# Base-2 exponentiation bug on Citizen SR-270X for $2^{255}$?

According to my calculator, $2^{255} = 0.5$.

Also, for the range $2^x, x\in[254.5, 255.5)$ the result spans $[0.3535533906, 0.7071067812]$. Outside of that, the answers seem correct.

Curiosly, $2^{255.4999999} = 0.7071062911 \approx 1/\sqrt{2}$ in the calculator's opinion, how about that!

Can any other owner of the Citizen SR-270X reproduce and confirm this? Besides that, is such behaviour to be expected and acceptable?

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I'd just like to comment that $255$ represented in binary is $11111111$, which is the two's complement representation for $-1$, so that the bug might be that the calculator is using $8$-bit integers for small numbers and misinterprets $255$. Just speculating, though. (See en.wikipedia.org/wiki/Two%27s_complement ) –  J. J. Jul 26 '11 at 19:22
I know, it was that which prompted me to enter it in the first time. –  Cecil Dishwasher Jul 26 '11 at 19:29
The obligatory xkcd link. –  Guess who it is. Jul 27 '11 at 2:26

Such behaviour is not to be expected, and is unacceptable. Not having a Citizen SR-270X handy, I can't investigate further, but it is clear that this machine has a bug in its floating-point arithmetic code.
Speculating further, perhaps they have a special exponentiation routine for powers of two, which increments the exponent for some reason, and then divides by $2$. But they forgot to check for overflow when incrementing the exponent.

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It gets better, this is one of only two calculators (other is HP-30S) allowed on exams on NTNU in Norway. But then it might be unique to my device. –  Cecil Dishwasher Jul 26 '11 at 19:39
I would like to see another SR-270X owner confirm this, but this was the only (but good!) answer I could get. –  Cecil Dishwasher Jul 30 '11 at 21:26

Confirmed the bug with my Citizen SR-270X, furthermore there are some calculations (I cannot recall at the moment exactly which) that freezes the calculator and the reset button on the back has to be pushed for continued operation

(also NTNU-student... so I guess we all "love" our calculators...)

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My SR-270X give 2^255=5.789604462*10^76

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