Math 110T
Final
Name____________________________
1.)Which of the following is the same as x6/x2?
a.) x3
b.) x4
c.) x62
d.) x8
2.) Fill in the blank: 55 x 103 = ______________ x 10-2
3.) Fill in the blank: 0.18 x 10-3 = ______________ x 103
4.) Write the following number in scientific notation: 346000000
5.) Write 0.0000047 in scientific notation.
6.) In binary, what number comes after 101011?
7.) In binary, what number comes before 10011?
8.) Convert the (base 10) number 29 to base 16.
9.) Convert the (base 2) number 10111 to base 10.
10.) Convert the (base 10) number 26 to base 2.
11.) Convert the (base 16) number 3A to base 10.
12.) Convert the (base 2) number 101000111111 to base 16.
13.) If the metric prefix “kilo” means 103 and the metric prefix “micro” means 10-6 then
how many centimeters are there in 4 kilometers?
14.) If the metric prefix “giga” means 109 and the metric prefix “kilo” means 103 then
how many kilobytes are there in 20 gigabytes?
15.) Add the two binary numbers together: 10111 and 11011 (without converting to base
10!)
16.) If statement A is true and statement B is false, which of the following statements is
true? (Circle the corresponding letter for each one that is true.)
a.)
b.)
c.)
d.)
A AND B
(NOT A) OR (A OR (NOT B))
(NOT B) AND ((NOT A) OR B)
((NOT A) OR B) OR (A AND B) OR (A OR (NOT B))
17.) For the logic network below, construct the corresponding truth table:
18.) For the truth table below, fill in the Karnaugh map and then construct the
corresponding simplified logical expression or logic network:
A
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
B
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
C
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
D
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
Y
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
For the next three questions, assume you have a set
X = {a, b, c, d, e, f}
With subsets
A = {a, b, c, d}
And
B = {b, d, e}
19.) What is the intersection A  B?
20.) What is the union A  B?
21.)What is the complement of A?
22.) List all the subsets of the set X = {a, b}
23)List the elements of the Cartesian product X x Y of the sets
X = {a, b, c}
Y = {1, 2}
24) How many ways can you select 4 people to be in a committee if out of a group of 25
people? (You can leave your answer in factorials.)
25) How many ways can a race with 7 horses finish with horses coming in first, second,
and third? (You can leave your answer in factorials.)
26) How many ways can you arrange 15 books on a shelf? ? (You can leave your
answer in factorials.)
27) Draw a directed graph corresponding the relation below:
28) For the graphs below, list all graphs that:
i)
Are a tree _______________
ii)
Have an Eulerian path (a path going through all edges) __________________
29) For the following machine, what is the output of the input string 11010010?
30) Analyze the behavior of the following machine: