Changing Of The Guard

[Mike Morrow]

(04-22-2014 01:50 AM)bshoring Wrote:  I believe the first HP with guard digits was the HP-91 printing scientific...

What an odd belief. :-)

That certainly is not true about the HP-91 nor none of the other machines that you mention...nor of the HP-67/-97, nor the HP-41C series, nor the HP-15C...etc. etc. etc. AFAIK, no HP calculator used any guard digits until machines based on the Saturn processor were developed. That would be around 1986...the HP-28C and later. Even then...the additional digits are strictly internal to the specific calculation and do not survive when the number reaches the display. For example, the HP-42S is said to use 15-digit precision during calculation. But for a simple example. pushing the PI button produces a display of 3.14159265359. Take the SIN of that, and the exact same result is produced that occurs when you key in 3.14159265359 and take the SIN. There are no hidden digits in the value that is displayed after PI is executed. The same is true for more complex examples.

TI machines used three guard digits at least as early as the SR-50 in 1974. Those non-displayed digits still exist when the value is presented for display. Subtracting a manually keyed-in value that appears identical to the displayed value will generally show the presence of the guard digits in the original value. Most Casio machines (like the fx-115ES Plus) show the same behavior, except that the 115ES has five guard digits! I personally always preferred TI's use of guard digits to HP's refusal to improve the precision of calculations on their machines. HP always bizarrely maintained that their failure to provide guard digits was a positive characteristic, compared to TI. That was pure HP BS. For example, I always got far better accuracy of results, due to far better precision, from a fourth-order Runge-Kutta program on a TI-59 than I ever got from the same program executed on a HP-67 or HP-97 or 41C. This is just another of many areas where HP screwed the pooch in its mythological age of excellence. :-)