CSC103 Exercises on Binary System and Boolean Logic

--D. Thiebaut 20:22, 31 January 2012 (EST)

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Exercise 1: Logic Expressions

Assume that we have several boolean expressions, labeled E1 to E6:

• E1: is a Smith student
• E2: is a senior
• E3: likes vanilla
• E4: has class on Monday
• E5: takes classes at Hampshire College
• E6: is on the crew team

What is the boolean expression that is a combination of E1, E2, E3, E4, and/or E5, and the logic operators AND, OR, and NOT, that will be True whenever I find somebody on campus who's a 5-college student who goes to class only on Tuesdays and Thursdays?

Hints: see if you can discard any of the boolean expressions, and write the truth table for the wanted expression.

Exercise 2: Logic

What is the truth table for the expression E9 = ( E7 or E6 ) and ( not E8 )

Exercise 3: Binary System

• In binary, what are the numbers that logically follow these numbers:
  • 00000000000111
  • 11011
  • 0000111
  • 112

Exercise 4: Binary Additions

• Perform the following additions of binary numbers by hand=

     111111
   +      1
        

     110011
   + 110011

Exercise 5: Base 3

• Assume that you have system with only three digits: 0, 1, and 2.

• Count in base 3, and list the first 15 numbers of the series, starting with 0.

• What is the numbers that logically follow the numbers base 3 listed below?
  • 101
  • 102
  • 112
  • 222

Exercise 6: Adding in Base 3

• Perform the following additions in Base 3:

      111222
   +       1

      120112
   +  122110