ex Introduce yourself and work with digital logic gates.

Read Orange Boxes

Well actually, read everything, but these call out important pieces, traps to avoid, etc.

Each CS 240 assignment will include basic info at the top, describing due dates (and any intermediate checkpoints), how to submit your work, a list of links to the reading topics that are good reference for the assignment, and an indication of what collaboration is allowed.

Introductions

Visit Ben within one week of our first class meeting to introduce yourself and chat for a couple minutes about:

  • your preferred name and pronouns;
  • CS courses you have taken, are taking, or hope to take in the future;
  • excitement, concerns, or questions about this course;
  • anything else you deem conversation-worthy, including when was the last time you played in the snow (or some other fact not about CS).

Exercises

  1. A logician walks into a coffee shop and says, “I want a large quadruple shot chai french press americano or a small soy mocha earl grey espresso and a blueberry scone.” Unfortunately, the baristas did not take CS240, nor do they really care whether “and” has precedence over “or.” As far as they’re concerned, one interpretation is as good as the other. Which of the following cases are valid interpretations of the order? (Note that English “or” means “exclusive or.”)

    1. Just a large quadruple shot chai french press americano
    2. Just a small soy mocha earl grey espresso.
    3. Just a blueberry scone.
    4. Both a large quadruple shot chai french press americano and a blueberry scone.
    5. Both a small soy mocha earl grey espresso and a blueberry scone.
    6. Both a large quadruple shot chai french press americano and a small soy mocha earl grey espresso.
    7. All three.
    8. Nothing. The baristas snub the logician for being clueless about hot drinks.

  2. Our assumption in this course is that logical “and” does take precedence over logical “or” and logical “or” is always “inclusive or” unless stated explicitly to the contrary. Which of the choices given in the previous question are valid interpretations of the order under these assumptions?

  3. Write truth tables and unsimplified Boolean expressions for each of the output signals F1 and F2 in the following circuit. Create the boolean expressions via a direct translation of the circuit.

    ciruit.png

    Please draw your truth table in the following order.

    A B C   F2 F1
    0 0 0      
    0 0 1      
    0 1 0      
    0 1 1      
    1 0 0      
    1 0 1      
    1 1 0      
    1 1 1      

  4. Use a truth table to show that P = (P AND Q) OR (P AND NOT Q). Show columns for the intermediate expressions and the final expression.

  5. Either write a Boolean expression or draw a circuit (your choice) in sum-of-products form for the output Y of this truth table.

    A B C   Y
    0 0 0   1
    0 0 1   0
    0 1 0   1
    0 1 1   0
    1 0 0   1
    1 0 1   1
    1 1 0   0
    1 1 1   1

  6. Draw unsimplified circuits to implement the following Boolean expressions. We use the apostrophe’ notation as an alternative to the overbar to indicate logical negation of the preceding term. The apostrophe binds tightly. For example, AB’ means (A)(B’).

    1. (A + B)(A + B’)
    2. ABC + A’B + ABC’
    3. A’B’ + A’BC’ + (A + C’)’

  7. Using elementary rules of Boolean algebra, find the simplest equivalent of the Boolean expressions from the previous problem using only products, sums, and negation (i.e., no XOR). Show your derivation step by step. Label each step with the name of the rule you apply.

    Optional: Do the same for this expression, but feel free to do similar steps all at once.

    • ABC + ABD + ABE + ACD + ACE + (A + D + E)’ + B’C’D + B’C’E + B’D’E’ + C’D’E’

  8. Draw circuits for the simplified Boolean expressions from the previous problem.