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Need help with understanding the solution (see comment for context)

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If you toss the coin 9 times this means the series will go from a0 to a8 with the corresponding factors of 2^(0)=1 till 2^(8)=256.

Now to get a value greater than 256 you defenitely need a8=1 and at least one of the other ai muat also be 1. Therefore the only series with a8=1 that dont work is if all ai=0.

Therefore you have 2^8 (a0 till a7 can be whatever they want and a8=1) - 1 (since a0=a1=...=a7=0 is not greater than 256)

So the answer is 2^8 - 1 = 255
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so i was working on this problem and i got stuck. i looked up the solution online and i understood it well (take the minimum value > 256 and subtract it from the greatest possible value, ie. 511-257+1); however, when i looked at the book’s answer key, it simply says 2^8 - 1 = 256. can someone explain to me why this solution also works? tya!

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