Assignment 2

Suggested Problems (not to be turned in)

• Rosen, Section 1.1, ex: 24ace, 25.
• Rosen, Section 12.4, ex: 4, 5
• Rosen, Section 1.5, ex; 5, 11, 39
• Rosen, Section 1.6, 3, 6, 23
• Rosen, Section 1.7, ex: 10, 11, 12, 13, 19, 20

Required Problems, due September 2

Submission Instructions

• Submissions are to be submitted on paper, with one submission from each assigned pair of students, unless a student has explicit (written) permission from the instructor.

• Both partners should collaborate on every problem, and both names should be at the top of the first page. Since this is a collaborative effort, both partners should agree that the work represents their agreement in the correctness of the answers, and the same grade will be recorded for each assignment.

• Problems for each section (each bullet item in the assignment) should begin on a new page, and problems within a section should be in numeric order.

• If a problem requires the writing of a Python program, then the submission should include a printout of the code, a listing of appropriate test runs, and a statement regarding how the test runs provide sufficient evidence to conclude the program works properly.

• Each problem from Rosen's text should be identified with its section number and problem number. Each problem written out as a separate bullet point should be identified in a phrase or sentence, so it is clear which question is being answered.

• When a problem asks for a conclusion, the solution must include both a statement of the conclusion and an argument justifying that conclusion.

• Answers should be placed in Section and problem order, so the first page (more if needed) should give answers for the problems in the first assignment bullet. Answers for subsequent bullets should be in the order of the bullets on the Assignment sheet.

• Although the rules of this course allow the use of sources beyond the discussions of a student pair, any outside references (e.g., from the textbook, from Web sources, from discussions with others, etc.) must be fully cited.

Problems to be Turned In

• Rosen, Section 1.1, ex: 24bdf
• Rosen, Section 12.4, ex: 6
• Rosen, Section 1.5, ex: 16, 40
• Rosen, Section 1.6, ex: 19
• Rosen, Section 1.7, ex: 15, 16
• Consider the expresson x y + x y
  • Draw a K-map for this expression
  • Use the K-map to find a minimal a minimal expression equivalent for this expression.
• Repeat the previous problem with the expression x y z + x y z + x y z + x y z + x y z
  (If several different minimizations are possible, any alternative is possible, as long as the overall number of needed gates is a minimum.)
• Suppose y = f(x) is a continuous function on the interval [a, b], where f(x), a, and b are given.
  Write a predicate with parameters c and d that states the Intermediate Value Theorem:
  if a ≤ c < d ≤ b and if f(c) and f(d) have opposite signs (e.g., f(c) > 0 and f(d) < 0, or f(c) < 0 and f(d) > 0, then there is a value w between c and d where f(w) = 0 ).

• Challenge Problem—Computing a Babysitter's Fee

  A baby sitter charges $10.75 per hour until 9:00 pm (while the kids are still up), $8.50 per hour between 9:00 pm and midnight, and $12.25 per hour after midnight (since late night baby sitting interferes with morning classes).

  Write a Python program that reads four integer values (the sitter's starting time in hours and minutes and the ending time in hours and minutes) and computes the sitter's fee. Assume all times are between 6:00 pm and 6:00 am, and hours should be specified as being between 0 and 12 (inclusive). Hours outside the range of 0 to 12 should be considered invalid.

  • The hour 6 should be considered as 6:00 pm, when it is entered as a starting time.
  • The hour 6 should be considered as 6:00 am, when it is entered as an ending time.

  The following table may clarify allowed time values for this problem.

  Starting	Starting	Ending	Ending	Starting	Ending
  Hour	Minutes	Hour	Minutes	Time	time
  8	0	3	30	8:00pm	3:30am
  6	0	0	45	6:00pm	12:45am
  12	0	6	0	12:00am (midnight)	6:00am

  Programming Note: You may NOT use loops or recursion in this program.

create July 22, 2021 revised August 24, 2021
For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.