Why Is This Important in Computer Science?

Binary Search Trees (BSTs) are like smart organizers. They make it easy to:

• Find things quickly: You can find a number without checking every single one.

• Add or remove numbers easily: Everything stays in the right order automatically.

BSTs are used in apps, games, and websites to store and organize data, making them faster and more efficient. Learning about BSTs helps you understand how computers keep things neat and easy to find!

Correct Answer: D) 2

Explanation:

This question uses the modulo operation, which tells us the remainder when one number is divided by another.

Step-by-Step Process:

1. Start with the total number of markers (83) and the box size (7):

   • Divide 83 by 7 to see how many full boxes you can make.

   • 83 ÷ 7 = 11 full boxes (this means 11 boxes can be filled completely) with a remainder of:
     83 - (11 × 7) = 83 - 77 = 6.

2. Distribute the remaining markers (6) among 4 students:

   • Divide 6 by 4. Each student gets 6 ÷ 4 = 1 marker, leaving a remainder of:
     6 - (1 × 4) = 6 - 4 = 2.

3. How many markers are left?

   • After dividing the markers equally among the students, there are 2 markers left over.

Final Answer:
The number of markers left after distribution is 2, which matches Option D.

Why Is This Important in Computer Science?

The modulo operation is a powerful tool used in computer science to solve problems like:

• Organizing groups: For example, when dividing items into equal groups and finding leftovers.

• Programming logic: Many programs use modulo to repeat actions in loops or decide actions based on remainders.

• Everyday use: Modulo is also used in calendars (e.g., finding the day of the week) and games (e.g., deciding player turns).

By understanding modulo, you learn how computers solve these problems quickly and efficiently!

Correct Answer: B) Sound B

Explanation:

To find the total number of samples recorded, multiply the sampling rate (how many samples are taken per second) by the duration (how long the sound is recorded). This gives the total number of snapshots taken for each sound.

Step-by-Step Process:

1. Sound A:

   • Sampling rate: 1,800 samples/second

   • Duration: 5 seconds

   • Total samples:
     1,800 × 5 = 9,000 samples

2. Sound B:

   • Sampling rate: 2,300 samples/second

   • Duration: 4 seconds

   • Total samples:
     2,300 × 4 = 9,200 samples

3. Sound C:

   • Sampling rate: 1,500 samples/second

   • Duration: 6 seconds

   • Total samples:
     1,500 × 6 = 9,000 samples

Comparison of Totals:

• Sound A: 9,000 samples

• Sound B: 9,200 samples (highest)

• Sound C: 9,000 samples

Final Answer:
Sound B has the highest total number of samples recorded: 9,200 samples, which matches Option B.

Why Is This Important in Computer Science?

Audio sampling is how computers store sound by breaking it into tiny pieces, or "snapshots." This is important for:

• Creating music and videos: Digital audio relies on sampling to save and replay sounds.

• Improving sound quality: Higher sampling rates and longer durations capture more detail.

• Real-world applications: Audio sampling is used in video games, music players, and sound-editing software.

Understanding audio sampling helps students learn how computers turn real-world sounds into data they can process and store!

Correct Answer: A) PBZPHGRE

Explanation:

The ROT13 encryption shifts each letter in a word 13 places forward in the alphabet. If the shift goes past "Z," it wraps around to the beginning of the alphabet.

Step-by-Step Process:

Let’s encrypt the word "COMPUTER":

1. Write down the alphabet to track the shifts:
   ABCDEFGHIJKLMNOPQRSTUVWXYZ

2. Shift each letter 13 places forward:

   • C → P (C + 13 = P)

   • O → B (O + 13 = B)

   • M → Z (M + 13 = Z)

   • P → C (P + 13 = C)

   • U → H (U + 13 = H)

   • T → G (T + 13 = G)

   • E → R (E + 13 = R)

   • R → E (R + 13 = E)

3. Combine the shifted letters to form the encrypted word:
   PBZPHGRE

Final Answer:
The encrypted version of "COMPUTER" using ROT13 is PBZPHGRE, which matches Option A.

Why Is This Important in Computer Science?

Encryption like ROT13 is used to:

• Protect information: Encryption methods are the foundation of online security, used in passwords, messaging apps, and websites.

• Build secure systems: Knowing encryption helps in designing programs that protect sensitive data.

ROT13 is a simple example of encryption, and understanding it helps students learn how computers keep information safe!

Correct Answer: C) Compass and binoculars

Explanation:

A bitfield is a row of bits (1s and 0s) that represent information. In this game:

• 1 means the player has the item.

• 0 means the player does not have the item.

The bitfield 0110 represents the following:

• First bit (0): The player does not have a map.

• Second bit (1): The player has a compass.

• Third bit (1): The player has binoculars.

• Fourth bit (0): The player does not have a sail.

Breakdown of 0110:

• 0: No map

• 1: Compass

• 1: Binoculars

• 0: No sail

Final Answer:
The player has a compass and binoculars, which matches Option C.

Why Is This Important in Computer Science?

Bitfields are a simple but powerful way for computers to store information efficiently:

• Save memory: Each bit stores only one piece of information, saving space compared to storing larger numbers or words.

• Quick processing: Computers can quickly check or change specific bits.

• Applications: Bitfields are used in games (to track items or levels), file systems (to store permissions), and hardware settings.

Learning bitfields shows how computers store and manage lots of small pieces of information!

Correct Answer: C) 10

Explanation:

We start with x = 14 and apply each rule step by step, updating x after each rule.

Step-by-Step Process:

1. Rule 1:

   • If x is even, divide it by 2.

   • 14 is even, so:
     14 ÷ 2 = 7

2. Rule 2:

   • If the result is greater than 12, multiply it by 2.

   • If the result is less than or equal to 12, subtract 3.

   • 7 ≤ 12, so:
     7 - 3 = 4

3. Rule 3:

   • If the result is an even number, add 1.

   • If the result is odd, subtract 2.

   • 4 is even, so:
     4 + 1 = 5

4. Rule 4:

   • If the result is a multiple of 5, add 10.

   • If it is not a multiple of 5, divide it by 2 (round down if necessary).

   • 5 is a multiple of 5, so:
     5 + 10 = 15

5. Rule 5:

   • If the result is less than 8, multiply it by 4.

   • If it is greater than or equal to 8, add 6.

   • 15 ≥ 8, so:
     15 + 6 = 21

6. Rule 6:

   • If the result is a prime number, add 5.

   • If it is not prime, subtract 4.

   • 21 is not a prime number (it is divisible by 3), so:
     21 - 4 = 17

7. Rule 7:

   • If the result is between 20 and 30 inclusive, multiply by 3.

   • If it is outside this range, subtract 7.

   • 17 is outside this range, so:
     17 - 7 = 10

Final Answer:
The final result after applying all the rules is 10, which matches Option C.

Why Is This Important in Computer Science?

Conditional logic is essential in programming because it:

• Makes decisions: Programs use conditions to decide what actions to take based on the input or situation.

• Handles complex rules: Conditions help computers process multiple steps in order, like this example.

• Builds smarter systems: Many apps, games, and websites rely on conditional statements to work correctly.

By learning conditional logic, you understand how computers make decisions step by step!

Correct Answer: D) Statement 2 ∧ (Statement 3 ∨ Statement 4)

Explanation:

In Boolean logic:

• ∧ (AND): The result is True only if both sides are True.

• ∨ (OR): The result is True if at least one side is True.

Let’s evaluate each option step by step.

Step-by-Step Evaluation

1. Option A: Statement 1 ∧ Statement 2 ∧ Statement 3

   • Statement 1: True

   • Statement 2: True

   • Statement 3: False

   • True AND True AND False = False

   • Result: False

2. Option B: Statement 3 ∨ (Statement 1 ∧ Statement 4)

   • Statement 3: False

   • Statement 1 AND Statement 4:

     • Statement 1: True

     • Statement 4: False

     • True AND False = False

   • False OR False = False

   • Result: False

3. Option C: (Statement 2 ∨ Statement 4) ∧ Statement 1

   • Statement 2 OR Statement 4:

     • Statement 2: True

     • Statement 4: False

     • True OR False = True

   • True AND Statement 1:

     • Statement 1: True

     • True AND True = True

   • Result: True

This is True, but let’s check Option D for accuracy.

4. Option D: Statement 2 ∧ (Statement 3 ∨ Statement 4)

   • Statement 2: True

   • Statement 3 OR Statement 4:

     • Statement 3: False

     • Statement 4: False

     • False OR False = False

   • True AND False = False

   • Result: False

Final Answer: D

Why Is This Important in Computer Science?

Boolean logic is a fundamental concept in computer science that helps process and make decisions about digital information. Understanding Boolean logic is important for various reasons:

• Program Control: Boolean logic is used to control program flow, making decisions based on true or false conditions.

• Data Validation: Boolean logic enables the validation of data, ensuring that input values are within expected ranges.

• Algorithm Design: Boolean logic is essential in designing algorithms, which are sets of instructions that computers follow to solve problems.

Boolean logic is a fundamental concept in computer science that helps process and make decisions about digital information. Understanding Boolean logic is important because it enables developers to create more efficient algorithms, validate data accurately, and design reliable software systems.

Correct Answer: B) 680 mb

Explanation:

To find the file size where the time for Option A (uploading) equals the time for Option B (driving), calculate the total time for both options and solve for the file size.

Step-by-Step Process:

1. Option A (Uploading):
   The total time to upload a file is:
   Time = 20 + (0.5 × File Size in mb)

2. Option B (Driving):
   The total time to drive is:
   Time = 8 blocks × 45 seconds per block = 360 seconds

3. Set the times equal to find the file size:
   20 + (0.5 × File Size) = 360

4. Solve for the file size:
   Subtract 20 from both sides:
   0.5 × File Size = 340
   Divide by 0.5:
   File Size = 680 mb

Final Answer:
The file size that makes the time for Option A equal to Option B is 680 mb, which matches Option B.

Why Is This Important in Computer Science?

Time complexity helps compare how efficient different methods (algorithms) are for solving a problem. Learning this concept helps you:

• Choose the best approach to save time and resources.

• Optimize processes by understanding how factors like file size affect performance.

• Apply these skills to real-world tasks like uploading files or processing data.

Correct Answer: B) 14

Explanation:

To find the value of w, we calculate each variable step by step based on the given assignments.

Step-by-Step Process:

1. a = 12

   • The value of a is directly given as 12.

2. b = a ÷ 3 + 4

   • Substitute a = 12:
     b = 12 ÷ 3 + 4 = 4 + 4 = 8

3. c = (b × 2) - a

   • Substitute b = 8 and a = 12:
     c = (8 × 2) - 12 = 16 - 12 = 4

4. d = c + (b - a ÷ 4)

   • Substitute c = 4, b = 8, and a = 12:
     d = 4 + (8 - 12 ÷ 4) = 4 + 5 = 9

5. e = d × 3 + c

   • Substitute 9 = 4 and c = 4:
     e = (9 × 3) + 4 = 27 + 4 = 31

6. w = e - (d + b)

   • Substitute e = 31, d = 9, and b = 8:
     w = 31 - (9 + 8) = 31 - 17 = 14

Final Answer:
The value of w is 14, which matches Option B.

Why Is This Important in Computer Science?

Variables are essential in programming because they:

• Store data: Variables hold values that can change as the program runs.

• Simplify calculations: Instead of repeating numbers, we can refer to variables to make code easier to read and update.

• Help with problem-solving: By breaking complex problems into smaller steps, we can find solutions systematically.

Learning how variables work helps you understand how programs perform calculations and make decisions.

Part 1: What is the compressed version of the string using RLE?

Correct Answer: D) 4P2Q6R4E9W5A3G4H

Explanation:

To compress the string using Run-Length Encoding (RLE), count how many times each character repeats consecutively and write the count followed by the character. Let’s break it down:

Original string: PPPPQQRRRRRREEEEWWWWWWWWWAAAAAGGGHHHH

1. Count consecutive characters:

   • 4P (4 Ps in a row)

   • 2Q (2 Qs in a row)

   • 6R (6 Rs in a row)

   • 4E (4 Es in a row)

   • 9W (9 Ws in a row)

   • 5A (5 As in a row)

   • 3G (3 Gs in a row)

   • 4H (4 Hs in a row)

2. Write the compressed version:
   4P2Q6R4E9W5A3G4H

Part 2: Calculate the percentage of space saved by using RLE.

Correct Answer: C) 57%

Explanation:

1. Length of the original string:

   • Original string: PPPPQQRRRRRREEEEWWWWWWWWWAAAAAGGGHHHH

   • Length = 37 characters.

2. Length of the compressed string:

   • Compressed string: 4P2Q6R4E9W5A3G4H

   • Length = 16 characters.

3. Space saved:
   Space Saved​ = Original Length − Compressed Length

= 37 − 16

= 21​

4. Percentage of space saved:
   Percentage Saved ​= (Space Saved ÷ Original Length) × 100

= (21 ÷ 37) × 100

≈ 57%​

Final Answers:

1. Compressed string: 4P2Q6R4E9W5A3G4H

2. Percentage of space saved: 57%

Why Is This Important in Computer Science?

Data compression reduces the amount of space needed to store or transfer information, which is critical for:

• Saving memory: Reducing file sizes means more data can be stored.

• Speeding up communication: Smaller files upload, download, or transmit faster.

• Everyday applications: RLE is used in images, audio, and video files to save space while keeping the data intact.

Learning about RLE helps you understand how computers handle large amounts of data efficiently!

Correct Answer: B) 16

Explanation:

The program involves looping through steps with specific conditions. Each loop iteration and instruction execution counts as one step. Let’s simulate the process step by step.

Step-by-Step Simulation:

[0]: Start with the counter at 1

counter = 1

next step = 1

[1]: Multiply the counter by A

counter = 3

next step = 2

[2]: If the counter is even, add B; otherwise, don't change it

counter = 3

next step = 3

[3]: If the counter is still less than the Target Value (50), go back to step [1]; otherwise don't change it

counter = 3

next step = 1

[1]: Multiply the counter by A

counter = 9

next step = 2

[2]: If the counter is even, add B; otherwise, don't change it

counter = 9

next step = 3

[3]: If the counter is still less than the Target Value (50), go back to step [1]; otherwise don't change it

counter = 9

next step = 1

[1]: Multiply the counter by A

counter = 27

next step = 2

[2]: If the counter is even, add B; otherwise, don't change it

counter = 27

next step = 3

[3]: If the counter is still less than the Target Value (50), go back to step [1]; otherwise don't change it

counter = 27

next step = 1

[1]: Multiply the counter by A

counter = 81

next step = 2

[2]: If the counter is even, add B; otherwise, don't change it

counter = 81

next step = 3

[3]: If the counter is still less than the Target Value (50), go back to step [1]; otherwise don't change it

counter = 81

next step = 4

[4]: Subtract C from the counter

counter = 76

next step = 5

[5]: If the counter is less than the Target Value (50), go back to step [1]; otherwise don't change it

counter = 76

next step = 6

[6]: Stop (Program stops here if counter is equal to or greater than the Target Value)

counter = 76

The program took 16 steps to complete.

Why Is This Important in Computer Science?

Assembling code involves translating high-level programming languages into machine-specific instructions that can be executed directly by a computer's processor. Understanding assembly language is crucial for:

• Low-Level Programming: Assembly language provides direct access to hardware resources, making it useful for systems programming, embedded systems development, and low-level optimization.

• Debugging: Disassembling binary files into assembly code helps developers understand how their program executes, facilitating error debugging and optimization.

• Performance Optimization: Analyzing assembly code enables developers to identify bottlenecks, optimize loops, and enhance overall system performance.

In this specific solution, understanding the steps involved in simulating a program's execution demonstrates the importance of low-level programming concepts like looping, conditional statements, and iteration.

Correct Answer: C) TREE

Explanation:

We use the password hashing algorithm to calculate the hash for each option and find the one that matches the given hash value of 101.

Algorithm Recap:

1. Convert each letter to its number in the alphabet (A = 1, B = 2, ..., Z = 26).

2. Multiply each letter’s value by its position in the word (1 for the first letter, 2 for the second, etc.).

3. Add up all the results for each letter.

4. Add 10 to the total to get the final hash.

Option A: DOG

• D = 4, O = 15, G = 7

• Multiply by positions:

  • 4 × 1 = 4

  • 15 × 2 = 30

  • 7 × 3 = 21

• Sum of results: 4 + 30 + 21 = 55

• Add 10: 55 + 10 = 65
  Result: Does not match the hash value of 101.

Option B: BEAR

• B = 2, E = 5, A = 1, R = 18

• Multiply by positions:

  • 2 × 1 = 2

  • 5 × 2 = 10

  • 1 × 3 = 3

  • 18 × 4 = 72

• Sum of results: 2 + 10 + 3 + 72 = 87

• Add 10: 87 + 10 = 97
  Result: Does not match the hash value of 101.

Option C: TREE

• T = 20, R = 18, E = 5, E = 5

• Multiply by positions:

  • 20 × 1 = 20

  • 18 × 2 = 36

  • 5 × 3 = 15

  • 5 × 4 = 20

• Sum of results: 20 + 36 + 15 + 20 = 91

• Add 10: 91 + 10 = 101
  Result: Matches the hash value of 101.

Option D: MOON

• M = 13, O = 15, O = 15, N = 14

• Multiply by positions:

  • 13 × 1 = 13

  • 15 × 2 = 30

  • 15 × 3 = 45

  • 14 × 4 = 56

• Sum of results: 13 + 30 + 45 + 56 = 144

• Add 10: 144 + 10 = 154
  Result: Does not match the hash value of 101.

Final Answer: C) TREE produces the hash value of 101.

Why Is This Important in Computer Science?

Password hashing algorithms are essential for:

• Enhancing security: They make it hard to reverse-engineer passwords.

• Ensuring data integrity: Even small changes in a password produce completely different hashes.

• Everyday applications: Used in login systems, databases, and secure communications.

Understanding hashing builds a strong foundation in cybersecurity and data protection.

Correct Answer: B) 26

Explanation:

To find the shortest path from A to P, we use the given grid and calculate the step costs. This involves trying different possible paths and summing up their costs to identify the path with the lowest total cost.

Step-by-Step Process

1. Understand the Grid: Each node (A, B, C, etc.) is connected by a number that represents the cost (or steps) to move between them. We need to find the path from A to P that has the smallest total cost.

2. Possible Paths from A to P: We evaluate different paths by summing the step costs along the way. For simplicity, we focus on the shortest one.

Shortest Path:

• Path: A → E → F → G → K → O → P

  • A → E: 6

  • E → F: 2

  • F → G: 6

  • G → K: 4

  • K → O: 5

  • O → P: 3

Total Step Cost: 6 + 2 + 6 + 4 + 5 + 3 = 26

Why Is This Path the Best?

• The shortest path avoids unnecessary detours and uses the smallest step costs for each movement.

• After evaluating all valid paths, A → E → F → G → K → O → P is the shortest with a total cost of 26.

Why Is This Important in Computer Science?

Pathfinding algorithms like this are used in:

• Navigation systems: GPS applications use algorithms to find the quickest route.

• Video games: Characters or units navigate through maps using pathfinding.

• Robotics: Robots calculate the most efficient paths to move between points.

By practicing these problems, you build an understanding of how computers solve optimization problems efficiently!