Ha ha ha, you, in the last lecture we introduced you to the map method of boolean simplification. - We do a Karnaugh map, which is a graphical representation of a truth table. We fill this graph with the cells whose midterms had an output of true and avoid cluttering by not marking zeros on the map. - The end device is purposely left out to avoid cluttering. - The objective is to identify groups of ones as large as possible, satisfying the adjacency rule, and removing as many variables as possible. This simplifies the representation of the given boolean function. - We will look at a few more examples today, including some special cases. - Let's take an example of a map with four variables, called ABCD. - There are ones in the following cells: 2, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, and 15. - The idea is to group adjacent ones as large as possible, without considering smaller groups that can be totally submerged in larger groups. - All ones should be covered, and it is okay for a one to be covered more than once. - In this case, there are only two groups of ones, both containing two ones. - Grouping them once is the most efficient way. There is no point in unnecessarily covering a one more than once if it doesn't result in a smaller group. - The groups in this case are: group 1, group 2, and group 3. - The expression for f in terms of the variables would be: A'CD, BCD, and A'CD'. - Now, let's consider marking the map slightly differently. - This may not be the most efficient way, but it is to demonstrate definitions from the last lecture. - An implicant is any group of ones, a prime implicant is the largest possible group of ones in the given...
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