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?
On
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...)
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.