What is Unc?

Unc is a calculator which runs on the 3Com PalmPilot and on Microsoft Windows. Unc is actually two calculators in one: a scientific calculator that allows arbitrary arithmetic on numbers containing UNITS, and a full featured programmer's calculator that supports word sizes up to 128 bits.

What does Unc do?

What do I need to use Unc?

To run the PalmPilot version of Unc, you need a 3Com PalmPilot version 2.0 or later (PalmPilot Personal, PalmPilot Professional, Palm III, Palm V, or Palm VII). You'll also need a PC or Macintosh computer with Palm Desktop or similar software to install Unc onto your PalmPilot.

To run the Windows version of Unc, you need Windows 95 or later (Windows 95, Windows 98, Windows NT 4.1, Windows 2000, Windows ME, Windows XP).

Getting started

Installing Unc

PalmPilot version

To install the PalmPilot version of Unc, you must load three files onto your PalmPilot:

unc.prc

This is the Unc program file.

uncDB.pdb

This is the database containing all the unit defintions.

MathLib.prc

This is the shared library containing math functions.

There are two versions of the database; uncDB.pdb contains unit definitions which are standard in the United States, and uncDB-UK.pdb contains unit definitions which are standard in the United Kingdom. If you wish to use the UK version, load uncDB-UK.pdb instead of uncDB.pdb. It is not strictly necessary to load either .pdb file; Unc will operate correctly without them, but you won't have any predefined units, and you will have to define all the units yourself.

Registering Unc

When you first start the Unc calculator, it will look like this:

Standard float buttons

(Note: all screen shots are from the PalmPilot version, but the Windows version looks very similar.) The alt button on the bottom left is special. When you press it, many of the buttons change to an alternate form. This gives access to more functions than would fit on the existing buttons. When you press alt, here's what you'll see:

Alternate float buttons

Notice that the alt button has changed to ALT to signal that you're seeing the alternate buttons. Many of the buttons now have different labels. You can press ALT again to return to the standard buttons.

The top row consists of unit buttons. The rightmost five buttons are the most common units (you can change these if you find you use other units more often). When you press the unit button at the top left, most of the buttons on the calculator will change to show you more units, 25 of them. When you do this, here's what you'll see:

Standard unit buttons

Using an RPN calculator

Unc is a Reverse Polish Notation or RPN calculator. If you're not familiar with RPN, it will take a little time to get used to, but you'll probably find it easier to use than standard algebraic calculators once you've adjusted to it.

In an RPN calculator, when you enter a number, you are placing (or "pushing") the number onto the stack. The stack is just a list of numbers. Unc always shows you the top four numbers on the stack. If there are more than four numbers on the stack you can scroll the display to see the others. When you do an operation, like pressing the + button, you are operating on the top number or top two numbers on the stack. For example, the + button adds together the top two numbers on the stack and replaces them with the result.

For example, suppose you want to add 15 and 7. First you press 1, then 5. Notice the underscore after the last digit you entered, which shows where the next digit will appear. Then you press the ENT button, to say you're done with that number. This pushes the number 15 onto the stack. The underscore disappears, to show that you are no longer entering a number, but instead are looking at the top number on the stack. Next you press 7. Then you can press ENT again to push 7 onto the stack. Now the stack has two numbers, 15 and 7. Then you press +, which adds the two numbers and replaces them with the result, 22. Now the stack has one number, 22.

In this example, it wasn't really necessary to press ENT after the 7. If you press an operation button like + while you're entering a number, Unc automatically pushes the number on the stack before doing the operation.

Whatever number you entered most recently is called the "top" of the stack. Each time you enter a number, any numbers already on the stack get "pushed down" and the new number becomes the top of the stack. The Unc display always shows the top number on the stack in the main display window, and the next three numbers on the three lines above it. Don't get confused by the fact that the top of the stack is actually at the bottom of the display. Once you start using the calculator, it will be obvious how it works.

Float and integer modes

Entering numbers

To enter a number, just start pressing digit buttons. You can press the +/- button to change the sign of the number you're entering.

Using the stack

The top four numbers on the stack are displayed on the screen. If there are more than four numbers on the stack, scroll arrows appear, which you can use to scroll the stack up and down. This merely changes what part of the stack you are looking at; it does not change the stack itself. You can also use the PalmPilot's up and down buttons (the physical buttons on the case) to scroll the stack. On the PalmPilot, if you tap a number on the stack, it changes places with the top number on the stack. This is an easy way to bring a number which you wish to use to the top of the stack. On Windows, double-clicking a number on the stack does the same thing.

The up and dn buttons "roll" the stack. Unlike scrolling, this does change the stack itself. Pressing the up button moves the bottom number on the stack to the top of the stack. Pressing the dn button moves the top number on the stack to the bottom of the stack.

Using memory

If you press the mem button, the display changes to a list of ten memory locations. Each memory location can hold one number. To store a number into a memory location, select a memory location and press the Store button. This copies the top number on the stack to the selected memory location. The number is also removed from the top of the stack. Then later, to recall a number from a memory location, select the memory location and press the Recall button. This copies the number from the selected memory location to the top of the stack. The number is not removed from the memory location, so it can be used again later.

There are three ways to select a different memory location: just tap it with the pen (or click it in the Windows version), or use the up and down buttons to move the selection, or write a Graffitti glyph for a number between 0 and 9 (press the appropriate digit key in the Windows version). Once you have selected a memory location, it will still be selected if you leave the Memory screen and return to it later.

Doing arithmetic

To perform an arithmetic operation, you simply press one of the buttons that represents an arithmetic operation. Some of the operations, like + and *, operate on the top two numbers on the stack, and replace them with the result of the operation. Other operations, like sqrt and sin, operate on just the top number on the stack, and replace it with the result.

You can also enter Graffitti glyphs (or press keyboard keys in the Windows version) for some of the more common arithmetic operations. Writing a "+" is equivalent to pressing the + button, which adds the two numbers on top of the stack. Similarly, "-" is equivalent to the - button (subtract); "*" is equivalent to the * button (multiply); and "/" is equivalent to the / button (divide).

Changing how numbers are displayed

Display mode

Precision

Full mode

Spacing

Entering units

Converting between units

To convert the top number on the stack to different units, enter the desired unit (thus making the number to be converted the second number on the stack). Then press conv. This changes the units of the second number on the stack to match the units of the (new) top number on the stack, if possible. For example, if "45 km" is the top number on the stack, press mi conv to convert it to miles. Note that when you press conv, the value of the top number is ignored; only its units are relevant.

If the units of the second number on the stack cannot be converted directly into the units of the top number, Unc will do its best to make the desired units appear in the result. Sometimes this will result in a sensible answer. For example, if "5 mi/s" is on top of the stack and you enter ft conv, you will get "26,400 ft/s". Although Unc was not able to convert the result to "feet", it converted it to a unit containing "feet". On the other hand, if you try to convert "5 mi/s" into pounds, you get "17.739981 lb*m/s*g". Again, the result contains "pounds", and is in fact equivalent to 5 mi/s, but this is probably not a very useful unit.

Defining new units

Unc has an extensive list of units, and you can add new units to this list. There are two types of units. Base units or primitive units are not defined in terms of other units; they are the "base" on which all other units are built. Examples of base units are "grams", "meters" and "seconds". Derived units are defined in terms of base units or other derived units. For example, an inch is defined as "2.54 cm", a foot is defined as "12 in", and a mile is defined as "5280 ft".

Changing and deleting units

Renaming a unit

To change the name of a unit, display the list of units by pressing the list button. Select the unit from the list. Select the "Rename" menu item and type the new name of the unit. If the unit is assigned to a button or appears in the stack, the name of the unit on the button or on the stack will automatically be changed.

Changing the category of a unit

Redefining a unit

To change the definition of a unit, enter the new defintion of the unit on the stack. Then display the list of units by pressing the list button. Select the unit from the list. Select the "Redefine" menu item and tap the Yes button on the dialog that appears. The new definition must have the same units as the original definition; only the magnitude can change.

Deleting a unit

To delete a unit, display the list of units by pressing the list button. Select the unit from the list. Select the "Delete" menu item and tap the OK button on the dialog that appears. Warning: if you delete a unit, any other units that are defined in terms of that unit, either directly or indirectly, will also be deleted. For example, deleting "m" (meters) will delete most of the units that are defined! If you are just trying to change a unit, use the Rename or Redefine menu items, rather than deleting and recreating the unit.

Changing unit buttons

Assigning a unit to a button

To assign a unit to a button, first enter the unit on the stack. If the unit is not already on a button, you can enter the unit by pressing list, selecting the unit from the list, and pressing Use. Once the unit is on the stack, select the "Set button" menu item. You will be prompted with the message "Key for ...", with the name of the unit. Just press the button to which you want to assign the unit, or press the none button if you change your mind and don't want to assign the unit to a button.

You can assign a unit to any of the 25 primary unit buttons, or press alt to assign it to any of the 25 alternate unit buttons. If you assign a unit to a button which already has a unit, the button's unit is replaced. The old unit will still appear in the unit list. A unit may appear on more than one button.

Removing a unit from a button

Using integer mode

In addition to float mode, Unc can operate in integer mode. In integer mode the base may be any number from 2 through 36, and numbers are integers, which may not have units.

Changing the base of numbers

To switch to a different base, tap the base indicator and select the desired base from the list that appears. To switch to an integer base other than 2, 8, 10, or 16, first enter the base on the stack, then tap the base indicator and select the "x (Stack)" item from the list.

Notice that there is a difference between float mode and decimal mode. Although both modes use base 10, in decimal mode numbers are integers and the buttons show the integer functions. In float mode, numbers may have a decimal point and units, and the buttons show the float functions.

When you switch from float mode to integer mode, all the numbers on the stack are rounded to the nearest integer and any units are discarded.

Changing the word size of numbers

Changing between signed and unsigned mode

Some examples of units calculation

Here are some examples of how Unc's built-in units knowlege can make calculations easier.

1. Metric conversions

A. You want to convert 28 gallons to liters.

Enter 28. Press the gal button. Press ENT. The display reads "28 gal". Now to convert, press the l button (that's L, for liters) and press conv. The display reads 105.991529952 l".

B. You want to convert 800 kilometers to miles.

Enter 800. Press the km button. Press ENT. The display reads "800 km". Now to convert, press the mi button and press conv. The display reads "497.0969537899 mi".

C. You want to convert 55 miles per hour to kilometers per hour.

Enter 55. Press the mi button, then the per button, then the hr button. Press ENT. The display reads "55 mi/hr". Now to convert, press km per hr and press conv. The display reads "88.51392 km/hr".

2. Mixed unit arithmetic

A. You want to express 5 feet 8.5 inches in inches.

Enter 5 and press the ft button. Press ENT. The display reads "5 ft". Enter 8.5 and press the in button. Press +. You've added 5 feet plus 8.5 inches. The display reads "68.5 in". What if you now want it in feet instead of inches? Easy: just press the ft button, then press conv. The display now reads "5.708333333 ft".

B. You want to find the area of a plot of land. You know it's 125 feet 5 inches long, and 16 yards wide.

Enter 125 and press the ft button. Press ENT. The display reads "125 ft". Enter 5 and press the in button. Press +. You've added 125 feet plus 5 inches, and the display reads "1,505 in". Now enter 16 and press the yd button. Press * to multiply. The display reads "668.888888889 yd²". What if you want to see it in square feet? Press ft twice, then conv. The display reads "6,020 ft²".

C. You want to find the volume in gallons of a rectangular swimming pool that is 25 feet long, 16 feet wide, and 6 feet deep.

Enter 25 and press the ft button. Press ENT. The display reads "25 ft". Enter 16 and press the ft button. Press *. The display reads "400 ft²" (that's the area of the surface of the pool). Enter 6 and press the ft button. Press * again. The display reads "2,400 ft³". To convert to gallons, press gal conv. The display reads "17,953.2467532 gal".

3. Physics problems

A. Find the force of gravity exerted on a 100 pound mass at sea level.

First enter the mass: enter 100 and press the lb button. Press ENT. The display reads "100 lb". Since force = mass x acceleration, we want to multiply by the Earth's gravitational acceleration. If you don't happen to remember it, you can look it up in the complete units list: press list and find the "grav" entry. Select it and press "Use". Now press * to multiply. The display reads "100 grav*lb". To convert to newtons, for example, press N conv. The display reads "444.8221615261 N".

B. Find the kinetic energy of a 2500 pound car travelling at 60 miles per hour.

4. Fun stuff

A. Find the volume of the earth in teaspoons.

The radius of the earth is about 4000 miles. Enter 4000 and press mi. Using the formula for the volume of a sphere (4/3 * pi * radius cubed), press x^3, enter 4 and press *. Enter 3 and press /. Enter pi and press *. The display reads "2.68082573 e11 mi³". This is the volume of the earth in cubic miles. To convert to teaspoons, press tsp conv. The display reads "2.26706164 e26 tsp".

B. How big an area would be needed if everyone on earth were gathered in one place?

Frequently Asked Questions

Currently Unc cannot do conversions that involve both multiplying AND adding a conversion factor. For example, converting a temperature measurement in degrees Celsius to degrees Fahrenheit involves multipying by 1.8 and adding 32. The main problem is that there is an inherent ambiguity in this type of temperature conversion, depending on whether the number being converted is interpreted as an absolute measurement, or as a relative difference between measurements. For example, as an absolute measurement 10 degC = 50 degF. But if the temperature rises from 5 degC to 15 degC (41 degF to 59 degF), that's a rise of 10 degC, but it's NOT a rise of 50 degF! There's no obvious way for Unc to know where a number came from, and therefore what type of conversion to apply. The problem also appears when temperature units are combined with other units. A temperature gradient of 10 degC/ft is NOT equal to 50 degF/ft. You can always do simple multiplicative temperature conversions, as long as you remember that absolute temperature measurements still need the offset (32) added or subtracted. But to avoid confusion, Unc does not come with predefined temperature units.

Reference Manual

Menu items on the calculator display

Undo

Restores the stack to its contents before the last arithmetic operation. This only works for arithmetic operations, which operate on the top number or top two numbers on the stack. You cannot undo operations that affect the whole stack, like CLR, BSP, up and dn.

Copy

Copies the number on the top of the stack to the Clipboard.

Paste

Pushes the number in the Clipboard to the top of the stack. The number you are pasting cannot have units.

Define unit

Defines a new unit. The definition of the unit is the value of the top number on the stack.

Set button

Assigns the unit of the top number on the stack to a button. Prompts you to press the button to which the unit is to be assigned. Only the unit portion of the number is used; the numeric portion of the number is ignored. If the stack is empty or if the top number does not have units, the button pressed will be cleared; that is, it will not be assigned a unit.

Make primitive

Converts the units of the top number on the stack to "primitive" or "base" units.

Import

(Only in the Windows version.)
Imports a set of units from a text file. All existing units are discarded and replaced with the new ones.

Export

(Only in the Windows version.)
Exports the current set of units to a text file.

Display

Preferences

Displays the Preferences dialog, which lets you set some options.

Display prefs

Displays the Display Preferences dialog, which lets you set some options which control the display of numbers.

Precision

Sets the precision (the maximum digits displayed to the right of the decimal point). The precision must be between 0 and 16. Changing the precision only affects the display of numbers; it does not affect how the numbers are stored internally.

Digits between separators

Sets the separator spacing value for each of the bases.

About Unc

Displays information about the version of Unc you are using.

Menu items on the unit list

Delete

Deletes the selected unit. This completely removes the unit from Unc's knowlege. It also removes any units that depend on the deleted unit, either directly or indirectly. Any buttons which are assigned a unit being deleted will be cleared. Any numbers on the stack which contain the unit being deleted will have their units removed.

Rename

Changes the name of the selected unit.

Redefine

Changes the definition of the selected unit. The new definition of the unit is the value of the top number on the stack. The new definition must have the same units as the original definition; only the magnitude can change.

Menu items on the memory screen

Clear Selection

Sets the selected memory location to zero.

Clear All

Sets all memory locations to zero.

Buttons

+

Adds the two numbers on top of the stack and replaces them with the result. If the two numbers have units and they are not the same, Unc will attempt to convert the second number into the units of the top number.

-

Subtracts the two numbers on top of the stack and replaces them with the result. If the two numbers have units and they are not the same, Unc will attempt to convert the second number into the units of the top number.

*

Multiplies the two numbers on top of the stack and replaces them with the result.

/

Divides the two numbers on top of the stack and replaces them with the result.

+/-

Changes the sign of the top number on the stack. If pressed while entering a number, changes the sign of the number being entered. If pressed while entering the exponent of a number in scientific notation (after pressing EEX), changes the sign of the exponent being entered.

1/x

Replaces the number on top of the stack with its reciprocal (1 divided by the number).

10^x

Replaces the number on top of the stack with 10 raised to the power of that number. The number may not have units.

acos

acosh

Replaces the number on top of the stack with the inverse hyperbolic cosine of the number.

alt

Switches all buttons to their "alternate" form.

and

Performs a logical AND of the two numbers on top of the stack and replaces them with the result.

and~

Performs a logical AND of the second number on the stack and the logical NOT of the top number on the stack and replaces them with the result.

asin

asinh

Replaces the number on top of the stack with the inverse hyperbolic sine of the number.

atan

atanh

Replaces the number on top of the stack with the inverse hyperbolic tangent of the number.

BSP

Pops (deletes) the number on top of the stack. If pressed while entering a number, deletes the last character which was entered.

bswp

Performs a byte-swap of the number on top of the stack and replaces it with the result.

cbrt

Replaces the number on top of the stack with its cube root. If the number has units, the exponent of all units in the number must be a multiple of three.

CLR

Deletes all numbers in the stack.

conv

Converts the units of the second number on the stack to match the units of the top number on the stack.

cos

cosh

Replaces the top number on the stack with its hyperbolic cosine.

deg / rad

Switches between degrees mode and radians mode. While in degrees mode, the button will be labeled deg; while in radians mode, the button will be labeled rad. In degrees mode, the input number to trig functions (sin, cos and tan) is assumed to be degrees, unless it has a unit. The result of inverse trig functions (asin, acos and atan) will be in degrees. In radians mode, the input number to trig functions is assumed to be radians, unless it has a unit, and the result of inverse trig functions will be in radians.

dn

"Rolls" the stack down. The top number on the stack is moved to the bottom of the stack, and all the other numbers are shifted accordingly.

e^x

Replaces the top number on the stack with e (the base of the natural logarithm) raised to the power of that number. The number may not have units.

EEX

Begins entering the exponent of a number in scientific notation.

ENT

Pushes the number being entered on the top of the stack. If pressed while not entering a number, pushes another copy of the top number on the stack.

full

Switches between normal mode, FULL mode, and FULP mode. In normal mode, numbers are forced to fit in the available display space. In FULL mode, numbers scroll if they are too long to fit in the available display space. FULP mode is like FULL, but in addition the precision is temporarily increased to the maximum.

hyp

Switches the trigonometric buttons sin, cos, tan to the hyperbolic functions sinh, cosh, tanh. While in this mode, the label of this button changes to HYP. Pressing HYP again restores the trigonometric buttons.

list

Displays the list of all units. Use the scroll bar at the right of the display to navigate in the list. You can also use the PalmPilot's up and down (physical) buttons to scroll in the list, or you can write a Graffitti letter to scroll to the first unit which begins with that letter.

ln

Replaces the top number on the stack with its natural logarithm (logarithm to the base e).

log

Replaces the top number on the stack with its common logarithm (logarithm to the base 10).

m<

Replaces the top number on the stack with a "left mask", consisting of N high-order one bits and the rest zeros, where N is the top number on the stack.

m>

Replaces the top number on the stack with a "right mask", consisting of N low-order one bits and the rest zeros, where N is the top number on the stack.

m2<

Creates a "left mask", consisting of N high-order one bits and the rest zeros, where N is the second number on the stack. This mask is then shifted right M bits, where M is the top number on the stack, and the top two numbers on the stack are replaced with the result.

m2>

Creates a "right mask", consisting of N low-order one bits and the rest zeros, where N is the second number on the stack. This mask is then shifted left M bits, where M is the top number on the stack, and the top two numbers on the stack are replaced with the result.

mem

mod

Divides the top two numbers on the stack and replaces them with the remainder of the division.

not

Replaces the top number on the stack with its logical NOT.

or

Performs a logical OR of the two numbers on top of the stack and replaces them with the result.

or~

Performs a logical OR of the second number on the stack and the logical NOT of the top number on the stack and replaces them with the result.

pad

Enables and disables pad mode. In pad mode, numbers are displayed with leading zeros. While in pad mode, the button will be labeled PAD; while not in pad mode, the button will be labeled pad.

per

Begins entering units with negative exponents.

pfx

pi

Pushes the number pi on the stack.

r<

Rotates the number on top of the stack left by one bit and replaces it with the result.

r>

Rotates the number on top of the stack right by one bit and replaces it with the result.

r2<

Rotates the second number on top of the stack left by N bits, where N is the top number on the stack, and replaces both numbers with the result.

r2>

Rotates the second number on top of the stack right by N bits, where N is the top number on the stack, and replaces both numbers with the result.

s<

Shifts the number on top of the stack left by one bit and replaces it with the result.

s>

Shifts the number on top of the stack right by one bit and replaces it with the result. In unsigned mode, the high order bit is set to zero; in signed mode, the high order bit is set to a copy of the sign bit of the original number.

s2<

Shifts the second number on the stack left by N bits, where N is the number on top of the stack. and replaces both numbers with the result.

s2>

Shifts the second number on the stack right by N bits, where N is the number on top of the stack. and replaces both numbers with the result. In unsigned mode, the high order bits are set to zero; in signed mode, the high order bits are set to a copy of the sign bit of the original number.

sign / usign

Switches between signed mode and unsigned mode. While in signed mode, the button will be labeled sign; while in unsigned mode, the button will be labeled usign.

sin

sinh

Replaces the top number on the stack with its hyperbolic sine.

sqrt

Replaces the number on top of the stack with its square root. If the number has units, the exponent of all units in the number must be a multiple of two.

tan

tanh

Replaces the top number on the stack with its hyperbolic tangent.

unit

up

"Rolls" the stack up. The bottom number on the stack is moved to the top of the stack, and all the other numbers are shifted accordingly.

word

Change the word size.

x^2

Replaces the number on top of the stack with its square.

x^3

Replaces the number on top of the stack with its cube.

xor

Performs a logical XOR (exclusive OR) of the two numbers on top of the stack and replaces them with the result.

xor~

Performs a logical XOR (exclusive OR) of the second number on the stack and the logical NOT of the top number on the stack and replaces them with the result.

y^/

Raises the second number on the stack to the power of the reciprocal of the first number on the stack, and replaces both numbers with the result. The exponent may not have units. If the number being exponentiated has units, the other number must be an integer, and the exponents of the units must all be multiples of that number.

y^x

Raises the second number on the stack to the power of the first number on the stack, and replaces both numbers with the result. The exponent may not have units. If the number being exponentiated has units, the other number must be an integer.

Unit buttons

Pressing any of the 50 unit buttons appends that unit to the number being entered.

Prefix buttons

Pressing any of the prefix buttons appends that prefix to the number being entered. The prefix should be followed immediately by a unit button, which causes the prefix to affect that unit.

There are three sets of prefix buttons. Switch between them by pressing the pfx button.

The first set of prefix buttons is:

The second set of prefix buttons is:

The third set of prefix buttons is:

These are the predefined US units. The UK units are the same, except that units which begin with "UK" in this list do not have the "UK" prefix in the UK list, and units marked with "(US)" in this list have a "US" prefix in the UK list.

1. You cannot Paste a number containing units.
2. If a number is more than 99 digits long, the scrolling indicators might not correctly show the number of off-screen digits.

Cook, James L. Conversion Factors. Oxford: Oxford University Press, 1991.

Dresner, Stephen. Units of Measurement. Aylesbury: Harvey Miller & Medcalf Ltd., 1971.

Selby, Samuel, ed. CRC Standard Mathematical Tables, Twenty-third Edition. Cleveland: CRC Press, 1975.