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"Factoring made easy" by Casio in 1986!

Was this CASIO fx-5500 the first calculator in the market able to do symbolic calculus (formula manipulation) although in a very limited format, otherwise known as C.A.S. these days?

This machine belongs to another local collector that kindly allowed me to have for some time for testing.




This is a handy little machine, almost of the same size and form as the HP Voyager series, although featuring totally different capabilities and operation philosophy.




Main features, based on the user manual:

• 24 digit LCD with 5x7 dot matrix alphanumeric capability.
• Analog contrast adjustment.
• Constant Memory.
• Power supply: 2xCR2032
• True algebraic logic operation. Replay for easy editing
• Display: 10 digits mantissa and 2 digits exponent.
• Internal: 12 digits mantissa and 2 digits exponent.
• Each result is rounded to 10 digits for display
• Stack sizes:
  - Manual operations: Numeric 8 levels, command 20 levels.
  - Formula manipulation: Numeric 15 levels, command 20 levels.
• Input buffer size for each entry: 79 steps storage area for numbers and commands
• Memories:
  - 3 x Formula memories (I, II, III). Each up to 79 steps.
  - 12 x Register memories (A to L)
• 34 functions
• Symbolic calculus (Formula manipulation):
  - Expansion
  - Factoring
  - Simplify
• Solver (one unknown quadratic and linear, three unknown linear)
  

Forensics test: arcsin (arccos (arctan (tan (cos (sin (9) ) ) ) ) )
Result: 9.000007164 the same as for the Casio fx-730P among others.
Doing (9-Ans) *1000000 to find additional internal digits gives just 7.164.




Using some expressions from the user manual examples to test the symbolic manipulation capability.
Well, it is not a powerful manipulation and we can't even consider it a full C.A.S. system, but in 1986 it was something rare, if not unique, to see on a pocket calculator.

Simplify 5X^2 + 7X - 6 - 3X^2 + 2X + 9
Took about 2 seconds to find this result: 2X^2 +9X + 3




Just for fun, tried to Expand (X + 3)^5
It took about 8 seconds to find this result: X^5 + 15X^4 + 90X^3 + 270X^2 + 405X + 243

Tear down.

Back cover.
Power supply: 6VDC, 0.01W




Serial number suggests a date of 1986, February (6B).
Removing the aluminum back cover by undoing the two screws reveals the metallic sliding battery cover.




Removing the inner plastic frame by undoing eight self taping screws. Lift it at the battery side first, then use a plastic pry tool to unlatch the remaining sides leaving the display side to the end.
Note the grounding/shielding spring at the lower left side, interconnecting the front face plate and back cover to the circuit common ground.




The PCA is free to be removed. Lift it on the battery side first, then gently pull the display assembly to remove it from the front cover bed.




Unfolding the display flat cable to uncover the main PCA components:

• Hitachi HD61747B32 6B 23 HM47B-32 Processor (1986)
• Hitachi HD61747B33 5M 13 HM47B-33 Processor (1985)
• NEC D1004G (uPD1004G) NM390 6527KK 4K 4-bit words or 2KByte SRAM memory (*)
• Toshiba 4071BF 86 10HB CMOS Quad 2-input OR gates
  

(*) Can't find information on the NEC uPD1004G IC.
However, Kyoro's Room Blog documents the Casio PB-770 internals and we know that it uses four of these chips for a total of 8KByte of SRAM memory.

The Hitachi HD61747 processors are used in several Casio models, only changing the firmware code. For example:

• fx-5200P:
  Hitachi HD61747B16
  Hitachi HD61914C 1KByte static RAM
• fx-4000P:
  - Hitachi HD61747B38
  - HD61914 8kbit static RAM
• FC-200:
  - HD61747B55
  - HD61914 1KByte static RAM.
• PB-120:
  - HD61747B57 9L 13
• PB-500:
  - HD61747B05 5K 13
  - HD61747B06 5H 13
• PB-770:
  - HD61747B13 5C 13
  - HD61747B14 5C 13
  

Membrane keyboard using rubber keys and painted labels.
Not the best solution but the painting was good and it never fails to register a key.

(02-22-2017 11:33 PM)jebem Wrote: [ -> ]
Simplify 5X^2 + 7X - 6 - 3X^2 + 2X + 9
Took about 2 seconds to find this result: 2X^2 +9X + 3

Font exponent changes only for "2"?

(02-23-2017 06:06 AM)Leonid Wrote: [ -> ]Font exponent changes only for "2"?

No, at least up to 5 as seen here:
https://3.bp.blogspot.com/-FUqllsi3JUQ/W...00_012.jpg

(02-23-2017 07:18 AM)damaltor Wrote: [ -> ]

(02-23-2017 06:06 AM)Leonid Wrote: [ -> ]Font exponent changes only for "2"?

No, at least up to 5 as seen here:
https://3.bp.blogspot.com/-FUqllsi3JUQ/W...00_012.jpg

Yap, there is no limitations concerning its ability to present exponents in superscript mode, up to the supported limits, of course.

The fx-5500 User Manual is available at the LeDuDu site, so you may have a more detailed look.

Here is another example:
Simplify 2X^6 x 3X^7 x 5X^89 + 3Y^8 - 7Y x 6Y^3
Result: 30X^102 + 3Y^8 - 42Y^4




And yet another example using huge negative exponents.
It turns out that it doesn't support superscripts on negative exponents, although it changes automatically to conventional algebraic notation.

Simplify 3X^9000 x 7X^-76543
Result: 21 / X^67543
(about 1 second to compute this)

I meant by changes font exponent before:
\(□■■□□\)
\(■□□■□\)
\(□□■□□\)
\(□■□□□\)
\(■■■■□\)
\(□□□□□\)
\(□□□□□\)


and after calculation:
\(□■■■□\)
\(□□□■□\)
\(□■■■□\)
\(□■□□□\)
\(□■■■□\)
\(□□□□□\)
\(□□□□□\)


This can be seen only for "2"?

@Leonid:

You have good eyes and attention to details!
Yes, I see your point.

When using the dedicated key "x^2", it will use a different font for the digit "2" than the one used for all the exponent digits when using the key "x^n".

Maybe this was made specifically to highlight for the various algorithms and therefore different calculation accuracy for x^2 vs. x^n(n=2) ?
Check it!)

I have checked a few calculations but it seems that it doesn't matter whether the dedicated square key "x^2" or the natural power key "x^n" are used. The results are the same.

Probably the reason is that a dedicated "x^2" key is faster to use (single key entry) than having to press two keys to get the same entry value ("x^n", "2" ).

Also, using the function "x^Y" (accessed using shift over the same "x^n" key) will also give the same results.
The function key "x^Y" allows to enter real numbers in the exponent, whereas the "x^n" only allows to enter natural digits.

Oooh now i know what you mean. there is another one of that series which does the same thing. give me a day or two, and i will pull it out of my collection.

Yes, the font is different, because the meaning is somewhat different: The first number two, obtained by the x^2 key, is a finite action (square the number "below" it) and the second two, obtained by x^n, is only a digit in a possibly multi-digit exponent. it is not possible to do "123^20" by pressing "1 2 3 x^2 0", because the two ^2 are not the same. i dont know if there is a technical reason to make the numbers different (and i highly doubt it too), but they have to be distinguished somehow as they are simply not the same. i wonder if that is mentioned in the users manual in any way.

I believe we discussed something similar before for the fx-5000F here.

Exactly, that is the one i was searching for.