How Compression Works by Hand: Run-Length Encoding, Symbol Frequencies, Entropy, Huffman Codes, Base-64 Overhead & Lossy Quantisation

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Measure four messages in characters and bits, work out how many bits a fixed-length code needs for a 27-symbol alphabet, and calculate how much that code saves compared with one byte per character.
• Split a scan line into single pixels with MID, flag where each new run starts, count the runs, and compare the run-length size with the raw size – then see why a noisy line gets bigger.
• Count how often each level code occurs in 32 sensor readings, turn the counts into probabilities, measure the surprise of each symbol in bits and chart the frequencies.
• Calculate the entropy of the river sensor step by step, compare it with a 2-bit fixed code, and compute the entropy of two other sources in one SUMPRODUCT formula each.
• Follow the merge table of a Huffman tree with SMALL, calculate the average code length with SUMPRODUCT, check the code with the Kraft sum and compare it with a fixed-length code and the entropy.
• Calculate the compression ratio and saving of five files, find the one that got bigger, work out the base-64 size of a compressed file for sending as text, and calculate the overall saving.
• Round twelve brightness values to multiples of a step with MROUND, measure the error, rate the quality with a signal-to-noise ratio in decibels and work out how many bits per pixel the coarser values need.
• Turn compression ratios into stored gigabytes per data type, add up what the archive really stores, calculate how long the monthly backup takes over the link and chart raw against stored volumes.