The famous HP35 ex(ln(2.02)) BUG
The HP35 was a historic electronic calculator - it was the first to provide exponential and trig functions (aka the Slide Rule Killer).
However the first production run of the HP35 was also famous for having what is known as the ex(ln2.02) bug - that gave the answer 2 rather than 2.02
While teaching myself about the Cordic algorithms used in the HP35, I wondered - what other values of X would give a similar error to 2.02
So using the PC to do an iterative scan - I found three other numbers that lead to about a 1% error.
I found (on the 14th February 2008):
ex(ln( 1.0201 )) = 1.01
ex(ln( 1.12211 )) = 1.111
ex(ln( 2.02 )) = 2 (the famous bug, known about since 1972)
ex(ln( 2.060602 )) = 2.0402
It is sobering to think - that if I had used the original calculator to find the above 3 new numbers, I would have worn out the keyboard or gone crazy, or both!
There could be other numbers, I searched from 0 to 10, in increments of 1E-6, so I tested 10 million numbers - just to find 4 mistakes. A needle in a haystack!
N.B. In later version of the HP35, the above bug was fixed. It is only on the initial 25,000 calculators (5,000 were returned to be fixed) that had this issue. Because of this bug, these original HP35's have become a collectors item. For those lucky collectors - I have now provided them with three new numbers to enter into their desirable machines.
LINKS:
For those who do not have the original (buggy) HP35, you can test the above four numbers on this HP35 Simulator.
The above Simulator is part of the great website of Jacques Laporte where you can find great information about the HP35 and the famous bug!
To simulate an early HP35, has only been possible due to the great work of many others - most notably Eric Smith for creating the simulator code and Peter Monta for extracting the ROM code.
This page written by Geoff Hitchcox, Christchurch, New Zealand.