Stone Free actually is copying rather than decoding here.
Emporio's sheet of binary numbers isn't a coded message in the way that, say, Bacon's cipher uses "00000" to represent the letter "A", "00100" to represent the letter "E", and so on. It's literally binary text in the sense that there are only two possible values: 0 or 1; on or off; white or black.
Say the numbers written on the sheet looked like this:
If I told you to replace each "0" with a period and each "1" with a pound/hash symbol, you'd get:
See the smiley? :)
This is basically how Jolyne turns the binary numbers into an image with Stone Free: replace each "0" with one shape, and each "1" with a second shape, and a pattern emerges. In your second image, the shaded areas have a white "1" superimposed while the unshaded areas have a black "0" superimposed; my opinion is that the numbers are a visual aid for the reader's benefit, while Jolyne could be forming her string into shapes that create a high contrast between light and dark.
The anime adaptation of this scene uses a more digital representation, with Jolyne making her string travel underneath each "0" and above each "1", moving vertically between numbers whenever they change to the other value.