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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.

[Image: Casio_fx-5500_002.jpg]


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.

[Image: Casio_fx-5500_000.jpg]


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.

[Image: Casio_fx-5500_003.jpg] [Image: Casio_fx-5500_004.jpg]


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

[Image: Casio_fx-5500_009.jpg] [Image: Casio_fx-5500_010.jpg]


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

[Image: Casio_fx-5500_011.jpg] [Image: Casio_fx-5500_012.jpg] [Image: Casio_fx-5500_013.jpg]
Tear down.

Back cover.
Power supply: 6VDC, 0.01W


[Image: Casio_fx-5500_008.jpg]

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.

[Image: Casio_fx-5500_020.jpg]


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.

[Image: Casio_fx-5500_021.jpg]


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.

[Image: Casio_fx-5500_022.jpg] [Image: Casio_fx-5500_023.jpg]


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


[Image: Casio_fx-5500_024.jpg] [Image: Casio_fx-5500_025.jpg]


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.

[Image: Casio_fx-5500_026.jpg] [Image: Casio_fx-5500_027.jpg] [Image: Casio_fx-5500_028.jpg]
(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

[Image: Casio_fx-5500_009.jpg] [Image: Casio_fx-5500_010.jpg]

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

[Image: SAM_3282.JPG]


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)

[Image: SAM_3286.JPG]
I meant by changes font exponent before:
\(□■■□□\)
\(■□□■□\)
\(□□■□□\)
\(□■□□□\)
\(■■■■□\)
\(□□□□□\)
\(□□□□□\)
[Image: Casio_fx-5500_009.jpg]

and after calculation:
\(□■■■□\)
\(□□□■□\)
\(□■■■□\)
\(□■□□□\)
\(□■■■□\)
\(□□□□□\)
\(□□□□□\)
[Image: Casio_fx-5500_010.jpg]

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".

[Image: SAM_3288.JPG]
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.
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