In a recent thread Karl Schneider wrote of the TI-30:

"Accuracy not fully justified by its three guard digits. Example: [1][INV][lnx] = 2.7182818 is displayed. Subtract 2.71 and multiply by 100: .82818301 is displayed; .82818284 are the correct digits. Why compute three extra digits that are not quite accurate?"

Page 25 of the Owner's Manual for the TI-30 discusses the guard digit methodology implemented in the TI-30. It states in part:

"Each calculation produces an 11 digit result. These 11 digits are more than are displayed. The result is therefore rounded to a 8-digit standard display or to 5 digits for scientific notation. The 5/4 rounding technique built into this calculator adds 1 to the least significant digit of the display if the next, non-displayed digit is five or more. If this digit is less than five no rounding is applied. In the absence of these extra digits, inaccurate results would frequently be displayed .. "

I did not own a TI-30 back in the olden days. I have several in my collection and also have several SR-40's which operate in the same manner. However, the only time I have seriously used a TI-30 to calculate anything was to demonstrate that it can easily solve the Mach Number challenge I did use the TI-59 extensively. The TI-59 used a similar guard digit methodology but with a 13 digit calculation and a 10 digit standard display. TI-59 users found that the guard digits could be used in many ways other than as guard digits; e.g., to expand printer control capabilities and to provide a thirteen digit factor finding capability.

There no doubt that the thirteen digit methodology used by TI (before the TI-95) is different from the ten digit methodology used by the HP-35 and subsequent HP calculators prior to the HP-28. Each methodology has both advantages and limitations. The fans of either side have been arguing about it for over thirty years.

Karl also wrote that the TI-30 has:

"Lack of rigor in display format: pi / 10 displays .31415927. pi / 1 [EE]1 displays "3.1416 00" (3.1416 x 100). Now, just try to get out of scientific-format display mode! Move the decimal place repeatedly to the left using [INV][EE], and watch the mantissa be obliterated, as significant digits fall into the "bit bucket" until "0 06" ( 0 x 106) is displayed. Not good. Perhaps TI's youthful customers didn't care, but HP's professional customers certainly would have. "

I agree with Karl's result for pi / 10 . I have been unable to get his result for pi / 1 EE 1 . I get the correct 3.1416-01 using three different TI-30's and two different SR-40's. I cannot explain why we should get different results. I do note that the display "3.1416 00 " is NOT 3.1416 x 100 but IS 3.1416 x 10^00.

Karl then writes "Now, just try to get out of scientific-format display mode!" That really isn't too hard. You can do it by multiplying the displayed value by the sequence 1 INV EE = as illustrated on page 12 of the Owner's Manual . If you do that after previously having generated 3.1416-01 in the display with the sequence pi / 1 EE 1 = you will get .31415927 in the display.

Karl also writes: " Move the decimal place repeatedly to the left using [INV][EE], and watch the mantissa be obliterated, as significant digits fall into the "bit bucket" until "0 06" ( 0 x 106) is displayed. Not good." NOT SO! The paragraph "Exponential Shift" on pages 13-14 of the Owner's Manual explain that the technique can be used to change the displayed value without changiing the value in the display register. To get back to the normalized display a user can simply press =, or if the user does not want to disturb any pending operations he can press EXC EXC.

Finally, Karl writes: "Perhaps TI's youthful customers didn't care, but HP's professional customers certainly would have." Some professional customers would have decided to read the Owner's Manual when they received results that they didn't understand. One can only hope and trust that HP's professional customers would have done the same.