Understanding Data Representation in Computing

Binary Numbers and Conversion

Your computer speaks only one language: binary. Instead of our usual base 10 system (denary), computers use base 2 - just 0s and 1s to represent everything.

Converting between binary and denary is straightforward once you get the hang of it. For denary to binary, write down the binary place values, put a 1 in the largest place that doesn't exceed your number, subtract that value, then repeat. Going the other way is even easier - just add up the place values where you see a 1.

Two's complement handles negative numbers in binary. To convert a negative denary number, write it as positive binary using full bit length, flip all the bits (invert), then add 1. Converting back? Subtract 1, invert, and stick a minus sign in front.

Quick Tip: Practice with small numbers first - once you master 4-bit conversions, 8-bit and 16-bit become much easier!

Floating Point Numbers and Character Encoding

Floating point representation lets computers handle decimal numbers using three key components. The mantissa contains the actual digits, the exponent shows where to place the decimal point, and the sign bit indicates positive or negative. Remember MARE - Mantissa Accuracy Range Exponent!

More bits for the mantissa means better accuracy, whilst more bits for the exponent increases the range of possible numbers. It's always a trade-off between precision and range.

For text, computers use ASCII $7-8 bits$ and Unicode (16 bits) to represent characters. ASCII works fine for basic English characters but uses less storage, while Unicode handles international characters and symbols - perfect for our globalised world. Python's chr() and ord() functions convert between characters and their numeric codes.

Pro Tip: Unicode's extra bits mean it can represent over 65,000 different characters - that's why you can use emojis and foreign language symbols!

Vector Graphics

Vector graphics store images as mathematical instructions rather than individual pixels - think of them as recipes for drawing shapes. This approach offers brilliant advantages for certain applications.

You can scale vector images to any size without losing quality, making them perfect for logos and illustrations. Individual objects can be edited independently, and they convert easily to bitmap formats when needed. File sizes stay relatively small because you're storing instructions, not every single pixel.

However, vector graphics struggle with realistic images like photographs. You can only edit whole objects, not tiny details, and their appearance depends on your output hardware or software.

Real-World Example: Company logos are almost always vector graphics - they need to look crisp whether they're on a business card or a billboard!

Bitmap Graphics and Comparison

Bitmap graphics work like digital mosaics - each image consists of individual pixels, with binary numbers representing each colour. The bit depth determines how many colours are possible.

Bitmaps excel at realistic images like photographs, allowing pixel-level editing for effects like blur or spray paint. They'll look identical on any system, regardless of hardware differences.

The downside? Scaling causes ugly pixellation, file sizes can be massive, and converting to vector format is nearly impossible. Enlarging images requires resampling, which increases file size significantly.

Quick comparison: Choose bitmaps for realistic images where you need pixel-perfect editing and consistent appearance. Pick vectors for scalable graphics like logos where you need to edit individual elements and keep file sizes manageable.

Memory Aid: Think "Bitmap = Photography, Vector = Illustration" - this covers most real-world applications you'll encounter.