How did this person code "Hello World" with Microsoft Paint?
I have just seen this within the past few days and cannot figure out how it works. The video I talk about is here:
It's the top rated answer from this Stack Overflow question: Why was this program rejected by three compilers?
How is this bitmap able to show a C++ program for "Hello World"?
A BMP (DIB) image is composed by a header followed by uncompressed1 color data (for 24 bpp images it's 3 bytes per pixel, stored in reverse row order and with 4 bytes row stride).
The bytes for color data are used to represent colors (ie none of them are "mandated" by the file format2, they all come from the color of each pixel), and there's a perfect 1:1 correspondence between pixel colors and bytes written in the file; thus, using perfectly chosen colors you can actually write anything you want in the file (with the exception of the header).
When you open the generated file in notepad, the color data will be shown as text; you can still clearly see from the header (the part from BM to the start of the text), that is mandated by the file format.
In my opinion this video was done this way: first the author calculated the size needed for the bitmap, and created a DIB file of the correct size filled with a color that expands to a simple pattern (eg all bytes 65 => 'A' ); then replaced such pattern with the "payload" code, as shown in the video.
Notice however that it's not impossible to hand-craft the whole thing with notepad - with the color chooser dialog, an ASCII table and a basic knowledge of the DIB format it can be done, but it would be much much slower and error-prone.
More info about the DIB format
I assume you're referring to the answer to one of the April Fools questions.
My guess is that each pixel has a binary representation for it. And that each character in source code has a binary representation for it.
The person who created the program must have worked out the color for each pixel that'd have a binary representation that'd correspond to each character.
From a theoretical computer science point of view, it would be interesting to ask, if every program can be written in such a way so that, viewed as a bitmap, you actually saw the source code that does the same thing. If you are seriously interested in such results, read eg about the Kleene's fixed point theorem.
Program-as-an-image can also be viewed as a form of code obfuscation. Not that it were particularly practical...
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