Review: Represent and Check Small Binary Data
Decode and encode unsigned values, distinguish pixel interpretation and test a toy parity check.
Bring the unit skills together
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Use the skills in a new task
Make a tiny paper packet containing an unsigned four-bit value for 14 and a separate 3-by-3 picture with rows 001, 010, 100. Add an even-parity check bit to the four-bit value. State the formats, decode the value, count picture cells and test a one-bit change to the value packet.
Work on paper or in your own document. Explain the choices you made.
- Encode 14 as 1110 and decode it as 8 + 4 + 2.
- Keep picture row interpretation separate and count 3 filled cells.
- Append 1 to 1110 to make packet 11101 with four 1s.
- Show that changing the first bit produces 01101 with three 1s and fails parity; acknowledge some multi-bit changes can pass.
Compare with a model response
Number format: four unsigned places 8,4,2,1. Value 14 → 1110 → 14. Picture format: 3 rows × 3 columns, row order top to bottom, 1 = filled. Rows 001,010,100 contain 3 filled cells. Number packet 11101 has four 1s. One-bit change 01101 has three 1s and fails the parity check. Parity cannot detect every multi-bit change.
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