Fundamentals of Data Representation
What's covered
Key facts
Binary Addition
0011 + 0011 = 0110 (3 + 3 = 6).
Binary Shifts: Logical Left and Right
A logical left shift by 1 multiplies an unsigned binary number by 2.
Character Encoding: ASCII (7-bit)
The ASCII code for the digit '0' is decimal 48; '1' is 49; '9' is 57.
Character Encoding: Unicode
Unicode uses more bits per character on average than ASCII because it must cover a far larger character set.
Converting Between Binary, Decimal and Hexadecimal
Binary 1010 = 8 + 0 + 2 + 0 = 10 in decimal.
Data Compression: Need and Benefits
The two compression methods named on the AQA spec are Huffman coding and run-length encoding (RLE).
Huffman Coding
Each branch from a Huffman tree node represents a binary digit (typically 0 = left, 1 = right).
Image File Size Calculations
A 1000 × 1000 image at 8-bit colour = 8 × 10⁶ bits ÷ 8 = 1 × 10⁶ bytes ≈ 1 MB (AQA decimal megabyte = 10⁶ bytes).
Image Representation: Pixels, Resolution, Colour Depth
1-bit colour depth allows 2¹ = 2 colours per pixel (typically black and white).
Number Bases: Decimal, Binary, Hexadecimal
Binary uses 2 digits: only 0 and 1.
Practice questions with answers
A taste of the 161 questions in this topic, answers marked. Sign up to practise the full set with spaced repetition.
What does 1 + 1 equal in binary?
- ✓10
- •100
- •11
- •2
What is 0011 shifted left by 1?
- •0001 (one in decimal)
- •0011 (three unchanged)
- ✓0110 (six in decimal)
- •1100 (twelve in decimal)
How many characters can 7-bit ASCII represent?
- ✓128 (2 to the 7)
- •256 (2 to the 8)
- •512 (2 to the 9)
- •64 (2 to the 6)
What was the main reason Unicode was developed?
- •To allow computers to process images alongside text
- •To reduce the file size of text documents
- •To replace binary with a more efficient encoding
- ✓To support more languages worldwide
What is binary 00001111 in decimal?
- •Eight (only the leftmost bit)
- ✓Fifteen (the value of nibble F)
- •Four (only middle bits set)
- •Thirty (double the actual value)
Why is data compression useful?
- •Files become easier to read by humans
- •Files become more secure from attackers
- •Files run faster on slower CPUs only
- ✓Files take less storage and bandwidth
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