GCSE Computer Science: Binary Addition, Units and Compression

Data representation questions on the computer systems paper are mostly short calculations, and the marks go to careful working: a carry forgotten in the fifth column, a gigabyte converted with the wrong factor, a run-length pair written the wrong way round. This material trains the calculations that sit alongside the basic conversions, based on the DfE GCSE subject content for computer science, which requires binary and hexadecimal, conversion between these and decimal, binary addition and shifts, the representation of text, sound and graphics, and data capacity calculations.

The quiz has thirteen questions. Three are binary additions: two 8-bit numbers, three numbers at once as some specifications require, for example AQA's, and an addition whose answer needs a ninth bit, so the overflow and the wrong stored value can be seen. Two convert between hexadecimal and denary in both directions. Three work with units: how many video files fit on a USB stick, which of four amounts written in different units is the largest, and the size of a text file from the number of characters. Two are run-length encoding, one encoding a bitmap row as frequency/data pairs and one decoding pairs back to pixels. Two use a small Huffman code, again named on some specifications, to decode a word and to count the bits saved against 7-bit ASCII. The last question asks what happens to a sound file when the sample rate is doubled. Units use 1 kB = 1,000 bytes throughout, and the flashcards note the 1,024 convention some boards also accept.

Each explanation gives the full working and a denary check where it helps. The flashcards cover the addition rules, overflow, hexadecimal digits, the unit ladder from bit to petabyte, the text file formula, RLE, Huffman coding and the effect of sample rate and bit depth.

The written work has eight longer tasks with model answers and marking points: an addition with carries and a denary check, an overflow explained with an example, hexadecimal conversions with a reason for using hex, a memory-card capacity calculation that also explains the 1,000 and 1,024 conventions, RLE on a friendly row and an unfriendly one, a Huffman calculation, a stereo sound file size, and why both compression methods are lossless.

An oral practice with an examiner completes the material: one calculation at a time, working explained aloud and brief feedback at the end. It suits Year 10 and Year 11 students preparing for the systems paper.

• Add two or three 8-bit binary numbers, showing carries
• Recognise and explain an overflow error
• Convert between hexadecimal and denary in both directions
• Use units from bit to petabyte and calculate storage requirements
• Calculate the size of a text file from the number of characters
• Encode and decode data with run-length encoding
• Decode Huffman codes and calculate bits saved against ASCII where the specification includes it
• Explain how sample rate and bit depth affect sound quality and file size

Practice material written by Zestly, based on the DfE GCSE subject content for computer science (binary and hexadecimal, binary addition, representation of text, sound and graphics, data capacity) and the data representation sections of the AQA (8525, 3.3) and OCR (J277, 1.2) GCSE Computer Science specifications, including Huffman coding and run-length encoding as listed by AQA.