Download Math 110T - Seattle Central College

Math 110T
Final
Name____________________________
1.)Which of the following is the same as x4/x2?
a.) x8
b.) x2/3
c.) x42
d.) xx
2.) Fill in the blank: 8 x 103 = _________ x 10-3
3.) Fill in the blank: 7.3 x 10-4 = ______________ x 102
4.) Write the following number in scientific notation: 6200000000
5.) Write 0.00000054 in scientific notation.
6.) In binary, what number comes after 10011?
7.) In binary, what number comes before 11100?
8.) Convert the (base 10) number 59 to base 16.
9.) Convert the (base 2) number 11101 to base 10.
10.) Convert the (base 10) number 22 to base 2.
11.) Convert the (base 16) number 2C to base 10.
12.) Convert the (base 2) number 1011010101101111 to base 16.
13.) If the metric prefix “kilo” means 103 and the metric prefix “tera” means 1012 then
how many kilobytes are there in 5 terabytes?
14.) If the metric prefix “micro” means 10-6 and the metric prefix “centi” means 10-2 then
how many micrometers are there in 7 centimeters?
15.) Add the two binary numbers together: 10011 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 OR B
A AND ((NOT A) OR (NOT B))
(NOT B) AND (A OR (NOT B))
(A AND (NOT B)) OR (A AND B)
17.) (Worth 2 questions.) 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
1
0
0
0
0
For the next three questions, assume you have a set
X = {a, b, c, d, e, f, g}
With subsets
A = {a, c, d}
And
B = {c, d, f}
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, c}
23)List the elements of the Cartesian product X x Y of the sets
X = {1, 2, 3}
Y = {a, b}
(Combinatorics) – You can leave your answers with factorials (that is, you don’t have to
multiply out the factorials).
24) How many ways are there to select 4 things out of 10?
25) How many ways are there to select 4 things out of 10 and put them in a row?
26) How many ways are there to form a committee of 5 people from a group of 30
students?
27) How many ways are there to make “words” (strings of symbols) 6 letters long out of
26 letters.
28) Which of the following graphs has an Eulerian path? Explain why.
29) For the following machine, what is the output of the input string 11010010?
30) Analyze the behavior of the following machine: