AQA GCSE Computer Science 3.3 Fundamentals of data representation: number bases, binary arithmetic, hex, units, characters, images, sound and compression

What area 3.3 actually demands

Fundamentals of data representation is the most numerical area of the course and a major part of Paper 2. You must move fluently between the number bases, add binary numbers and shift bits, recall the units of information, and calculate file sizes for text, images and sound. You also need to explain how characters, images and sound are encoded as binary and why and how data is compressed.

This guide ties together the eight dot-point pages for the area.

Number bases and binary arithmetic

The foundation is the three number bases: denary (base 10), binary (base 2, which computers use because components have two states) and hexadecimal (base 16). You convert binary to denary by adding place values, and denary to binary by subtracting them. Binary arithmetic adds the rules of binary addition (with carries), the idea of overflow when a result needs more bits than are available, and binary shifts (left multiplies by 2, right divides by 2).

Hexadecimal and units

Hexadecimal is a shorthand for binary: one hex digit is four bits, so two hex digits make a byte, which is why hex is easier for people to read. Units of information run from the bit (one binary digit) through the nibble (4 bits) and byte (8 bits) up through kilobyte, megabyte, gigabyte and terabyte, each 1000 times the last in the AQA convention, and underpin all file-size calculations.

Encoding text, images and sound

Character encoding uses a character set: ASCII (7 bits, 128 characters) or Unicode (more bits, far more characters including other languages and emoji). Representing images uses pixels and colour depth, where resolution and colour depth both affect quality and file size, plus metadata. Representing sound uses sampling, where the sample rate and bit depth affect quality and file size.

Compression

Finally, compression reduces file size to save storage and transfer faster. Lossy compression removes data permanently for big savings (MP3, JPEG); lossless compression keeps all the data so the original can be rebuilt exactly, using methods such as run-length encoding and Huffman coding.

Check your knowledge

A mix of conversion, calculation and recall questions covering area 3.3. Attempt them, then check against the solutions.

1. Convert the binary number 00110010 to denary. (2 marks)
2. State why computers use binary. (2 marks)
3. State the effect of shifting a binary number right by one place. (1 mark)
4. Convert the hexadecimal value 1A to denary. (2 marks)
5. State how many bits are in a byte. (1 mark)
6. State how many characters 7-bit ASCII can represent. (1 mark)
7. Calculate the file size in bytes of a 200 by 100 pixel image with a colour depth of 8 bits. (2 marks)
8. State one difference between lossy and lossless compression. (2 marks)