CSC103 Homework 1 2013

--D. Thiebaut (talk) 07:25, 10 September 2013 (EDT)

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This homework assignment is due on Tuesda Sept. 17th, 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 the first 35 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
33
34

Perform the following additions in binary:

    10110 + 10011 =

    11110 + 10110 =

Question #2

Assume that we live in a universe where everybody has only 3 fingers. Just as we did in class for a counting system with 2 digits (binary code), we invent a system for counting with only 6 digits (3 fingers + 3 fingers): 0, 1, 2, 3, 4, and 5.

• Write the first 30 numbers of a system with 6 digits. To help you out, I will start with the first 9 numbers of the series:

0
1
2
3
4
5
10
11
12
...

Continue on until you have 20 consecutive numbers of a system in base 6.

Question #3

Perform the addition of the following numbers in base 4.

    1003 + 2301 = 

    2232 + 3101 = 

Question #4

What is the truth table for this boolean function? You may want to refer to the "ice cream" example in the instructor's notes posted in the weekly schedule:

       f = ( a and b ) or ( a and not c )  or ( not b )

The result should be a truth table where the last column contains all the possible values (T or F) that the function f can take for all the combinations of a, b and c.