CSC103 Exercises on Binary System and Boolean Logic
--D. Thiebaut 20:22, 31 January 2012 (EST)
Contents
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