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Q: A Few Simple Boolean Algebra Questions ( No Answer,   0 Comments )
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 Subject: A Few Simple Boolean Algebra Questions Category: Science > Math Asked by: bildy-ga List Price: \$25.00 Posted: 30 Mar 2003 06:13 PST Expires: 04 Apr 2003 10:38 PST Question ID: 183173
 ```I need the answers to these questions to study for a test from. I would like these questions answered withing the next few hours. Only question 2a and 2b require all work to be shown. Please feel free to post an questions comments or concerns. 1. In a small town, trains arrive at the train station every hour on the hour every day of the week. They arrive on the half-hour, as well, only during rush hours. They also arrive on the half-hour all day Saturday but never on Sunday or holidays. Assume the following variable assignments: A = It is rush hour B = It is Saturday C =It is a holiday D = It is Sunday Write, in terms of A, B, C, and D, the Boolean Expression for F = Trains arrive on the half-hour = You need not simplify your expression. 2. Simplify the following Boolean Expressions algebraically. Show your work. a. A+ABC+A'BC+A'B b. (AB+C+D)(C'+D)(C'+D+E) 3. Put the following Boolean Expressions into Disjunctive Normal Form (DNF) a. A + B b. AB' + C(A' + B') 4.Determine whether the following Boolean Expression can be rewritten using only the XOR operator. If it can, rewrite it using only the XOR operator. A'B'C'D+A'B'CD'+A'BC'D'+AB'C'D'+ABCD'+ABC'D+AB'CD+A'BCD``` Clarification of Question by bildy-ga on 30 Mar 2003 08:44 PST ```Does anyone need any clarification to these questions? I really need them as soon as possible. If anyone is able to answer them, I am willing to give a generous tip. Thanks```
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 The following answer was rejected by the asker (they received a refund for the question). Subject: Re: A Few Simple Boolean Algebra Questions Answered By: answerguru-ga on 30 Mar 2003 09:29 PST Rated:
 ```Hi bildy-ga, Here are the answers to the questions you requested: 1. In a small town, trains arrive at the train station every hour on the hour every day of the week. They arrive on the half-hour, as well, only during rush hours. They also arrive on the half-hour all day Saturday but never on Sunday or holidays. Assume the following variable assignments: A = It is rush hour B = It is Saturday C =It is a holiday D = It is Sunday Write, in terms of A, B, C, and D, the Boolean Expression for F = Trains arrive on the half-hour. ANSWER: F = C'(A+B) This is basically stating that trains arrive on the half-hour as long as it is not a holiday and either it is rush hour or a Saturday. 2. Simplify the following Boolean Expressions algebraically. Show your work. a. A+ABC+A'BC+A'B A + BC + A'B // combining ABC+A'BC as they are collectively exhaustive A + B(C + A') // factoring out a common term of B b. (AB+C+D)(C'+D)(C'+D+E) (AB+C+D)(C'+D+E) // removing redundant term (AB+C)(C'+E)+D // factoring out common term of D 3. Put the following Boolean Expressions into Disjunctive Normal Form (DNF) a. A + B ANSWER: Assuming that this expression is only a function of A and B the DNF form is: f(A,B) = A(B+B')+(A+A')B b. AB' + C(A' + B') ANSWER: f(A,B,C) = AB'(C+C') + A'(B+B')C + (A+A')B'C 4.Determine whether the following Boolean Expression can be rewritten using only the XOR operator. If it can, rewrite it using only the XOR operator. A'B'C'D+A'B'CD'+A'BC'D'+AB'C'D'+ABCD'+ABC'D+AB'CD+A'BCD ANSWER: Yes, the expression can be written only using the XOR operator as follows: A'B'C'D (XOR) A'B'CD' (XOR) A'BC'D' (XOR) AB'C'D' (XOR) ABCD' (XOR) ABC'D (XOR) AB'CD (XOR) A'BCD The reason this conversion is possible is that for any given values of A,B,C,D at most one of the "ANDed" terms can be true. It is important to notice, however, that although these terms are mutually exclusive, they are NOT collectively exhaustive (there are 8 other combinations that have not been represented in the original equation). I hope you have found this helpful - since I know you needed the actual answers quickly I aimed to provide a concise set of solutions rather than a comprehensive one. However, please do post a clarification if any of the answers require further explanation :) Cheers! answerguru-ga Google Answers Researcher``` Request for Answer Clarification by bildy-ga on 30 Mar 2003 09:54 PST ```I need a few clarifications as soon as possible: 1. Why isnt the term D = It is Sunday used in your boolean expression, when i did this proble it looked as follows: F = (C'+D')(A+B). Please clarify. 2. Same as mine, looks good. 3. Same as mine, looks good. 4. Shouldnt using the exclusive or operator simplify the equation down. Please get back to me asap``` Clarification of Answer by answerguru-ga on 30 Mar 2003 10:30 PST ```Hi again, For the first question, I did not include a "D'" term like you did because it seemed redundant. The reason for this is that from my understanding, rush hour only occurs at certain times on weekdays. By including rush hour as a term, Sunday is automatically excluded unless it is stated explicitly (like Saturday in this case). Regardless, I believe either statement can be deemed accurate based on the interpretation of the term's real meaning. For the fourth question, I'm not quite sure where you are having a problem - did you understand the written explanation I provided under the answer? Essentially, the reason XOR can be used here is because XOR=OR as far as functionality in this equation. The reason for this is that at most one of these terms is possible at any one time. Hope this helps... answerguru-ga``` Request for Answer Clarification by bildy-ga on 30 Mar 2003 10:52 PST ```Ok, I believe I understand where these answers are coming from. But when i do the truth tables for #1, using your answer as well as mine, I come up with two different answers. For your answer I get: A B C D f 0000 0 0001 0 0010 0 0011 0 0100 1 0101 1 0110 0 0111 0 1000 1 1001 1 1010 0 1011 0 1100 1 1101 1 1110 0 1111 0 When you create a truth table from my boolean expresion, you come up with the following: A B C D f 0000 0 0001 0 0010 0 0011 0 0100 1 0101 1 0110 1 0111 0 1000 1 1001 1 1010 1 1011 0 1100 1 1101 1 1110 1 1111 0 Please verify these results, and let me know which one you feel to be more correct. Thanks again for the clarification.``` Request for Answer Clarification by bildy-ga on 30 Mar 2003 11:00 PST ```Also, for #3, for the answer to be considered to be in Disjunctive normal form, doesnt it need to be simplified further? Or is that enough? Look forward to hearing back from you one these last 2 clarifications. Thanks``` Clarification of Answer by answerguru-ga on 30 Mar 2003 11:18 PST ```In response to your two previous requests: The assumption I made for #1 does actually result in different truth tables, and that is not a problem because we both interpreted the question differently. As I said before, either answer is correct given that the assumption made is stated clearly. The assumption I made to arrive at my answer for this question resulted in a more simplified answer, so don't think there really is a "most correct solution". The safest bet would be to provide both solutions and explain why they could both be right. Disjunctive normal form is defined as meeting the following conditions: "A Boolean expression is in disjunctive normal form (DNF) if: 1. the variables within each term are ANDed together, 2. the terms are ORed together, and 3. every variable or its complement is represented in every term (i.e. either A or ~A is in each term, B or ~B is in each term, etc.). 4. No parentheses or other Boolean operations appear in the expression." http://mathforum.org/library/drmath/view/51857.html Hope that clears everything up :) answerguru-ga``` Request for Answer Clarification by bildy-ga on 30 Mar 2003 11:30 PST ```You have parentheses in your answers for this problem, which you state are incorrect. Please clarify``` Clarification of Answer by answerguru-ga on 30 Mar 2003 11:51 PST ```Yes, you're right - the expression just needs to be expanded one step further. 3. Put the following Boolean Expressions into Disjunctive Normal Form (DNF) a. A + B ANSWER: Assuming that this expression is only a function of A and B the DNF form is: f(A,B) = A(B+B')+(A+A')B = AB + AB' + A'B b. AB' + C(A' + B') ANSWER: f(A,B,C) = AB'(C+C') + A'(B+B')C + (A+A')B'C = AB'C + AB'C' + A'BC + A'B'C answerguru-ga```
Reason this answer was rejected by bildy-ga:
```The answers to some of the questions were incorrect / unsatisfactory,
even after several requests for clarification.  I look forward to
as I have oh so many times in the past.```
```I posted 4 questions for the researcher to answer.  Out of these 4