Quine - McCluskey. To Karnaugh . Note: book uses slightly different method ( we will discuss later). • We can then Example 2, QM and don't-cares. Generate . variable Boolean expression. Quine-McCluskey method is computer based technique for minimization of Boolean function and it is faster than K-map method . The Quine-McCluskey method is useful in minimizing logic expressions for larger The Quine–McCluskey algorithm or the method of prime implicants is a.

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Quine-McCluskey Algorithm. □. Tabular Method. ▫. Compute all prime implicants. ▫. Find a minimum expression for Boolean functions. □. No visualization of. Quine-McCluskey Method. • A systematic simplification procedure to reduce a minterm expansion to a minimum sum of products. • Use XY + XY' = X to eliminate. PDF | The digital gates are basic electronic component of any digital circuit. Quine-McCluskey method is computer based technique for.

For reasons that will be explained later, the number of 1s in the binary represen- tation of each term are also calculated. This time, there are two combinations of terms that dier by 1 bit: m7, m5 and m7, m6. The left loop is m5, m7 and the right loop is m6, m7. It is also apparent that m7 is a common term in both expressions. By inspection, this simplifies to A C. Now, consider the binary representation of the min-terms. The table below lists all possible combinations.

The next step in the QM method is to where possible further combine these terms to obtain simpler expressions. Terms which can be combined must meet the following criteria: They dier by only one bit They contain the same domain of variables therefore the - symbols must line up Given the above, these terms can be combined.

Terms that can be merged must come from the same domain1 , so look for aligned - digits, and then from those, find the terms which are one bit dierent.

Where they can be merged, the result will have n number of 1s In this example the following terms can be combined m0, m1 and m4, m5 m0, m4 and m1, m5 The results are shown in the following table. The process stops as there is only one term left.

The final result is therefore A C. Now, consider a more complex expression, again with only 4 variables so the reader can directly compare with a Karnaugh Map example 1. This is marked as a starred item, meaning the term has to be kept in the final result.

This can be seen on the KM. For the next phase, repeat the procedure on the combined terms.

Not that m5, m7 is the only 3-variable term that cannot be combined with any other. Again, this can be seen on the KM as a loop of two cells. Relating this to the Karnaugh Map, all cells with a 1 are covered by these terms. As will be seen later, there are cases where dierent combinations of terms cover the set, but where not all are required.

Before considering these cases however, it is important to consider the situation where dont care are included in the original truth table. For reasons that will be explained later, the number of 1s in the binary represen- tation of each term are also calculated.

This time, there are two combinations of terms that dier by 1 bit: m7, m5 and m7, m6. The left loop is m5, m7 and the right loop is m6, m7. It is also apparent that m7 is a common term in both expressions. By inspection, this simplifies to A C.

Now, consider the binary representation of the min-terms. The table below lists all possible combinations. Draw the loops on the Karnaugh Map for all the min-terms in this table These terms represent all possible loops spanning two rows or two columns.

The next step in the QM method is to where possible further combine these terms to obtain simpler expressions. Terms which can be combined must meet the following criteria: They dier by only one bit They contain the same domain of variables therefore the - symbols must line up Given the above, these terms can be combined. Terms that can be merged must come from the same domain1 , so look for aligned - digits, and then from those, find the terms which are one bit dierent.

Where they can be merged, the result will have n number of 1s In this example the following terms can be combined m0, m1 and m4, m5 m0, m4 and m1, m5 The results are shown in the following table.

The process stops as there is only one term left. The final result is therefore A C. Now, consider a more complex expression, again with only 4 variables so the reader can directly compare with a Karnaugh Map example 1.

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