of quine mccluskey method only combines with 9 and The three terms left in column III are duplicate terms and were formed by combing the same set of four minterms in a different order.

Make a table of four columns.

This prime implicant is quine mccluskey method. Always start with group 0. We will discuss remark column in second table. These minterms are represented in a binary notation and combined as follows: Finally, the following table is of prime implicants. Looking at chart, some terms have quine mccluskey method been checked off; this is because they cannot possibly be combined with other terms, these terms are called prime implicants.

The given min terms are 2, 6, 8, 9, 10, 11, 14 and The American Mathematical Monthly.

Digital Circuits Quine-McCluskey Tabular Method

What advantages and disadvantages do they have? These terms can now be checked off in column II as they have been used to simplify the Boolean function. Mccluekey this point, one can start combining minterms with other minterms. If two terms vary by only a single digit changing, that digit quine mccluskey method be replaced with a dash indicating that the digit doesn’t matter.

Quine–McCluskey algorithm

Now here is second table. A prime implicant of a function F is quine mccluskey method product term implicants which is no longer an implicants if any literal is deleted from it.

The Quine—McCluskey algorithm or the quine mccluskey method of prime implicants is a method used for minimization of Boolean functions that was developed by Willard V. If two terms have already been combined with metohd terms, they must still be compared and combined if possible.


If a prime implicant is quine mccluskey method then, as would be expected, it is necessary to include it in the minimized boolean equation. Fill the remark column of second table when you select minterms for next table. Although more practical than Karnaugh mapping when dealing with more than four variables, the Quine—McCluskey algorithm also quine mccluskey method a limited range of use since the problem it solves is NP-hard.

Match up the ‘-‘ first. The min term 15 mcclusley covered only by one prime implicant WY.

In this example problem, we got three prime implicants and all the three are essential. 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 But, it is difficult to simplify the Boolean functions having more than 5 variables by using this method.

To find all prime implicants, all possible pairs of minterms should be compared and combined whenever possible. If quine mccluskey method variables differ in exactly one variable, the two minterms will combine together.

You May Also Like: Minterm 15 also has only 1 “X”, so m quine mccluskey method is also essential. This expression says that the output function f will be quine mccluskey method for the minterms 4,8,10,11,12 and 15 denoted by the ‘m’ term.

No matter when two terms are combined, the corresponding decimal numbers differ by a power of 2.