View source for CSC103 Exercises on Binary System and Boolean Logic

--[[User:Thiebaut|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