Question

Using Quine-McClusky Algorithm find the minimized forms F(w,x,y)=

∑0,2,3,4,6 (This is also part of HWO5)

Answer 1

To find the minimized forms of F(w,x,y) = ∑0,2,3,4,6 using the Quine-McClusky algorithm, follow these steps: 1) Write down the minterms, 2) Group the minterms based on the number of 1s in their binary representation, 3) Compare the minterms pairwise and make combined terms, 4) Repeat the process iteratively until no more pairings can be made, 5) Write down the final minimized terms.

Step-by-step explanation:

The Quine-McClusky algorithm is used to minimize boolean functions. To find the minimized forms of F(w,x,y) = ∑0,2,3,4,6, follow these steps:

1. Write down the minterms: 0, 2, 3, 4, and 6
2. Group the minterms based on the number of 1s in their binary representation. Start with grouping the minterms with 1 1 (binary representation has one 1) and continue up to grouping the minterms with 3 1s (binary representation has three 1s).
3. For each group, compare the minterms pairwise to identify any pairs that differ by only 1 bit position. If such pairs are found, write down their combined term and mark the bit position that differs as '-'. For example, if minterm 0 and minterm 2 differ by the second bit, you would write down the combined term as 0- and 2-.
4. Continue this process iteratively until no more pairings can be made. Repeat step 3 for each new set of combined terms until the process ends.
5. Write down the final minimized terms obtained from the Quine-McClusky algorithm.