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OCR H446 1.3.1 Run-length encoding

Part 2 of 7 · H446 1.3.1 · Compression, encryption and hashing

Run-length encoding is examined at H446 1.3.1 as an exact, reversible process, and most lost marks come from the field order convention or from claiming a saving the data does not support. Students encode, decode and round-trip check streams under a stated convention, including the case where the representation grows.

Students will:

  • segment a sequence into runs and store each run as a symbol and a count
  • explain why two separated runs of the same symbol cannot be merged into one pair
  • decode a supplied stream and check the reconstructed length
  • use run counts and stored overhead to say when run-length encoding helps and when it expands data
  • work to a count-then-symbol key and describe the error made by assuming the other order

Inside: 6 explanation cells, 1 multiple-choice question, 2 fill-in-the-blanks cells and 3 written answers. 26 marks, about 40 to 50 minutes.

Series: H446 1.3.1 · Compression, encryption and hashing, part 2 of 7.

Shared by Coding PathwayVerified teacher

  • 12 cells
  • About 45 minutes
  • CC BY-SA 4.0
  • Shared 31 Aug 2026
  • Updated 3 Sept 2026

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The whole resource, exactly as a class sees it. Answers and marking are held back.

Run-length encoding

Run-length encoding (RLE) replaces each run of identical adjacent symbols with a pair. This worksheet uses symbol then count as its primary convention because that matches OCR's recent assessed form. The order is always a supplied convention, not a universal law.

Worked model: segment, pair, reconstruct, verify

Run-length encoding with an explicit symbol-count convention Supplied convention: symbol then countMMMMQQRRR segment adjacent runs M4 · Q2 · R3decode, then verify length 4 + 2 + 3 = 9

For MMMMQQRRR, the adjacent runs are MMMM | QQ | RRR. Under symbol-count, the encoded form is M4 Q2 R3. Decoding repeats M four times, Q twice and R three times. The reconstructed length is 9 and the sequence exactly matches the original, so the lossless round trip is valid.

A second representation: one bitmap row

Treat 0000011100 as a row of ten black/white pixel symbols. Its runs are 00000 | 111 | 00, so symbol-count gives 05 13 02.

RLE operates on repeated adjacent symbols, not on “images” as a category. The first and last runs both contain 0, but they must remain separate because a run of 1s lies between them. If rows are encoded separately, a run does not silently continue across a row boundary.

Multiple choice1 mark

Why can the two 0-runs in 0000011100 not be combined as one 07 pair?

  • ARLE permits each symbol only once
  • BRLE records adjacent runs, and the 1-run separates them
  • CThe final two zeros are lossy
  • DCounts may never exceed five
Fill in the blanks3 marks
Using symbol-count, gap 1 decodes to MMMMQQRRR. Using the explicitly supplied count-symbol key, gap 2 decodes to the same sequence. Both reconstruct gap 3 symbols.
  • M4 Q2 R3
  • 4M 2Q 3R
  • 9
  • 3
Written answer6 marks

Using symbol-count pairs, encode KKKLLMMMMMN, decode T2 U4 V1, and show a reconstructed-length check for each.

Separate runs before pairing. For decoding, repeat each symbol by the count that follows it.

Students type their answer here.

Written answer5 marks

Explain why RLE is likely to help AAAAAAAAAABBBBBB but may increase the representation of ABABAB. Use the number of runs and the stored-pair overhead rather than saying one is ‘an image’ or ‘text’.

Count the pairs. Every alternating symbol becomes its own one-symbol run.

Students type their answer here.

Apply the model independently

The remaining tasks change the context or reduce the support. Complete them without copying the worked model, then check that each explanation connects a mechanism to its consequence.

When the representation grows

For ABABAB, symbol-count is A1 B1 A1 B1 A1 B1: six input symbols become six stored pairs. RLE has not lost data, but it has added count fields.

Suppose an exercise states that each original symbol uses 8 bits and each stored count also uses 8 bits. Then the original uses 6 × 8 = 48 bits, while six pairs use 6 × (8 + 8) = 96 bits. This is a calculation from supplied widths, not a compression-ratio formula to memorise.

Written answer7 marks

A device manual defines each pair as count then symbol. Encode PPPPQRRR under that key, then decode 2A1B4C. Explain the error made by someone who assumes symbol-count without reading the key.

Write the convention first. Verify both reconstructed sequences.

Students type their answer here.

Fill in the blanks4 marks
RLE stores each adjacent checkpoint gap 1 as a symbol/count pair. Pair checkpoint gap 2 must be read from the supplied convention. RLE is checkpoint gap 3 but can still make a representation checkpoint gap 4 when runs are short.

Review your understanding

Before submitting, check that you can explain the main distinction in your own words, apply it in an unfamiliar context and justify each consequence rather than only naming a feature.