Lesson Outcomes
By the end of this worksheet, you should be able to:
- Define the basic units of data storage: bitA single binary digit (a zero or a one) written with a lower case b, nibbleA group of 4 binary digits or half a byte, ByteA group of 8 binary digits or two nibbles, it can hold 256 unique values.
- List the standard prefixes for storage units (KBAbbreviation for the unit that means 1000 bytes, MBTwo-letter abbreviation for Megabyte, GBA billion bytes, abbreviated to two letters, TBA thousand GB is which unit, shortened to two letters?, PBA Petabyte in two letters) in order of size.
- Understand the relationship between units (e.g., 1 KB ≈ 1000 Bytes).
- Perform simple conversions between different units of data storage.
- Explain why computers use binaryA number system using only two digits: 0 and 1..
Starter Task (Not Scored)
Quick check! Let's recall the basics of bits and Bytes.
1. How many bits are in one Byte?
2. In one sentence, why is the Byte a more common unit than the bit for measuring file sizes?
A single Byte (8 bits) can represent a useful piece of information like a character, while a single bit can only be 0 or 1, making Bytes more practical for measuring meaningful data.
Introduction: Measuring Digital Data
Computers store everything using binaryA number system using only two digits: 0 and 1. digits. We need units to measure how much data is being stored or transferred.
This lesson covers the standard units of data storage, from the smallest bitA single binary digit (a zero or a one) written with a lower case b up to large units like Petabytes1000 Terabytes, or a million Gigabytes, the long name. We'll also look at why computers use binary.
Hover over keywordsThis is an example tooltip! for definitions.
Task 1: Order the Units (Max 8 points)
Drag the units from the pool below into the numbered slots in the correct order, from smallest (1) to largest (8).
Hint: Remember the mnemonic: But Now Burger King Makes Great Toasted PaninisHow to remember file size order: Bits, Nibbles, Bytes, Kilobytes, Megabytes, Gigabytes, Terabytes, Petabytes!
Task 2: Match Definitions (Max 8 points)
Match the unit or abbreviation on the left with its correct definition or equivalent size on the right. Click one item from each list to make a pair.
Unit / Abbreviation
- bit
- nibble
- Byte
- KB
- MB
- GB
- TB
- PB
Definition / Size
- A group of 8 binary digits
- 1000 Megabytes
- A single binary digit (0 or 1)
- 1000 Gigabytes
- A group of 4 binary digits
- 1000 Terabytes
- 1000 Bytes
- 1000 Kilobytes
Task 3: Why Binary? (Max 1 point)
Computers fundamentally work with electrical circuits. Why is it easier and more reliable for these circuits to represent data using binary (two states)?
The core reason is reliability. Electrical circuits can easily and reliably distinguish between two distinct states, such as:
- Voltage being present (ON / 1) or absent (OFF / 0).
- A switch being closed (1) or open (0).
- Current flowing (1) or not flowing (0).
Trying to reliably detect many different voltage levels (e.g., for decimal) would be much more complex and prone to errors due to electrical noise or fluctuations.
Task 4: Simple Conversions (Max 10 points)
Calculate the answers to these common unit conversions. (Remember: 1 Byte = 8 bits, 1 KB = 1000 Bytes, 1 MB = 1000 KB, etc.)
Task 5: Interactive Unit Converter
Experiment with converting between different units of data storage. Enter a value, select the starting and target units.
Note: Uses standard prefixes (1 KB = 1000 B, etc.). This tool is for practice and is not scored.
Task 6: Build a File Simulation
See how file sizes grow! Choose a file type and add content or files to visualize the size in different units.
Current File Size:
Note: This simulation uses approximations (e.g., 1 KB = 1000 B, 1 char = 1 Byte/8 bits) for simplicity. It is not automatically scored.
Task 7: Binary Conversion Practice
Binary-to-denary conversions (and vice-versa) are essential for understanding data representation. Here are the methods:
Binary to Denary (Place Value Method)
- Write down the binary number.
- Above each digit, write its corresponding place value (powers of 2, starting from 1 on the right: ..., 128, 64, 32, 16, 8, 4, 2, 1).
- Add up the place values for every position where the binary digit is a '1'.
Example: 101102 = (16) + (4) + (2) = 2210
Denary to Binary (Subtraction Method)
- Start with the denary number you want to convert.
- Find the largest power of 2 (e.g., 128, 64, 32...) that is less than or equal to your number. Write a '1' in that position in your binary number.
- Subtract this power of 2 from your number.
- Take the remainder and repeat steps 2 and 3 until the remainder is 0.
- Fill any unused place value positions to the right of your leftmost '1' with '0's.
Example: Convert 2510: Largest power ≤ 25 is 16. Put '1' in 16s place. Remainder = 25-16=9. Largest power ≤ 9 is 8. Put '1' in 8s place. Remainder = 9-8=1. Largest power ≤ 1 is 1. Put '1' in 1s place. Remainder = 1-1=0. Fill gaps: 110012
Use the linked spreadsheet below for practice questions.
Open Binary Practice Questions (Excel)Note: This task is for practice and is not automatically scored on this page.
Key Takeaways
- Binary Basis: Computers use binaryA number system using only two digits: 0 and 1. (0s and 1s) because circuits reliably represent two states (on/off).
- Smallest Units: The smallest unit is a bitA single binary digit (a zero or a one) written with a lower case b. 4 bits make a nibbleA group of 4 binary digits or half a byte, and 8 bits make a ByteA group of 8 binary digits or two nibbles, it can hold 256 unique values.
- Standard Prefixes (Decimal): Units increase by factors of 1000: KilobyteFull name of the unit that represents 1000 bytes (KB), Megabyte1000 Kilobytes, or 1 million bytes, its full name (MB), Gigabyte1000 Megabytes, or 1 billion bytes, the full name (GB), Terabyte1000 Gigabytes, or a million Megabytes, in full (TB), Petabyte1000 Terabytes, or a million Gigabytes, the long name (PB).
- Order: Remember the order: bit, nibble, Byte, KB, MB, GB, TB, PB.
- Conversions: Be able to convert between units (e.g., bits to Bytes, KB to MB).
- Binary Prefixes (Optional): Operating systems sometimes use 1024-based units (KiB, MiB, GiB) which can cause apparent discrepancies in reported sizes.
Task 8: Final Quiz (Max 5 points)
Task 9: Exam Practice Questions
Apply your knowledge to these exam-style questions.
1. Arrange the following units of data storage in order from smallest to largest: MB, bit, TB, Byte, GB. [1 mark]
2. A file is 2000 KB in size. How large is this file in MB? [1 mark]
3. Explain why computers use binary to represent data. [2 marks]
4. A digital camera stores photos that are 5 MB each. How many photos can be stored on a 1 GB memory card? Show your working. [2 marks]
5. What is the difference between a bit and a Byte? [2 marks]
Task 10: Worksheet Progress
Check your score based on the interactive quiz questions and activities.
Your Score: 0 / 0
Note: Score based on Tasks 1, 2, 3, 4, 8. Starter Task, Converter, Simulation, Binary Practice & Exam Practice are not auto-scored.
Extension Activity: KB vs KiB (1000 vs 1024)
You might notice that a 1 TB hard drive often shows up in your operating system (like Windows) as having only around 931 GB available. This isn't necessarily lost space!
Storage manufacturers typically use decimal prefixes where 1 Kilobyte (KB) = 1000 Bytes, 1 Megabyte (MB) = 1000 KB, and so on. This is the standard SI definition.
However, operating systems often use binary prefixes where 1 Kibibyte (KiB)A unit representing 1024 (or 2^10) bytes. = 1024 Bytes, 1 Mebibyte (MiB) = 1024 KiB, etc. They sometimes confusingly display these using the symbols KB, MB, GB.
Calculation Challenge:
If your operating system reports a drive capacity as 465 GB (likely meaning 465 GiB), what was the approximate 'advertised' size of the drive in Terabytes (TB), assuming the manufacturer used the 1000-based definition?
Use the space below for rough work:
Hint:
- Convert the OS-reported size (465 GiB) into Bytes using the 1024 multiplier (465 * 1024 * 1024 * 1024 Bytes).
- Convert this total number of Bytes back into Terabytes (TB) using the 1000 multiplier (Total Bytes / 1000 / 1000 / 1000 / 1000).
- The result should be close to a round number commonly used for drive sizes (e.g., 0.5 TB).
Answer: Approx 0.5 TB