The calculator can be driven by clicking the buttons or from the keyboard. On the keyboard all the obvious keys, like +, - and * work. Some other buttons have keyboard equivalents as shown here:
Keyboard Equivalent Button
e exp exponent
enter = equals
return = equals
delete Cx clear x
clear Cx clear x
s sin
c cos
t tan
l log log base 10
n ln log base e
b lg2 log base 2
r 1/x reciprocal
q square root
w cube root
f +/- change sign
Most buttons offer an alternate function, shown above the button. Hold down the shift or option key to get this. You can also get the alternate function by pressing the Alternate button first.
This button prepares for an alternate function
Sound
The clicking noises can be switched on or off in the preferences dialog.
1.2 NUMBERS
Floating/Fixed/Exponential
Use the Numbers menu or the Numbers button to choose how numbers are displayed.
• Floating is the most general format.
• The fixed format limits the number of digits displayed after the decimal point,
the number of digits can be set by the ‘Fixed Digits’ item on the Numbers menu.
• Both floating and fixed formats switch to exponential if the number gets too big
or too small. Choose exponential to show numbers in exponential format at all
times.
This button changes number format
Entering Exponents
In any mode an exponent can be entered using the [exp] button or the ‘e’ key. For example; 2e2 means ‘2 times ten to the 2’ which is 200. Similarly 2e-3 means 0.002 . The exponents are always integers.
International Formats
The calculator is aware of international number formats. For example, on a British or US Mac you get ‘.’ as a decimal point and on a French or German Mac you get ‘,’. The calculator is aware of the thousands separator, but will reject it at the keyboard, it is only significant when copying or pasting a number.
If you change number formats in the Numbers control panel, SlideRule will change its display as soon as you use it.
Results that are larger than 9.999999e999 are displayed as INF (infinity).
Accuracy
Internally SlideRule uses binary arithmetic. Binary can lead to small rounding errors when it is converted to decimal for display, so SlideRule carefully tracks the precision of the numbers it uses and displays them with only the precision that they actually have. This virtually eliminates the display of rounding errors, but it is as well to be aware that the program is fundamentally binary and not decimal in nature.
1.3 OPERATIONS
Precedence
Operations are not performed from left to right but according to their precedence, for example multiplication and division are performed before addition or subtraction. So expressions are evaluated as they are conventionally written. For example;
1 + 2 * 3 means 1 + ( 2 * 3 ) the result is 7, not 9.
The full order of operator precedence from lowest to highest looks like this:
level operators
1 add, subtract
2 multiply, divide
3 power, root
4 combination, permutation
Brackets and Signs
Brackets change the order of evaluation, they can be nested 9 deep.
1 + 2 * 3 = 7 but ( 1 + 2 ) * 3 = 9
+ and - can be applied monadically like this:
2 + -1 = 1
Permutations and Combinations
The number of permutations of x objects taken from y different objects is yPx = y! / (y - x)! For example, how many unique arrangements are there of any three different letters of the alphabet?
ABC, ABD, ABE, ABF, ... , XYU ,XYV, XYW, XYZ
26 yPx 3 = 15600
The number of combinations of x objects taken from y different objects is yCx = y! / ( (y - x)! * x! ) For example, how many ways can we be dealt a hand of four cards from a deck of fifty two (the order in which they’re dealt is irrelevant)?
52 yCx 4 = 270725
Permutations and combinations use factorials, so y must be less than 499. Also, y must be greater than x, by definition.
1.4 FUNCTIONS
Precedence
Most functions are obvious and work like other calculators, in other words they are NOT used as you would write them down. They have the highest precedence and are evaluated immediately. For example (where √ means the square root button);
7 + 9 √ = means 7 + ‘square root of’ 9
Similarly, to find 10 sin(30˚) enter
30 sin * 10 = or 10 * ( 30 sin ) =
Angles
This button changes angles mode
Trigonometric functions interpret angles as radians or degrees depending on the setting on the Numbers menu, or the angles button. An angle can be converted between radians and degrees at any time using the Convert menu.
Ranges
Some functions have limited ranges of input. If they are exceeded the calculator will beep and if the log window is open it will display an error message.
function range
log(x) log base 10 x must be greater than 0
ln(x) log base e x must be greater than 0
lg2(x) log base 2 x must be greater than 0
arcsin x must be inside -1 ... +1
arccos x must be inside -1 ... +1
arccosec x must be outside -1 ... +1
arcsec x must be outside -1 ... +1
arccosh x must be greater than or equal to 1
arctanh x must be inside -1 ... +1
root(x) x must be positive
sqr root x must be positive
cube root x must be positive
1/x reciprocal x cannot be zero
x! factorial x must be less than 499 *
These functions have limited ranges of output:
arccos(x) result is in [0...pi]
arcsin(x) result is in [-pi/2...pi/2]
arctan(x) result is in [-pi/2...pi/2]
Note
* Factorial is an integer function, but if you ask for the factorial of a real number, the calculator will (1) make it positive and (2) truncate it, so:
2.3! is evaluated as 2!
-6.8! is evaluated as 6!
1.5 PERCENTAGES
The percentage function is a variation on ‘=’, it evaluates x = y*(x/100) first. In practice it’s used like this:
50 + 10 %= 55
50 - 10 %= 45
50 * 10 %= 250
Precedence of operators still applies here:
20 + 50 * 10 %= means 20 + (50 * 5) = 270
This is unusual but possible:
2 ^ 400 %= 256 because 2^8 is 256
2.1 CLEAR
Clear x and Clear All buttons
[Cx] clears x, so if you make a mistake you can correct it;
10 + 20 [Cx] 30 = means 10 + 30 =
[Ca] means clear all, it clears everything except the memory.
If you have pressed the wrong button and only want to clear a single digit you should use Undo…
2.2 UNDO/REDO
Undo undoes the last action performed. It completely reverses the action, restoring the calculator to the state it was in before the action. Once undone, an action can be redone by selecting Redo.
This is the undo/redo button
Undo/Redo can be selected from the keyboard with command Z.
The following actions are undoable:
Digits, Constants
Operators and Functions
Clear
Equals
Memory, Push and Pop
Brackets
Conversions
Paste
The following cannot be undone:
Copy and Cut
Clearing the log
The following are not affected by undo, and do not affect it:
Altering preferences.
Altering angle or number modes.
2.3 MEMORY
There are 10 memories, m and k1 to k9. They are identical, but there are some extra things you can do with them independently. The memories are saved when you quit (into the preferences file).
Store or Recall any memory
The memories are accessed using popup menus under the ST and RC buttons. ST stores x in the memory. RC recalls x from the memory. There are two extra items at the bottom of the RC menu, ‘pi’ and ‘e’, these are constants that can be recalled but not stored.
Accumulating m
There are some extra ‘accumulator’ functions that apply to the m memory:
m+x add x to the memory m
m-x subtract x from the memory m
m*x multiply the memory m by x
m/x divide the memory m by x
Push and Pop k
The k memories can treated as a stack. Pushing and popping a stack is common in programming but may be a strange idea elsewhere.
Push makes the content of each k memory move downwards: k1 moves to k2, k2 moves to k3, and so on, with k9 falling off the bottom. The value of x is copied onto the top at k1. This is what it looks like:
Before and after pushing x
Notice how the content of k9 is lost, and how m is unaffected.
Pop does the reverse. k1 is copied out to x, then all the values move upwards, with k9 at the bottom being filled with 0.
The easiest way to get the hang of it is to experiment; put a value in x, Push and then have a look at the memories. Push a few more values to see the stack moving downwards, then try popping. It is important to remember that every time you push, k9 falls off the bottom and is lost forever. Remember too that memory m is not affected by pushing or popping.
2.4 COPY & PASTE
Cut, Copy and Clear are enabled whenever the displayed number x is not 0. Paste is enabled whenever there is text to paste that is a number.
Clear on the Edit menu is the same as pressing the clear x button [Cx].
Note: International formatting is applied to the clipboard.
3.1 THE LOG
The log window displays two columns. On the right it shows the value of x and on the left it shows the operation or function that produced it. The log is maintained when it is open but inactive when closed. Entries are added to it as operations are actually evaluated. This is often some time after the operation has been entered because the calculator is having to look ahead to the following operation in order to get precedence right.
Opening
The log is opened from the File menu. You can also set it to open automatically whenever you launch the calculator using the check box in the preferences dialog.
Clearing
The log can be cleared by selecting Clear Log from the Edit menu. This cannot be undone so save the log first if you need it.
Saving
Select Save Log from the File menu. The log is saved as a SimpleText document with the two columns separated by spaces. You can choose to have tabs instead of spaces (though SimpleText doesn't understand tabs). Select this option from the preferences dialog.
Closing
Close from the File menu or by clicking the window’s close box. If the log is not empty, and hasn’t been saved, you will be prompted to save it.
Notes
There is a limit of 800 lines in the log. You will get a warning that you need to clear it before you reach this limit (at 790 lines). In practice it is wise to save the log long before it gets this big.
You can use the keyboard to drive the calculator even when the log window is in front.
3.2 CONVERT MENU
Changing the Convert Menu
The Convert menu is organised into submenus which contain common units, and submenus which contain more specialist units. The specialist submenus can be switched on or off using the popup menu on the Preferences dialog.
Select ‘All’ to show all the submenus.
Select ‘Minimum’ to switch off all of the more specialist submenus.
Select any number of items at the bottom of the menu to switch on a selection of
specialist submenus.
A selection may switch on a number of menus. For example, ‘Nautical’ switches on both nautical distance and nautical speed. Also, some menus are switched on by more than one selection. For example, both ‘US’ and ‘Imperial’ switch on US/Imp units of force.
Your selection is remembered and you can switch between ‘All’, ‘Minimum’ and ‘Custom’ at any time without loosing your selection.
Repeating a Conversion
The item at the top of the convert menu remembers your last conversion so that you can repeat it. This item is not affected by the undo.
The Conversions
Most of the conversions are worked out from first principle and are exact (to the limit of displayed digits). For example, the inch is defined internationally to be exactly 25.4mm. Where approximations are used they are to at least 8 significant digits. Approximate conversions are indicated by italics.
Angles
Conversions between radians and degrees work at any time, the Numbers menu
only affects trig functions as they are used.
Distance
Miles are statute miles, equal to 5280 feet.
Nautical miles are international standard nautical miles (1852 metres).
A fathom is an (old) unit of depth, equal to six feet.
Points are set in the preferences dialog. For general typographic work with
applications such as Photoshop or Pagemaker use DTP points (72 per inch exactly).
Didot and traditional points are very rare nowadays. A pica is 12 points.
The astronomical units are all approximations. There is some ambiguity about what
a light year is, as there is no ‘official’ definition. Here, it is the distance travelled by
light in one sidereal year (365.2526 days).
Mass
Units like the ounce are both imperial and US.
A tonne is 1000 kg, or a ‘megagramme’.
UK cwt and tons are also known as ‘long’ (1 cwt = 112 lb).
US cwt and tons are also known as ‘short’ (1 cwt = 100 lb).
Time
...
Area
Hectares are rather trivial to convert but are the standard measure of land,
1 hectare = 100 ares, or 1/100th of a sq km.
Volume
The SI unit is the cubic metre, but the more practical litre is used here,
1 cu metre = 1000 litres, or 1 litre = 1 cu decimetre.
There are two varieties of US measure; dry and liquid. The liquid measures are
the most common.
A barrel of oil is an international unit, but is under ‘US’ because it happens to be
exactly 42 US wet gallons.
Speed
Knots are nautical miles per hour (see distance).
Force
1 kgF is the force exerted by 1 kilogramme under 1 Standard Earth Gravity.
1 Standard Earth Gravity is defined to be 9.80665 [m/s2] exactly.
Pressure
The basic unit is the Pascal which equals 1 newton per sq metre. This is a very
small pressure, kiloPascals (kPa) and even megaPascals (MPa) are more common.
Temperature
Temperatures below absolute zero (0K) are treated as potential errors, though they
are not necessarily wrong because they may be temperature differentials.
Notes
Here are two web sites for more information on units and conversions:
www.ex.ac.uk/cimt/dictunit/dictunit.htm *
www.unc.edu/~rowlett/units/index.html
*This is where most of the data SlideRule uses comes from.
3.3 PREFERENCES
On Startup... Open Log
Make a new log open automatically when the program starts.
Save log with
...either spaces or tabs. Use spaces unless you want to open the log in a word processor to format it. Note: log files saved with tabs are smaller than those saved with spaces.
Convert Menu
Choose what you want to see on the Convert menu.
Points
Affects conversions. Use DTP points if in doubt.
Case, Buttons
...to match your iMac?
Sounds
Loud is slightly less than the general volume level set in the Sound control panel, soft is about half that.
3.4 TECHNICAL NOTES
System requirements
System 7.0 or later.
At least a 68020 processor.
220k of free ram.
SlideRule is written in C and compiled using MPW and SC to produce 68k code. So it should run on just about everything. A pure PowerPC version is for the future.
SlideRule understands the four required AppleEvents, but only responds to ‘Quit’ (issued when the system closes down).
