RPN-35 SD - An HP-35 Simulator for iOS Devices

About HP-35 — Facts and Trivia

Using the HP-35

Being the first of a new kind of calculator, the HP-35 doesn't appear as polished and easy to use as today's calculators. Here are a few points you may want to try out. Make sure RPN-35 is set to Vintage Mode.

Entering negative numbers
As the page from the manual shown at right explains, you may enter negative numbers by pressing CHS before or after you enter the first digit.
For example, if the display shows Pi = 3.141... and you press CHS, you see -3.141...
Now enter 2. The display shows -2, while the original, positive 3.141... has been pushed on the stack.
Press "+" and you get 1.141..., the sum of Pi and -2.

While convenient, this feature was also confusing, so HP dropped it in later models, never implementing it again.

x^y
The HP-35 was the only model to use x^y instead of y^x.
It made sense because there was no 10^x function. To get the antilog of the display value, you simply entered 10 and pressed x^y.

Leading Zeros
When entering a number, leading zeros were not suppressed. For example, typing
00000.000, then EEX would be shown as 00000.0001 00. Pressing x<>y twice would then reveal the formatted number, 1. -04.

No stack lift after STO
The RCL key or a keyboard entry, including EEX and Pi, did not raise the stack.

Numeric precision

The HP-35's numeric precision was limited to 14-digit BCD numbers. Errors exceeding the last significant digit were rare. On the other hand, about 10,000 calculators produced in 1972 exhibited a ROM bug which caused a calculation like 2.02 LN e^x to return 2.

Some noteworthy "bad" results:

Calculation	Correct	HP-35	Error
e^ln(2.02)	+2.020000000	+2.000000000	20000000E-9
ln(0.9995)*10000	-5.001250417	-5.001250000	417E-9
1.000001^1E6	+2.718280469	+2.718281828	1359E-9
tan(89.99)/1000	+5.729577893	+5.729569869	8024E-9
arc sin(0.0002)*100	+1.145915598	+0.5729577893	572957786E-9
arc cos(0.0002)/10	+8.998854084	+8.999427042	572958E-9
arc tan(0.0002)*100	+1.145915575	+0.5729577893	572957786E-9
arc tan(1.00020002)/10	+4.500572958	+4.500000000	572958E-9
arc sin(xx)/10	+4.500572958	+4.500000000	572958E-9
arc cos(xx)/10	+4.499427042	+4.500000000	572958E-9
ln(1E-10)/10	-2.302585093	-12.30258509	huge

Notes:
1. RPN-35 SD simulates these errors on HP-35 v1 in vintage mode.
2. xx is any of the numbers: 0.7071774882, 0.7071774883, 0.7071774884, 0.7071774885
(not simulated yet)

Technology

As can be seen in the picture below, the HP-35 is basically built on five chips - a register and arithmetic chip, a timing chip, and three ROM (read-only memory) chips. Each ROM chip holds 2560 bits (that's bits, not bytes), arranged in 256 words of 10 bits each. The entire program, including all mathematical functions, fits in 768 words! A total of 30,000 transistors were involved - about 100,000 times less than the A8X chip inside the iPhone 6 Plus.

Data is shifted around serially, bit-by-bit. This is one reason for the rather low speed of operation. Another reason is the clock rate of 200 kHz. The design goal was to execute transcendental functions in less than a second. This was achieved quite nicely:

Operation	Time (in ms)
Add, Subtract	60
Multiply, Divide	100
Square Root	110
Logarithmic and Exponential	200
x^y	400
Trigonometric	500

Register space was so scarce that trigonometric operations had to use the stack
register T. After completion of the operation, the content of stack register Z was
copied to T.

Miscellaneous

Battery life was about three to five hours, mainly due to the LED display's power consumption. To extend operating time without turning the calculator off (thereby losing stack and memory contents), users would enter a single decimal point without digits. On the iPhone, this trick is probably of doubtful value.

Just for fun, enter the following numbers, then turn the calculator upside down:

710.77345
57738.57734 EEX 40

Evaluate the following expression:

(e.g.: 9 ENTER x 19 ENTER x 22 / + √x √x )

Compare the result with Pi.

Popular Electronics, May 1972

Enjoy one of the first articles on the HP-35.

Inside the HP-35

From the Operating Manual

(click image to enlarge)

Entering negative numbers

(click image to enlarge)

Entering exponents in v1 ("Red Dot")

(click image to enlarge)

Note how E EX "causes no visual change in the display."
In addition, "CH S must immediately follow E EX, otherwise CH S is ignored."

Entering exponents in later versions

(click image to enlarge)

Now, "press CHS after pressing EEX and either before or after keying in the power of ten."

RPN-35 simulates these variants in version 1.8 and later.