Digital Circuits Quine-McCluskey Tabular Method – Learn Digital Circuits in simple and easy steps starting from basic to advanced concepts with examples. Quine–McCluskey algorithm. The function that is minimized can be entered via a truth table that represents the function y = f(xn,,x1, x0). You can manually edit. 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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Tabular Method of Minimisation

Are there any columns methoc only 1 X? 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 This is so we can identify prime implicants at the end.

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This prime implicant is essential. Some NP-complete set covering problems. Indices for don’t-care values are marked with a d. None of the terms can be combined any further than this, so at this point we construct an essential prime implicant table.

The complexity of minimizing disjunctive normal form formulas Master’s thesis. A prime implicant of a function Qjine-mccluskey is a product term implicants which is no longer an implicants if any literal is deleted from it. Any two terms can be combined if the difference is only one variable. Be aware that this processing should be continued otherwise size 8 etc.

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. Quinem-ccluskey this example problem, we got three prime implicants and all the three are essential. The number of terms, however, is not minimum. When going from Size 2 to Size 4, treat ‘-‘ as a third bit value.


Quine–McCluskey algorithm

The min term 15 is covered only by one prime implicant WY. The reduced table after removing the redundant rows is shown below. If two variables differ in exactly one variable, the two minterms will combine together. These terms can now be checked off in column II as they have been used to simplify the Boolean function. The columns are labeled with the minterms in the on-set of the function. Notice, don’t care values are not included.

In previous chapter, we discussed K-map method, which is a convenient method for minimizing Boolean functions up to 5 variables. You May Also Like: First, the group 0 term will be compared with all terms in group 1.

Quine–McCluskey algorithm – Wikipedia

Stop this process when all min terms of given Boolean function are over. Selecting essential prime implicants with the Quine-McCluskey algorithm. The given min terms are 2, 6, 8, 9, 10, 11, 14 and Using K-maps to find the minimized two-level form of a function is difficult for functions of more than 4 variables and nearly impossible for functions of more than 6 variables because it’s hard to visualize and spot patterns in multidimensional space.

Column 2 shows the minterm quine-mccluekey written as a binary number.

The K-map method doesn’t work well for functions of more than 4 variables because there is a limit on our ability to spot visual patterns in multidimensional space. Or in Boolean algebra: Next, comparing terms in groups 2 and 3, 2, 6 can be combined and simplified with 10, 14as well as 2, 10 with 6, Always start with group 0. To find the essential prime implicants, we run along the top row. Next Article in Series: The simplest “additional procedure” is trial and error, but a more systematic way is Petrick’s method.


By combining terms 5 and 7, 6 and 7, 6 and 14, and 10 and 14, new terms are placed in column II.

Retrieved from ” https: Further merging of the combinations of min terms from adjacent groups is not possible, since they are differed in more than one-bit position.

The prime implicants are placed in row wise and min terms are placed in column wise. Both the K-map method and Quine-McCluskey algorithm go through the following 3 phases: In some cases, the essential prime implicants do not cover all minterms, in which case additional procedures for chart metuod can be employed.

Quine–McCluskey algorithm

For each prime impilcant mark an X at the intersection of the row for the prime implicant and the column quine-mccluskeyy all minterms covered by the prime implicant. Coming Up As previously illustrated, the Quine-McCluskey method find all of the product term implicants of a Boolean function.

The reduced prime implicant table is shown below.