COT3100 Discrete Structures Print Your Name ______________________________ February 13–15, 2020 Quiz II Discussion Period _____ Leaders _________/_________ Instructions
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Exam Evaluation
This exam is worth 50 points and it has six problems.


Problem Points Max Problem Points Max Problem Points Max

1 _______ / 12 3 _______ / 12 5 _______ / 3

2 _______ / 12 4 _______ / 8 6 _______ / 3







TOTAL _______ / 50


February 13–15, 2020 COT3100 Quiz II Page 2 of 2 Score _______


1. [12 pts] Given () = 2' + 5 − 3, find the () such that () is .()/. Prove your answer.

2. [12 pts] Use pseudocode to describe an algorithm for the procedure: String int_to_binary_string(
int number ). The procedure receives a positive int [ ∈ 7] into its corresponding binary
bit string and returns the binary string. Prove the time complexity of your solution.

3. [12 pts] Use pseudocode to describe an algorithm for the procedure: int[][] find_pairs( int array[],
int value ). Given a sorted array of distinct integers and a single integer value, find all pairs of
indexes in the list whose product is equal to the value. Return the index pairs on the same row of a
two-dimensional array. Note, will be the number of rows and total number of pairs found, while 2 will be the number of columns along every row [the first and second index position. Prove the
time complexity of your solution. If you solve the problem in () time, +3 Extra Credit Points.

Example Data
Array: [ 1, 2, 4, 5, 6, 9, 10, 15, 20 ]
Value: 20

Return: 0, 8
1, 6
2, 3

4. [8 pts] Given ≡ ( ) and ≡ ( ), = 60, = 83, and = 4, find and prove
the general case(s) representing the possible values for and , such that + ≡ + ( ).

5. [3 pts] Convert the decimal value 300 into the corresponding bases.

Binary
Octal
Decimal 300
Hexadecimal


6. [3 pts] Convert the 2s Complement value 1101 0010 into the corresponding bases.

2s Complement 1101 0010
Octal
Decimal
Hexadecimal