APCSP Data Representation 2 — Questions and Answers
Question 1: Which of the following best describes why computers use binary (base-2) rather than decimal (base-10) to store data?
- Binary arithmetic is faster than decimal arithmetic
- Electronic circuits naturally represent two states (on/off), making binary practical (Correct answer)
- Binary uses fewer digits so storage is smaller
- Decimal numbers cannot be converted to machine code
Correct answer: Electronic circuits naturally represent two states (on/off), making binary practical
Electronic components like transistors naturally exist in two stable states (on/off or high/low voltage), making binary the most practical number system for hardware.
Question 2: How many unique values can be represented using 4 bits?
- 4
- 8
- 16 (Correct answer)
- 32
Correct answer: 16
With n bits you can represent 2^n unique values; 2^4 = 16.
Question 3: The hexadecimal value 0xFF is equivalent to which decimal value?
- 15
- 160
- 255 (Correct answer)
- 256
Correct answer: 255
F in hex equals 15, so 0xFF = 15×16 + 15 = 240 + 15 = 255.
Question 4: A color image is stored using 24-bit color (8 bits per channel for red, green, blue). How many distinct colors can it represent?
- 256
- 65,536
- 16,777,216 (Correct answer)
- 4,294,967,296
Correct answer: 16,777,216
24 bits total gives 2^24 = 16,777,216 distinct color combinations.
Question 5: Which encoding standard assigns a unique number to every character and supports over 140,000 characters from multiple languages and symbol sets?
- ASCII
- UTF-8 / Unicode (Correct answer)
- Base64
- EBCDIC
Correct answer: UTF-8 / Unicode
Unicode (with UTF-8 as a common encoding) assigns code points to over 140,000 characters covering most of the world's writing systems.
Question 6: What is the decimal equivalent of the binary number 1010?
- 5
- 8
- 10 (Correct answer)
- 12
Correct answer: 10
1×8 + 0×4 + 1×2 + 0×1 = 8 + 0 + 2 + 0 = 10.
Question 7: Lossless data compression differs from lossy compression in that lossless compression:
- always produces a smaller file than lossy compression
- allows the original data to be perfectly reconstructed (Correct answer)
- works only on text files
- removes data that is perceptually unimportant to humans
Correct answer: allows the original data to be perfectly reconstructed
Lossless compression encodes data so the original can be reconstructed exactly, while lossy compression permanently discards some information.
APCSP Data Representation 2
Which of the following best describes why computers use binary (base-2) rather than decimal (base-10) to store data?