Re: HP35 blind buy but buggy! Message #8 Posted by Dieter on 11 Nov 2013, 5:56 p.m., in response to message #1 by Max Stone
Quote:
But I've found another bug: 2 ENTER 3 XY (3^2) gives me the result 9.000000006 and 2^3 gives 8.000000003.
10^2 is correct (100), but 2^10 gives 1023.999999. 2^9 is correct (512) but 9^2 gives 80.99999995.
This is not a bug but simply the consequence of limited accuracy. Unlike later devices, the 35 did not use additional digits for internal calculations. It displayed 10 digits, and that's what it used internally. Since powers are evaluated as e^(exponent * ln base), this is what you get with 10 digits:
3^2 = e^(2 * ln 3) = e^2,197224578 = 9,0000 00005 974...
which is then rounded to 10 digits = 9,0000 00006
2^9 = e^(9 * ln 2) = e^6,238324625 = 511,99 99999 797...
which is then rounded to 10 digits = 512,00 00000
That's why HP later added three more digits to overcome this limitation (well, at least in most cases). The respective HP Journal article has been mentioned already.
Dieter
