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work needed Word Sign in -0 File Home Insert Draw Design Layout References MailingsReviewViewTell me what you want to do Share ?Align Group Text Forward - Backward- Pane Rotate Spacing ?Line Numbers* _ Left: 0. Before: Auto Margins Orientation Size Columns Position Wrap Bring Send Selection After Auto Page Setup Paragraph Arrange This format will assist the Faculty in determining par for you without having you to scan the actual circled Kmaps and submit them Assignment 7.1 Using your K-Maps from Assignment 6 3, provide a minimal Boolean cover Assignment 7.2 for each of the Boolean Variables, P, O, R, S, T, U, and V Example Here's an exampic of how you should use the Assignment 7.1 Submission For the P variable function in Assignment 63, complete "blue" data and green selection input circles to each Mulliplexer when isolating for varables w, X, Y, and Z Note: The numbering of the rows and columns are dinterent for each isclated variable Assuming in your Kman,for function P you have enter a"1 in the cells: 4, 8, 8 12, 13, and 14, then you would enter in the P section of the Assignment: Here's the beginning of the lable that isolates for X (consider how the X-bit value is changing) Groupings of Term Circled Cell Sincc you probably cannot afford another we dollar fine, we will not ask you to do this same assignment for the Q, R, S, T, U, and V functions, but, you should be able to do it with little trouble and some busy work 4.6. 12. 14 8, 12 2. 13 Aer the Minimization for P' enter the full minimization using the symbol for the complement (instead of an over-score bar) In each row, enter the minimization groupings. For example, for the X-Z tem we circled in the corresponding KMan the cells 4, 6, 12, 14 as a group of four so we enter these cell numbers in table Page 2 of 2 305 words +60% O Type here to search 1:40 AM 4/8/2018Explanation / Answer
1.Gather all minterms & don't care terms (if there are any) and convert them to binary form, then sort them in groups and list them in a list (call it List 1).
Example: If we have these terms (0,1,2,3,4,7,6), then the groups should be like this:
We can see in these groups that they are sorted according to the number of ones in each binary number.
2.Compare group 1 with group 2 & group 2 with group 3 & group 3 with group 4, the comparison is achieved by comparing each term in the first group with all terms in the next group.The comparison concept is that if two terms have only 1 different bit, then this bit must be replaced with (-) like: (000 , 001) ==> (00-).
After the comparison is done in (List 1), move to List 2 and do the same comparison, but we will find a new element, the dash (-) that we must handle it in the comparison. When we compare two dashed terms, the comparison is legal only if the dash position is the same in the two terms, otherwise we can't compare those terms like: (00- , 01-) ==> (0--), but (00- , 0-1) is illegal.
If two terms compared successfully, a check character is put next to the compared terms (say the check chr is 't'), if not, I mean that the two terms have more different bits or the dash position is not the same in the two terms, then a check character must be put next to the uncompared terms (say check chr is '*')
group 3
3.Determine the prime implicants (if they are found in any list above).
Note: The prime implicants are terms that can't be compared any more and indicated with '*', like: (0-- , --0 , -1-).
4.Form the coverage table to determine the essential prime implicants. To form this table, we will put the minterms horizontally & the prime implicants vertically, then we should determine which terms a prime implicant cover like (0--) covers 0,1,2,3. and put an indicator (say 'X') in the cells corresponding to the row of prime implicant and its terms.
0
1
2
3
4
6
7
0-- (0,1,2,3)
x
x
x
x
x
x
x
x
x
x
x
x
Now after we finished the table, we can determine the essential prime implicants by dominating the row and column of a term that has only 'X' in his column, like : (1 , 4 , 7). By dominating these rows, we can say that the prime implicants corresponding to these rows became essential prime implicants.
5.Finding the Simplified function. As we know, our example gives us these terms to simplify (0, 1, 2, 3, 4, 6, 7). Those terms without simplifying should form this function:
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where, A, B, C are variables and A', B', C' are their compliment variables & their compliments are called literals representing the binary form of the terms.
After simplifying, the function looks like this:
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List 1 List 2 List 3 group 0 000t 00-t 0--* 0-0t --0* -00t group 1 001t 0-1t -1-* 010t 01-t 100t -10t 1-0t group 2 011t -11t 110t 11-tgroup 3
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