CSC103 Homework 1 2012f

--D. Thiebaut 07:53, 11 September 2012 (EDT)

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This homework assignment is due on Thursday Sept. 20th, at 9:00 a.m. Please print it or write it on paper, and bring it to class on the due date. No late assignments will be accepted.

Question #1

Count in binary and write down first 33 numbers of the series. In other words, complete the second column in the list below.

Decimal      Binary
0                 0
1                 1
2                10
3                11
4                ...
5
6
7
8
9
10
11
12
13
14
15
16
17
18 
19
20
21 
22
23
24
25
26
27
28
29
30
31
32

Perform the following additions in binary:

    10011 + 10011 =

    10111 + 00110 =

Question #2

Assume that we live in a universe where everybody only has 4 fingers. Just as we did in class with a system of 2 digits (binary code), we invente a system for counting with only 4 digits: 0, 1, 2, and 3.

• Write the first 20 numbers of a system with 4 digits. To help you out, I will start with the first 7 numbers of the series:

0
1
2
3
10
11
12
...

Continue on until you have 20 consecutive numbers of a system in base 4.

Question #3

Perform the addition of the following numbers in base 4.

    1002 + 2301 = 

    2222 + 3301 = 

Question #4

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 is a Hamshire College student and who does not like vanilla?

Hints:

1. see if you can discard any of the boolean expressions, and write the truth table for the wanted expression.
2. generating the truth table for what you want will help you get the boolean expression.