Decode a Tiny Binary Picture
Use bit positions as pixels instead of number places.
Supplied materials
- Paper and pencil; an adult may read aloud. No device, account or purchase is needed.
Learn the idea
The same symbols can represent different kinds of data, so the interpretation rule matters. In this lesson a bit is a picture cell: 1 means filled and 0 means empty. It is not a binary place value. Read three rows of three bits from left to right, then move to the next row.
Supplied 3-by-3 picture rows are 010, 111, 010. Draw three cells for each row and fill cells marked 1. The result is a plus sign containing five filled cells. The format includes dimensions and row order; without that information the nine bits alone would not specify this layout.
- Draw a 3-by-3 grid and label rows top, middle and bottom.
- Map 010 to an empty, filled, empty top row.
- Map the middle and bottom rows in the same way.
- Count filled cells and compare their locations with the supplied bits.
See the method in action
Top row has 1 filled cell, middle row has 3, bottom row has 1: 1 + 3 + 1 = 5 filled cells. In row order the flat message is 010111010.
Check your reasoning
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See the answer and explanation
3
Each row contains exactly one 1. The three filled cells form a diagonal, giving 3 total.
Take it further
Change only the original top row from 010 to 111. Expected rows: 111, 111, 010, with 3 + 3 + 1 = 7 filled cells.
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