DM32 User Manual

While in Calculator mode, the operating system (DMCP) black status bar has 3 sections:

These two rows consist of icons, or annunciators, which turn on or off to reflect various calculator states or to make the user aware of a certain condition.

This is the main number-crunching area. It is made up of four 12-character lines, one for each level of the RPN stack. Each line also has an extra space on the left to display a minus sign for negative numbers.

The calculator responds to certain situations by displaying a message. The triangular warning annunciator turns on with every message.

If the triangular warning annunciator appears alone to indicate that an inactive key has just been pressed (a key that has no meaning in the current situation, such as 3 in binary mode).

The DM32 can operate in 3 different modes. When this manual refers to one of the modes, the initial is capitalized as below.

The calculator can use two fonts with variants, for a combined total of 5 font options. See section Stack Font from chapter DM32 Setup for a preview and details.

The row of blank keys at the top of the keypad, right under the LCD, are designated from left to right as F1 to F6.

When the calculator is displaying a file selection dialog, like in the File menu, the Available States list or the help file selection dialog:

In addition to entering numbers and executing functions as they are labeled in white, each of these keys has 2, sometimes 3 additional functions. They can switch the calculator to Equation or Programming mode, summon menus (from which further functions can be invoked), execute math operations or add program instructions, perform conversions, act as a letter input keypad, and more. The labels to these extra functions are printed on the bezel, around each key, in orange, blue and white.

The keypad has two color keys,      and     , just above the C key. To execute a function printed in orange or blue, press the corresponding color once before pressing the key. For example, number π can be entered by using key SIN. To do so, press and release the blue shift key      and the blue shift annunciator appears at the top left corner of the display:

Press SIN and number π appears in the x-register:

The annunciator automatically disappears and the next key press is unshifted. To clear the annunciator if shift has been pressed by mistake, press the same shift key again. In this manual, shifted function calls are depicted by their color label as it appears on the calculator bezel (the shift key press is omitted), for instance π or ASIN.

Keying in a letter is done by pressing the corresponding key when appropriate, to store or recall variables, execute a program, or when writing an equation. In this manual letter-key presses are depicted by the letter between square brackets, for instance [A] or [F]. Depending on context, entering a letter might require pressing RCL beforehand.

Clear or Cancel key. When the calculator is off, pressing C turns the calculator on. When the calculator is on, it clears the x-register, exits menus and cancels input; orange-shifted, it opens DM32 Setup, controlling general calculator settings, OS and hardware functions; blue-shifted, it turns the calculator off.

Also useful to exit menus or cancel actions. DMCP, the calculator’s operating system, sometimes refers to this key as the “EXIT” key.

Note that the calculator retains the state it was in when turned off, i.e. it will turn on in the same state and mode it was turned off in.

Depending on the situation and what needs to be achieved, the appropriate way to clear or backspace is different. There is also a CLEAR menu with functions usable as program instructions. See appendix Clearing functions for a complete reference.

The stack is a memory space made up of 4 registers. These registers are visible at all times as the 4 lines on display while in Calculator mode. Numbers used for calculations are invariably inserted in stack registers before performing operations. These registers are volatile in the sense that every new value introduced destroys the oldest value, as explained below. The 4 registers of the stack are named x, y, z and t, with x at the bottom. In the rest of this manual, registers are sometimes designated implicitly, i.e. simply with an italic x, y, z or t instead of the more complete “x-register”, “y-register”, “z-register” or “t-register”.

Here is an example chain of operations to illustrate how values move within the stack. First, initialize the calculator with CLEAR ALL Y (warning: this will delete contents of the calculator). Also make sure the display mode is set with DISP FX 1. This limits the display to one decimal place so numbers are easier to read for the example.

The stack is now empty (or filled with value zero), and the display shows:

When a new number is keyed in, it is placed on the “bottom of the stack” in the x-register. Let’s key in 2, the stack now looks like this:

The underscore character on the right of value 2 means that digit-entry is still active. To terminate entry and key in a new number, press ENTER. The following happens:

The value is now on registers x and y because two things actually happen at the same time when ENTER is executed: the entered value is immediately pushed up to y-register (this is called stack lift) and a copy is placed in the x-register. This is useful to perform an operation using two identical numbers. Since it isn’t our goal here, let’s key in number 1 • 2 3 4 5. The following changes happen:

Note how this new value replaces the copy placed in x-register. This is because key ENTER disables stack lift, which means that any key press following ENTER won’t lift the stack.

Pressing x⇄y swaps values between the x- and y-registers. Press it and the stack changes like this:

This simple swap operation is very often useful when working with the stack. It also terminates digit-entry. (Note that number 1.2345 is truncated to 1.2, or 1 decimal place; that’s because of the active display setting that has just been set with DISP FX 1. Internally the number is represented complete, as 1.2345.)

To proceed with our example, let’s insert values 5 and 0.5 like so:

5 ENTER • 5

Now all four registers are filled:

Press ENTER one more time and the stack is modified so:

The value 1.2345 in the t-register has been pushed out of the stack and lost. The stack has 4 registers; every time the stack lifts, the value in the t-register is pushed out and permanently lost.

Key R↓ “rolls” the stack downwards, which means that the value in t goes to z, the value in z goes to y, the value in y goes to x, and the value in x wraps around to t. Press it and the stack changes like this:

A function opposite to R↓ exists to “roll up” the stack. Press R↑ and the stack rolls up. In this case it simply returns to its previous state:

The stack as it now stands can be used for the upcoming example.

Operators use values (or operands) in the x- and y-registers. Press + and the stack transforms like this:

The following has happened:

Now press –. The following happens:

The value in the x-register has been subtracted from the value in the y-register and the result placed in the x-register. The stack drops again. Note how, because the t-register retains a copy of its value every time the stack drops, all registers except x now have the same value.

Now press ×. The following happens:

The value in the x-register has been multiplied by the value in the y-register and the result placed in the x-register. The stack drops again, although this didn’t produce any visible change, since the value in the t-register gets duplicated upon stack drop.

Now press ÷. The following happens:

The value in the y-register has been divided by the value in the x-register and the result placed in the x-register. The stack drops again. The displayed value 0.3 is internally represented as 0.25, but it is shown rounded with only one decimal place because of the current display setting. To view the entire number in the x-register, change the display mode with key sequence DISP FX 2 :

The t-register’s duplicating behavior during stack drop allows for calculations with a constant. Since all stack levels (except the x-register) are filled with value 2, it’s easy to repeatedly multiply the value in x-register by 2. Press ×:

Press × again:

Press × one more time:

Since a new copy of value 2 is inserted at the top of the stack after every two-number operation, the constant calculation can go on indefinitely (or at least until OVERFLOW is met — see Appendix C: Messages).

To proceed, clear memory with CLEAR ALL Y.

Here’s an example expression:

( 2 × ( 27 ÷ 2.5 ) - ( 2 + 4 ) ) × π

Start from the inner parenthesis that has a division and key in 2 7 ENTER 2 • 5 ÷. The result is:

Then multiply this with 2 ×. The display now shows:

Calculate the value of terms between the other parentheses with 2 ENTER 4 +. The display changes to:

Subtract x from y with – and the display changes to:

Put π on the stack and multiply with ×:

The result is ≅ 49.0088 (and shows as 49.01 because of current FIX 2 display format).

Parentheses are not used when writing and evaluating expressions with RPN. The stack holds intermediate results and allows for chain calculations following a natural course.

To recap, here is the expression written in algebraic form (as it would be keyed in, without the final press on “equal” key):

( 2 × ( 27 ÷ 2.5 ) - ( 2 + 4 ) ) × π

And here it is in RPN, as it was entered in the calculator (character ↑ representing ENTER key-presses) :

27 ↑ 2.5 ÷ 2 × 4 ↑ 2 + - π ×

which saves four key presses compared to algebraic entry (five if considering the need to press the “equal” key).

Most of the time, when a number is keyed in, the stack is lifted: values are pushed up the stack (x goes to y, y to z, z to t and t is pushed out and lost). Whether an action lifts the stack or not depends on the stack lift status at the moment the function is executed. Stack lift is usually enabled, but certain operations disable it. When stack lift is disabled, the next number keyed in overwrites the one present in the x-register without pushing numbers up the stack beforehand. Calculator functions have either 3 effects on stack lift status, they either:

Disabling functions

Neutral functions

If the first entered number was erroneous, key in the correct first number, press LASTx to reclaim the second number, and execute the function. Press C to remove the incorrect result from the stack first.

Examples of LASTx use
Let’s consider the following calculation:

Here are the three types of possible errors, and how to use LASTx to correct them:

LASTx can be used to reclaim a number in a calculation, like a constant.

Let’s assume European astronauts Garrett and Neil need spacesuits that fit them. To make the suits, their size in feet is required. There are 3.28084 feet in a meter.

Garrett is 1.76 meter tall.
Neil is 1.85 meter tall.

Numbers on the stack are aligned to the left by default:

The Stack Align setting in DM32 Setup allows to change this to right-alignment. In the screen image below, where the display format set to FIX 4, decimal separators of all stack levels align, potentially allowing better readability of numbers. Ultimately, which side the stack aligns to is a matter of personal preference.

See Clearing functions for more detail.

Use exponent key E to enter numbers multiplied by powers of ten. To enter Einstein’s cosmological constant \$1.089×10^-52\$:

Powers of ten without multipliers can be entered easily. For \$10^23\$, press E 2 3. Display shows 1E23_.

Numbers up to 34 digits long can be manually entered, plus a 4 digit exponent up to ±6144. If more digits are entered, nothing happens, except a warning annunciator briefly turning on. The calculator can represent numbers between –9.999999999999999999999999999999999 × 10⁶¹⁴⁴ and 9.999999999999999999999999999999999 × 10⁶¹⁴⁴

These limits are more easily crossed while making calculations:

Numbers with an exponent of ten are displayed with an E preceding the exponent. For instance, number 3.2×10^-6 displays as

Any number too large or too small for the current display format is automatically displayed in exponential form. For instance, if the calculator is in FIX 3 mode, keying in • 0 0 0 7 8 ENTER displays the rounded number on the stack (full precision is preserved internally):

But keying in • 0 0 0 4 4 ENTER gives:

because otherwise, no significant digit would be visible.

Functions from the DISP menu are used to control the way the calculator displays numbers in decimal formats. There are 4 formats to select from:

Here are a few examples. Make sure the calculator is in the correct mode by using DISP FX 4. Let’s put π in the stack:

The calculator shows 4 decimal places. To change this to 6 decimal places, use DISP FX 6. The displayed number changes to:

Make sure the calculator is in the correct mode by using DISP FX 4. Let’s put a number smaller than 1 on the stack with π 1/x:

Switch to scientific format with 3 decimal places by using DISP SCI 3:

Now switch to engineering format with 2 digits after the most significant digit with DISP EN 2:

Revert to fix-decimal FIX 4 with DISP FX 4:

If a fraction is so long that it won’t fit in the display, the integer part is shoved off screen to the left and the display is focused on the fractional part. A …​ to the left indicates this. Long fractions can’t be scrolled, but the integer part can be shown using SHOW.

Example: enable fraction display with FDISP and calculate e¹⁵ with 1 5 eˣ:

The …​ on the left shows that the integer part is only partly visible. The fractional part is always entirely shown. Now press SHOW to see the number in full precision (see Function SHOW to display long numbers for details); the integer part is visible:

To indicate how the displayed fraction compares to the internal decimal number, annunciator ▲ or ▼ can turn on. If no annunciator is lit, the displayed fraction represents the internal number exactly. If ▲ is lit, the internal decimal number is slightly greater than the displayed fraction. More precisely, it means that the exact numerator is 0.5 or less above the displayed numerator. Annunciator ▼ means the same thing but the other way around, that is, the internal decimal number is slightly less than displayed fraction.

A set of rules, called Fraction format, determines how the calculator handles fractions. These rules are determined by the status of fraction flags 7, 8 and 9 plus the setting of maximum denominator. Depending on how the rules are defined, a fraction might be automatically changed when entry is terminated. In the default fraction format (flag 8 and 9 clear), the following rules apply:

The following table shows a few numbers: how they are entered as fractions, the value as represented internally, and how the calculator displays them. The meaning of annunciators ▲ or ▼ is explained above.

Fractions are represented as \$a\$  \$b//c\$, where \$//c\$ is the value of the denominator. Function /c is used to set the maximum denominator, which can be any integer between 0 and 4095. Enter the value and press /c to use it as the maximum denominator value. Function /c uses the absolute value of the integer part of the number in the x-register and doesn’t change the value of the LASTx register.

There are three possible formats fractions can be displayed in:

Fraction display configuration is controlled by flags 7, 8 and 9. Flags 8 and 9 are used to configure fraction format.

Here is how value 4.89 is displayed with different fraction formats and /c values:

To further illustrate how fraction configuration influences number display, here is how different numbers are represented for a /c value of 16:

If fraction display is active, function RND rounds the internal number to the closest decimal representation of the fraction. The rounding is done according to maximum denominator and fraction format configuration.

In equations and programs, RND function does fractional rounding if fraction display is active.

Fractions which are keyed into equations or programs are held in fraction form internally, although they always display as decimal numbers. The recorded fraction can be viewed by pressing SHOW with the relevant equation selected in the Equation list, or with the cursor at the relevant program line in Program mode.

For instance, here is the display while entering fraction 1²/₃ as a program line:

Once digit-entry is terminated, the fraction is expressed as decimal number 1.6666…​:

Pressing SHOW produces 1.2.3, which is exactly how the fraction has been keyed in:

A running program shows values as fractions if fraction display is active. Programs can control fraction display and configuration by setting or clearing fraction flags.

Here is an example illustrating the momentary mode of SHOW:

The SHOW box can be held on display indefinitely. Press SHOW ENTER. The SHOW box remains on display until either C or ← is pressed. Pressing any other key clears the SHOW box as well, and executes that key’s function.

STO arithmetic uses STO +, STO –, STO ×, STO ÷, writes the result of the operation to the designated variable and leaves the x-register untouched.

Press STO +, and the calculator prompts for a variable name to store to:

Press [A]. The value in the x-register (1.41 if the example has been followed from the beginning) has been added to the number in variable A (value 5), and the result written there. Press RCL [A] to check. The value of variable A, now 6.41, is copied to the x-register:

RCL arithmetic uses RCL +, RCL –, RCL ×, RCL ÷, writes the result of the operation to the x-register and leaves the designated variable untouched.

Press RCL +, and the calculator prompts for a variable name to recall from:

Press [B]. The value in variable B (value 60 if the example has been followed from the beginning) has been added to the number in the x-register, and the result written there. The x-register is now 66.41:

Functions like +/—, √x, LN, ➞°F or 10ˣ use x as the operand. Enter the number and press the function key immediately. There’s no need to press ENTER beforehand.

For example, keystrokes to get the reciprocal of 8 are 8 1/x.

Functions like ÷, ˣ√y, yˣ, ➞y,x or ➞Θ,r use numbers from both x- and y-registers. Key in the first number, press ENTER, key in the second number and then press the function key.

For example, keystrokes to get the cube root of 27 are 27 ENTER 3 ˣ√y.

For two-number operations, order must be observed in non-commutative functions. When using –, the number in x is subtracted from the number in y. When using ÷, the number in y is divided by the number in x. Other functions, like yˣ, explicitly identify which number is where, on the stack (in this case, the number in y is elevated to the power of the number in x). If two numbers have been entered the wrong way around, they can be swapped before execution of the function with x⇄y.

Calculations are made using values in the x- and y-registers.

Coordinates are measured as shown in the illustration below.

When the coordinate is in rectangular format, the x-register contains the x-axis value and the y-register, the y-axis value. When the coordinate is in polar format, the x-register contains radius (r) and the y-register, the angle (Θ).

Angle Θ uses units set by the current angular mode. Results for angle Θ are between:

Example
Considering the triangle below:

To find angle Θ and radius r in the above example, first make sure the unit is set to degrees mode with MODES DG. Then key in 3 ENTER 4:

Then press ➞Θ,r:

Angle Θ is placed in the y-register and radius r in the x-register.

These are one-number functions. Key in the number and press the function key without using ENTER. The answer replaces the contents of the x-register.

The conversion works for time and clock angles from and to either of two number formats:

Here are some example calculations. To get the sexagesimal format of 3 1/3 hours, key in the fraction 3 • 1 • 3:

Now press ➞HMS and the calculator returns:

which is 3 hours, 20 minutes and zero second.

Practical example
If a constant power engine has a fuel consumption of 1.23 gallons per hour, and runs for 5 hours, 43 minutes and 21 seconds, the total fuel consumption can be calculated as follows. Key in 5 • 4 3 2 1 as in 5h 43m 21s:

Execute ➞HR to convert time value to decimal format:

Multiply by 1.23 gallons with 1 • 2 3 ×:

The engine run consumes about 7 gallons.

These are one-number functions. Key in the number and press the function key without using ENTER. The answer replaces the contents of the x-register.

These are one-number functions. Key in the number and press the function key without using ENTER. The answer replaces the contents of the x-register.

Pressing x! calculates the factorial of number in the x-register and replaces it with the answer. The number in x must be a positive integer from 0 to 2123.

To calculate the gamma function of a noninteger x, \$Γ(x)\$, key in (x-1) and press x!. The value for x cannot be a negative integer.

This menu is opened with PROB and provides with functions to calculate combinations and permutations. It also includes a RANDOM function which yields a sequence of pseudo-random numbers based on a seed, which can also be set manually. Here is a description of all four options from the menu:

Combinations example
To win the Swiss national lottery, one must have ticked 7 winning numbers out of the available 50. A same number cannot be picked twice. To calculate the probability of picking the right combination, put the two operands on the stack with 5 0 ENTER 7:

Select the Combinations option from the Probability menu with PROB Cn,r and the total number of combinations displays:

Which means the chance to win the jackpot is a little over one in a hundred million.

Permutations example
A racing team with 4 drivers must set up a 3-driver strategy to take part in an endurance race. To calculate how many different parties and orders of driving are possible, put the two operands on the stack with 4 ENTER 3:

Select the Permutations option from the Probability menu with PROB Pn,r and the total number of strategies displays:

Function RANDOM, invoked using PROB R, uses a seed to generate a random number. This number becomes the seed for the next random number. Therefore, any sequence of random numbers can be reproduced that start with the same seed. A seed can be input manually by keying it in and using PROB SD. The current seed value is saved to the Statefile, so that when loading a State, the pseudo-random sequence is restored.

To perform two-number complex operations with numbers z₁ and z₂:

Note that the display of n replaces the contents of the x-register; to recall the just-entered value, use LASTx.

Σ+ actually always accumulates both x- and y-series of data; the y-series is simply ignored when subsequent statistical analysis is based on one-variable data points. It can still be reviewed but obviously has no meaning in such a context.

When data consist of two variables, for each data point, x is the independent variable and y is the dependent variable. Because of how data lands on the stack, remember to enter an x,y pair in reverse order y,x, so that y ends up in the y-register and x in the x-register.

To correct an error, the wrong data point must be first deleted using key Σ–.

The statistics registers are updated accordingly. For two-variable series of data, both the x- and y-values must be deleted and re-entered for the data point to correct.

If the wrong data point is the one just entered, simply press LASTx and Σ– (the incorrect y-value was still in the y-register and function LASTx recalls the x-value, which has been replaced by n, to the x-register).

The mean is the arithmetic average of a group of numbers. The available functions are:

Example: mean
David intentionally drains various lithium cells to test for their capacity. 5 of them gave the following values in mAh (milliampere hour): 174, 182, 188, 194, 205.

Here is the way to find the average capacity of the tested units:

Example: weighted mean
Michael purchases the same semiconductor component every year. After 5 years, he has accumulated the following data.

To find the average price for this component across the years, and taking into account the quantity for each purchase, proceed like so:

Standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean (“variability”). A low number means data are clustered about the mean, and high standard deviation indicates data are more spread out. More specifically, an empirical rule states that 68% of the collected data points fall around the mean plus or minus the standard deviation value. The calculator can compute standard deviation in two ways:

Example
Using the lithium cell capacity test example above, here is how to calculate standard deviation:

This indicates that 68% of the tested cells have a capacity equaling the mean, plus or minus the standard deviation, that is to say between approximately 178 and 199 mAh.

Pressing S,σ sx returns the sample standard deviation, estimating the spread for a hypothetical larger set:

Linear regression is a statistical method to find a straight line that fits the points on a graph drawn using values from the x- and y-series of data. The available functions are:

Example
Bob has been going on the same hike for a few years and has accumulated hike time and ambient temperature data.

Here is how to enter and analyze this dataset.

To estimate how long the hike would take if ambient temperature was 110°F based on the accumulated data, key in 1 1 0 and then invoke the y-estimation function L.R. ̂y. The calculator returns the estimated y-value:

Convert the result to sexagesimal format with ➞HMS. The answer is a little over 4 hours and 24 minutes:

About the correlation coefficient
As explained above, L.R. r returns the correlation coefficient, which is a value between –1 and 1. Here is what this number means in more detail.

EQN LIST TOP represents the top of equation memory. Scrolling down past the last equation in the list rolls back to EQN LIST TOP. Conversely, scrolling up past this line wraps around to the last equation in the list.

Equation scrolling can be deactivated with SCRL. The equation is scrolled back to its beginning and annunciator 🠷 is turned off. Top row keys √x eˣ LN yˣ 1/x Σ+ now perform their normal, non-shifted function. Scrolling must be turned off this way to enter a new equation starting with one of these functions, like LN, for instance.

Example: scrolling an equation
To view the equation entered in the above Practical example of equation evaluation:

A long equation can also be displayed by holding down SHOW while viewed in the Equation list (for details on function SHOW, see Function SHOW to display long numbers).

The image below demonstrates the SHOW box used on the TVM equation, described later in this manual.

With the Equation list open, the currently selected equation can be evaluated by pressing ENTER. (While writing an equation, key ENTER terminates entry and saves the equation, it doesn’t evaluate it.)

See Practical example of equation evaluation for a demonstration.

With the Equation list open, the currently selected equation can be evaluated by pressing XEQ. The entire equation is evaluated, regardless of the type of equation. The value of the equation is returned to the x-register.

When equations are evaluated, a prompt appears for each needed variable. The prompt shows the variable name and its currently stored value, for instance X?3.1416. From here, there are several options.

Each prompt puts the variable value in the x-register and disables stack lift. Numbers entered at the prompt thus replace the value in the x-register. Pressing R/S enables stack lift.

Any of the 28 calculator variables — from A through Z, plus i and (i) — can be entered into an equation, as many times as necessary. (See Indirect addressing for information about i and (i)). To enter a variable, press RCL variable or STO variable. When RCL or STO is pressed, annunciator A..Z is lit to indicate that the next key press will invoke a letter (printed in white on the keypad bezel).

Any base-10 number can be entered in an equation. Numbers in equations are always shown in ALL display format.

Numbers are entered like in normal operation with usual number keys and •, E and +/–. To enter a negative number, key in at least the first digit of the number before pressing +/–.

When number entry starts, block cursor █ changes to _, indicating active number entry. It returns to █ when the next non-number key is pressed.

Many of the DM32’s functions can be used in an equation. See the complete list of available functions below, or the Appendix D: Functions index, which gives this information as well.

Functions in equations are used much like they would in an algebraic equation. But each function uses one of the following notations:

Parentheses in equations can be used to control the order of operations when normal operator precedence isn’t adequate.

Use ( and ) to enter parentheses.

Expression \$A(B(C+1))\$, requires parentheses to evaluate correctly. Here is how to enter it: