Modular Arithmetic Math Worksheet With Answers - Grade 7/8, University Of Waterloo, 2016 Page 11
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13Solution 2:
We can also approach this question by drawing a tree where the first level represents
the first digit, which can only be filled by a 1. The second row represents the second
digit which can be filled with a 1 or 0 and so on.
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
1 0
Counting the number of nodes on the last row, we get an answer of 16.
(b) How many different 5-digit binary numbers are there that have 1 as the last digit?
Solution 1:
Using a similar table from part (a), we have the following:
1
1
1
1
1
0
0
0
1
2
2
2
1
=
8
Notice that it is just half of our answer in part (a), because half of the possible 5-digit
numbers end in 1 and the other half end in 0.
Solution 2:
A tree for this question would look something like this:
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
Counting the number of nodes on the fifth level, we get an answer of 8.
11
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education