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**Casio fx-1 Scientific Calculator**

Updated 7/26/2019

The Casio *fx-1* was the first true
scientific calculator made by Casio, and, if not the first, one of the very
earliest LSI IC-based scientific calculators. The *fx-1* was introduced in
February of 1972, with this particular model being built fairly early in production, likely
sometime in late February of '72.
It was purchased by its original owner from W.T. May Company in Jackson,
Mississippi on March 29, 1972. This machine is in wonderful original
condition, and is fully functional. The W.T. May Company warranty sticker
is still in place on the bottom of the machine, indicating its original
12 month parts and labor warranty.

*Dietzgen's ESR-1 and Sperry/Remington's 1259S, Both OEM versions of the Casio fx-1*

Along with being marketed world-wide
by Casio, the same Casio-manufactured machine was marketed through
Chicago, Illinois-based Dietzgen as the model ESR-1. The Dietzgen ESR-1
was identical electronically and functionally, only cabinetry color,
badging, and keyboard color changes differentiated it from the *fx-1*.
Sperry/Remington also marketed a version of the *fx-1* as the Remington
1259S, with only differences in color scheme (cabinet, keyboard bezel, and
key cap colors). Casio later introduced
an update of the *fx-1* called the *fx*-2, with the sole difference being that
the Nixie tube display of the *fx-1* was replaced by vacuum-fluorescent
tubes (reducing the cost). From a circuitry point of view, the *fx*-2
likely shared the same calculating engine. Only the display-related
driver and power supply components were changed to support the lower
current/voltage requirements of the VF tubes. At this time, it is unclear
exactly when the *fx*-2 was announced. It is unclear if Casio's OEM
customers (Dietzgen and Sperry Remington) offered their own branded versions
of the *fx*-2.

*The Casio fx-1 Opened Up*

The *fx-1* is built with three circuit
boards which stack one atop another. The bottom-most board in the stack
consists of all of the calculator logic. This board contains a whole
slew of various small and medium-scale integration IC's made by
NEC, Toshiba, and Hitachi, serving as glue to integrate the 5 LSI IC's
made by NEC which make up the main calculating engine of the machine. The
second board contains the tiny Nixie display tubes, an LSI decoder/driver
IC for the Nixies, and various discrete components as support for driving
the 12-digit display. The top-most board consists of power supply electronics.
The keyboard assembly, based on magnetically activated switches, connects
to the calculator board via an edge connector, and the power supply board
and display board plug into edge connectors at the rear of the machine
which have hand-wired connections to the calculating board.

*Nixie Tube Display Detail*

The *fx-1* has quite a complement of scientific functions, some of
which are uncommon even on today's advanced scientific calculators. Among
the functions the machine provides are sine, cosine, tangent, arctangent,
and hyperbolic sine and cosine. The machine also has keys for conversions
from degrees to radians and back, square root, cube root, conversion
of degrees/minutes/seconds to decimal degrees, natural logarithm, base 10
logarithm, *e*^{x}, and a^{x} functions.
The machine has an accumulator-style memory register, with [M+] and [M-] keys,
a [MR] memory recall key, and an [MC] memory clear key. It also has a
separate store/recall memory register. The [K IN] key saves the number in
the display into this register (not a constant, more on function of constant
later), and the [K OUT] key recalls
the content of the K register. The K register is retained through all but
the power being turned off. The machine has a capacity of 12 digits.
It can be set for full floating decimal point, or in fixed positions
at 0, 2, 3, 4, 6 or 8 digits behind the decimal point, via slide
switches at the left side of the keyboard panel. In fixed point mode,
the machine can be set to round off results to the least significant
digit displayed, or drop any digits behind the last displayed digit.
The machine has an automatic constant feature which is activated for
multiplication or division by simply pressing the function key twice.
e.g., to repetitively multiply by two, starting with one, you would press
"[1] [X] [X] [2] [+=] [+=] [+=] ...". Also included in the complement of keys
is the [CHG Sign] key for toggling the sign of the number in the display,
and an [EXC] key to exchange the display and operand register with each
other. While the scientific functions of the machine are quite admirable
for the day, there are a number of restrictions upon some of the functions
which are interesting, indicating either a limited amount of ROM space to store
the programs for the functions, or other restrictions in the internal
logic of the machine. For example, the *e*^{x} function
will not allow an operand of any more than 9.99999999999, and the cube root function will not allow an operand of more than
999999.999999. Any larger
operands will cause an error condition, even though the actual result is
still within calculating range of the machine. The a^{n}
function is also interesting, and unique. The first number (the number
which is to be raised to a power) is entered, then the [a^{n}]
key is pressed. Then, the keyboard accepts a SINGLE digit, and raises
the first entered number to the power specified by that digit immediately. If any other than a key from zero through nine
is pressed, the a^{n} operation is canceled.
Basically, this means that this function can raise numbers from the 0th
power to the 9th power only. While the operation is in progress, you can
see that the machine simply does successive multiplications to calculate
the result.

Error/overflow detection on the machine is OK, but not totally comprehensive. Taking the square root of a negative number yields a negative result with no error indicated. There is no dedicated error or overflow indicator, with the machine opting instead to clear the display to all zeros and ignoring key-presses. Pressing the [AC] (all clear) key will clear the entire machine (except the K register) including any error lock condition. Pressing the [C] key clears any entry currently in the display.

*Keyboard Layout of Casio fx-1*

When using some of the machine's scientific functions, it is quite obvious that it relies on ROM-based programs (sequences of key-presses) for performing them. An example is the cube root function. The machine can take up to 16 seconds to perform some cube root functions, while square root (likely implemented directly in microcode rather than as a sequence of programmed key-presses) takes a little over 1/2 second. During execution of the cube root function, it is apparent that some kind of successive approximation algorithm is used, as the displays cycle through patterns of digits that converge on the result (see VIDEO). Some of the trigonometric functions can take upwards of 6 seconds to complete. While some of the slower scientific functions are being performed, the Nixie tube display digits dance in an almost mesmerizing pattern. The standard four math functions operate as is typical for machines of this vintage, with the ubiquitous all nines divided by 1 benchmark taking about 1/2 second.