I chose a B&W image from the submissions from 2.
For the third question in the “Activity Guide - B & W Pixelation Widget” it asks “How many bits would it take to represent the smallest possible image (i.e. an image with one pixel)?” and after discussing the two previous questions, most of my students responded with “3 bits - 2 for the 1 x 1 metadata grid size, and 1 for the image itself”. The answer key says the answer is 17. But I was leaning with my students response, based on the question. Why do I need 16 bits for the metadata? If the grid is 1 x 1, with 1 bit for the image itself, could this not be represented using just 3 bits? MUST the metadata, regardless of grid size, be stated using 8 + 8 bits of information?
Short answer: Yes - according to the format given.
Because we don’t know the image dimensions ahead of time, we have agreed to reserve the first 8 bits to communicate the width, then another 8 bits to represent the height. (And the rest is pixel data.) That’s all we know ahead of time.
So let’s say given this agreement, I try to read your 3-bit file. What would happen? (We wouldn’t be able to interpret it following our rules.)
Does that also answer your question “Why do I need 16 bits for the metadata”? If we agreed on 16 bits of metadata beforehand, I won’t be able to interpret anything you send me that doesn’t follow that agreement.
Now, it IS possible to represent a 1-pixel image the way you describe, but we would have to change the image format - in other words, change our agreement on how we represent the data.
Maybe the question was phrased in a way it’s unclear whether we get to change the formatting “protocol”, but it seems if we interpret it to mean we get to change the format, there’d be no point in even setting aside pixels to communicate width and height if the image format you stated (1 bit for width, 1 bit for height) ever only allows an image to be 1x1 - if that were the case, you would only need 1 bit total to communicate pixel data.
I hope that’s helpful to you and your students.
I think it would be good to have some graph paper available for students who would like to design their own image separate from the widget. We were working with paper copies of the Activity Guide - B&W Pixelation Widget which made copy and pasting their image pretty tedious as well.