Data Storage Needed for All 8x8 Pixel Icons: Black & White vs 32-Bit Color

One of my collegues at lunch yesterday asked me the question:
bq). "If you have a black and white 8x8 pixel icon, how much data storage is required to hold all the possible permutations of the graphic?"
The calculation for this is quite simple, but the results are mind-blowing!
*Bonus*: Do the calculation again using 32-bit color

It is quite incredible alright and this is how QR codes have become so popular. There are so many different arrangements of the blocks, giving huge data retention. QR is even better again as it uses matrices from 21x21 to 177x177 all black and white. If they ever included other colours, the possibilities would be incredible.

QR codes were originally created by Toyota for car manufacturing, I wonder what other uses it will see in the future.

Good point Mike. Thanks for sharing...

Isn't this basically the same as the old legendary Chinese chessboard question ?
If I put one grain of rice on the first square of the board, two on the second, and so on, how many grains will be on the board when I finish ?

You're right, it gives the same number, which is 18,446,744,073,709,551,616.

The Chinese chessboard question is actually place one grain of rice on the first square, place double that on the next square (2), double on the next square (4) and so on so forth. The number above is calculated by adding the 64 numbers together. Whereas it's just as easy to calculate 2^64.

The only difference between the two things is that in the Chinese chessboard scenario, each square is given an arbitrary value of double the previous square. For calculating the black and white squares, each square can be either black or white and this provides us with a huge number of permutations (ie all white, all white and one black (64 different possibilities alone), all white and two blacks, a black, all black and one white).

In the case of 32 different possibilities for each square gives us 32^64, which gives us roughly 2.136x10^96.