Assignment 1

Suggested Problems (not to be turned in)

• Rosen, Section 1.1, ex: 16, 23, 26, 29, 35, 47
• Rosen, Section 1.2, ex: 44, 46, 47
• Rosen, Section 1.3, ex: 5, 7, 8, 35, 36
• Rosen, Section 12.3, ex: 1, 4, 5, 6bc

Required Problems, due August 26

• Rosen, Section 1.1, ex: 30, 37
• Rosen, Section 1.2, ex: 45 (but add an inverter on the wire between input p and the attached AND gate.
• Rosen, Section 1.3, ex: 18, 24
• Rosen, Section 12.3, ex: 6ad
• Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces the output (p ∧ q) ∨ (¬ p ∧ r) from input bits p, q, and r.
• Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces the output ((¬ p ∧ ¬ q) ∧ r) ∨ ((p ∧ q) ∧ r) from input bits p, q, and r.
• (This problem is motivated by a sign on a stairway door in a hotel hallway, in the Washington, D.C. area.)
  Consider the following two statements:
  • Sign on door: "This door is to remained closed at all time"
  • Logical proposition: "If a person leaves a hallway, then they must pass through an open door."

  What conclusion(s) can you draw from these two statements. Briefly justify your answer.

• Write a Python program that generates a truth table to show that the expression in Section 1.3, exercise 27, is a logical equivalence.

• Challenge Problem (source hidden for this problem set)(extra credit): Three logicians, A, B, and C are each wearing a hat containing a positive integer. The logicians can see the hats of the others, but cannot see their own hat. In this problem, it is known that one of the numbers is the sum of the other two.

  A announces, "I don't know my number," after which B announces, "My number is 10." What numbers are on A and C? Briefly explain your reasoning.

  Note: In this problem, you may assume that each logician is error-free in his or her reasoning.

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