Data Representation — Practice Questions
8 questions · Original exam-style content
Short-Answer Questions
Write your answer, then reveal the mark scheme.
Q1Show your working to convert the binary number 1001 0110 to its denary equivalent.[2 marks]Click to reveal mark scheme ↓
Mark Scheme
- Correct identification of place values with a 1: 128, 16, 4, 2[1]
- Correct total: 150[1]
Command word: Show
Q2Show your working to convert the denary number 173 to an 8-bit binary number.[2 marks]Click to reveal mark scheme ↓
Mark Scheme
- Correct working showing repeated subtraction or division (e.g. identifies 128 fits, remainder 45; 32 fits, remainder 13; 8 fits, remainder 5; 4 fits, remainder 1; 1 fits)[1]
- Correct 8-bit answer: 1010 1101[1]
Command word: Show
Q3A music file has a size of 5 megabytes (MB). Calculate the size of this file in bytes. Show your working.[2 marks]Click to reveal mark scheme ↓
Mark Scheme
- 1 MB = 1024 KB AND 1 KB = 1024 bytes, OR 1 MB = 1024 × 1024 bytes = 1,048,576 bytes[1]
- Correct calculation: 5 × 1,048,576 = 5,242,880 bytes[1]
Command word: Calculate
Multiple Choice
These are also available as an interactive knowledge check within each lesson.
Q1What is the denary value of the 8-bit binary number 0110 1010?
- ○A. 96
- ✓B. 106
- ○C. 108
- ○D. 112
Columns with a 1: 64, 32, 8, 2. Sum: 64 + 32 + 8 + 2 = 106.
Q2What is the maximum denary value that can be stored in an 8-bit binary number?
- ○A. 128
- ○B. 254
- ✓C. 255
- ○D. 256
1111 1111₂ = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. The value 256 requires 9 bits.
Q3Which 8-bit binary number is equal to the denary value 47?
- ✓A. 0010 1111
- ○B. 0011 0000
- ○C. 0010 1100
- ○D. 0011 1111
47 = 32 + 8 + 4 + 2 + 1 = 0010 1111. Check: 32 + 8 + 4 + 2 + 1 = 47 ✓
Q4How many bits are there in one byte?
- ○A. 2
- ○B. 4
- ✓C. 8
- ○D. 16
One byte consists of 8 bits. A group of 4 bits is called a nibble.
Q5In an 8-bit binary number, what is the place value of the leftmost (most significant) bit?
- ○A. 16
- ○B. 64
- ✓C. 128
- ○D. 256
The 8-bit columns are (left to right): 128, 64, 32, 16, 8, 4, 2, 1. The most significant bit has the value 2⁷ = 128.