GCSE Computer Science: U3 Data Representation Notes

Number Systems and Data Basics

Every piece of information on your computer - whether it's a photo, song, or text - gets converted into binary code using just 0s and 1s. Think of binary as the computer's native language, whilst we humans prefer decimal (base 10) for everyday counting.

Hexadecimal (base 16) acts as a brilliant shortcut for programmers. Instead of writing out long strings of binary digits, hex lets you represent four binary digits with just one character. It's faster to type, easier to remember, and way less likely to contain errors when you're coding.

Memory sizes follow a simple pattern: 1 byte equals 8 bits, and from there it scales up - kilobytes, megabytes, gigabytes, and terabytes. Converting between these number systems becomes straightforward once you understand the place values: in binary, each position represents powers of 2 (1, 2, 4, 8, 16...).

Quick tip: Remember "Make Great Toys" for MB, GB, TB - it'll help you recall the order of memory units!

Binary Operations and Character Encoding

Binary addition follows simple rules, but watch out for that carry bit when 1+1=0 (carry 1). Binary shifts are your mathematical shortcuts: shifting left doubles a number, whilst shifting right halves it. These operations are lightning-fast for computers to perform.

Character sets like ASCII and Unicode give every letter, number, and symbol a unique binary code. ASCII started with 128 characters using 7 bits, but that wasn't nearly enough for global communication. Unicode expanded this massively using 16 bits, accommodating everything from Korean characters to your favourite emojis.

The beauty of these systems is their logical organisation - numbers, letters, and symbols are grouped together in sequence, making it predictable to work with. ASCII remains a subset of Unicode, so older systems still work perfectly with newer ones.

Remember: When adding binary numbers, overflow errors occur when your result exceeds the available bits - the extra data simply disappears!

Image Representation

Digital images are made up of tiny squares called pixels, and each pixel stores colour information as binary data. A bitmap image is essentially a massive grid of these pixels, with file formats like JPEG, PNG, and GIF storing this data in different ways.

Colour depth determines how many colours each pixel can display - more bits per pixel means more colour combinations and better image quality. The formula is simple: 2^n colours, where n is the number of bits. So 8 bits gives you 256 different colours per pixel.

File size calculations are straightforward: width × height × colour depth ÷ 8 gives you the size in bytes. Higher resolution and greater colour depth create stunning images, but they'll eat up your storage space quickly.

Don't forget about metadata - the invisible information about your image like when it was created, camera settings, and file format. This data doesn't count towards the basic file size calculation, but it's stored alongside your image.

Pro tip: Understanding these calculations helps you balance image quality against file size - crucial for web design and digital media work!

Sound Representation and Compression

Sound waves are analogue by nature, but computers need digital data to work with them. This conversion happens through sampling - measuring the sound's amplitude at regular intervals, like taking thousands of snapshots per second of a constantly changing wave.

Sampling rate (measured in Hertz) and sample resolution (bits per sample) determine your audio quality. Higher values create more accurate digital representations of the original sound, but they also create much larger files. The trade-off between quality and storage space is constant in digital media.

Data compression tackles this storage problem through two main approaches. Lossy compression (like MP3) permanently removes some data to shrink file sizes, whilst lossless compression (like PNG) rearranges data more efficiently without losing anything.

Run Length Encoding is a clever lossless technique that replaces repeated data with frequency/data pairs. It works brilliantly with images that have large areas of the same colour, but it can actually increase file sizes when there aren't many repeating patterns.

Key insight: The file size formula is sampling rate × sample resolution × duration - this helps you predict how much storage your audio projects will need!

Advanced Compression Techniques

Huffman coding represents one of the most elegant compression algorithms you'll encounter. It works by giving shorter binary codes to frequently used characters and longer codes to rare ones, dramatically reducing overall file size whilst maintaining perfect data integrity.

Looking at the example with "SHE SELLS SEA SHELLS", Huffman coding achieves a 65% reduction in file size compared to standard ASCII encoding. The most common letters like 'E' and 'S' get the shortest codes, whilst less frequent characters receive longer binary representations.

This technique proves particularly effective with text that has predictable patterns - English text, programming code, and structured data all compress beautifully. The algorithm builds a custom code tree for each file, ensuring optimal compression for that specific content.

The beauty of Huffman coding lies in its mathematical precision - there's no guesswork involved, and the original data can always be perfectly reconstructed. This makes it ideal for situations where losing even a single bit would be catastrophic.

Amazing fact: Huffman coding is so efficient that it's used in popular formats like JPEG and MP3, often as part of more complex compression systems!