EC-4044 (650-0808) Equation Operating System Faxback Doc. # 3573
The Equation Operating System enables you to enter numbers along with
operations into the calculator in a simple, straightforward sequence.
This system incorporates the standard priorities of mathematical
operations and also has parentheses for grouping an expression.
Algebraic Without a fixed set of algebraic rules, an expression
Hierarchy such as 16 - 8 + 6 might have several possible answers,
depending on the order in which the operations are
completed. However, the established hierarchy of
operations calls for completing the division first
(8/2) and then completing the subtraction and addition.
Therefore, 16 - 8/2 + 6 = 18.
Purpose of the The calculator supports the rules of the algebraic
Equation hierarchy with its Equation Operating System. The EOS
Operating decides whether an operation is to be completed or
System temporarily delayed based on the priorities shown in
the following table.
Priority Operations
1 (highest) Functions that are entered after their
argument: square, factorial, reciprocal,
conversions, percent.
2 Functions that are entered before their
argument: square root, negation of an
expression, round, absolute value, signum,
integer portion, fractional portion, real
part, imaginary part, logarithms,
hyperbolic functions, trigonometric
functions, not, two's complement, y', x'
3 delta percent, combinations, permutations
4 universal power, universal root
5 multiplication, division
6 addition, subtraction
7 logical and
8 (lowest) logical or, logical xor
When the calculator is executing a calculation, it
starts at the left and progresses to the right. As the
calculator proceeds with an expression, it must decide
whether to delay each operation or to perform it.
-> If the current operation is in the top priority of
the algebraic hierarchy, it is performed.
-> If the current operation is below the top priority,
it is delayed. The operation and its associated
value (if appropriate) are placed in temporary
storage areas.
-> If the current operation is encountered when the
calculator is already delaying operations, it
performs the delayed operations that have equal or
higher priority than the current operation.
When the calculator reaches the end of the expression,
it performs any remaining delayed operations to arrive
at the answer.
When a priority 2 operations is delayed, it has no
associated pending value. When a lower priority
operation is delayed, it has an associated pending
value. The maximum number of pending operations is
always 24. The maximum number of pending values is
ordinarily eight (real or complex). During the
following activities, the maximum is reduced to six
real or three complex.
-> Finding polynomial roots.
-> Solving a system of simultaneous equations.
Although the calculator internally may manage several
pending operations, arrive at many intermediate values,
and ultimately combine the whole expression into one
answer, it all happens in the brief time it takes the
answer to appear.
Parentheses Parentheses enable you to control how the calculator
handles an expression by giving priority to specific
sections of the expression. When the calculator
encounters "(" during execution, it reprioritizes the
operations within the parenthetical expression to
complete them before other parts of the entry, creating
a pending open parenthesis. When the calculator
executes ")", it completes back to the most recent open
parenthesis.
The calculator requires each close parenthesis to match
with an open parenthesis. If the number of consecutive
open parentheses exceeds 16, the calculator stops with
an error condition when you press =ENTER.
Using parentheses for implied multiplication such as
7(3 + 5) is invalid. The calculator requires the times
symbol whenever multiplication is intended.
You can omit any close parentheses at the end of a
calculation. All open parentheses are automatically
closed when you press =/ENTER.
Revising an Expression
By recognizing when an expression contains an error,
you can correct it before proceeding with the
calculation. Instead of handling a mistake by clearing
the entire entry and starting over, you can correct the
mistake by selectively deleting and retyping or
inserting only parts of the entry.
Possible Entry A number that contains any of the following mistakes
Errors causes the calculator to stop with an error condition
at that point in an expression.
-> An extra decimal point
-> Misplaced negation
-> Invalid exponent of scientific notation: a
character other than negation or 0 through 9 is
present
-> more than 13 digits in a number, or an extra, comma
or angle symbol in a complex number pair.
-> Inappropriate characters for a decimal number: a
DMS number with scientific notation, more than 13
digits in a number, or an extra comma or angle
symbol in a complex number pair
-> Inappropriate characters for a nondecimal number:
scientific notation, a decimal point, a DMS number,
a complex number, or more than 10 digits in a
number
Syntax mistakes also cause an error.
-> Mismatched close parenthesis
-> Adjacent symbols that do not belong together
-> Functions that belong before their argument but
occur after their argument
-> Using a variable that is not defined
Ways to Make a If you notice a mistake in your current entry before
Correction you press =ENTER, you can position the cursor at the
mistake and:
-> Type over incorrect symbols.
-> Delete extra symbols with 3rd [DEL].
-> Insert missing symbols with 3rd [INS].
If you realize a mistake is present after you press
=ENTER, you can use the last equation feature
(discussed in the next section) to retrieve the
expression, and then revise it.
Inserting Numbers To insert at a desired position in an entry:
Numbers and
Functions 1. Use <- and -> to position the cursor at the
character that belongs just after the inserted
material.
2. Press 3rd [INS]. The INS indicator appears.
3. Type the inserted material.
4. Decide how to end the insert.
-> To insert the material you just typed, move the
cursor with <- or ->.
-> To insert the material you just typed and delete
the next character, press 3rd [DEL].
-> To insert the material you just typed and execute
the expression, press =ENTER.
To delete an item in the entry:
Deleting 1. Use <- and -> to position the cursor at the first
Numbers and character that is to be deleted.
Functions
2. Press 3rd [DEL]. Numbers and variables are deleted
one character at a time. All the characters of a
function that is represented by a group of
characters (such as log) are deleted together.
Using the last If you need to view or modify the most recently entered
equation Feature equation, you can use the last equation feature to
retrieve the equation as the current entry.
Retrieving the To retrieve the last equation, press 2nd [EQU].
Last Equation Retrieving the last equation replaces the current
entry. The last equation is updated each time you
press =ENTER to execute an equation.
The last equation feature is especially helpful after
an error condition. Execution stops when an error
condition occurs. For most types of errors, the
calculator locates the error for you.
-> To see the last equation with the cursor at the
error, respond to an error condition by pressing
2nd [EQU]. If the cursor is at the end of the
expression, it usually means an overflow occurred.
-> To clear the error without viewing the point at
which execution stopped, respond to an error by
pressing CLEAR, 2nd [EXIT], or 2nd [OFF].
Clearing with these key sequences and then
retrieving the last equation places the cursor at
the start of the equation.
Other than the four responses listed above, the
calculator ignores any keys you press during an error
condition.
Degrees/Minutes/ A degrees/minutes/seconds (DMS) number can have up to
Seconds Numbers three digits for degrees, up to two digits for minutes,
up to two digits for whole seconds, and up to two
digits past the seconds decimal. The maximum DMS value
is 999 degrees 59/59".
The appearance of a DMS number depends on the
circumstances of your viewing it:
-> When entered or revisable, the punctuation is
DEGREES DEGREES DEGREES
-> When shown as a result, the punctuation is
DEGREES ' "
You can use a DMS number in many kinds of calculations
including arithmetic, conversions to radians or grads,
and trigonometric functions. When using a DMS number
in a trigonometric function, set the angle units to
degrees.
When you perform a calculation on DMS numbers and would
like to see a DMS result, you should include the
conversion to DMS. Otherwise, the result is a decimal
value.
Entering a DMS number whose seconds part is 60 or
greater causes the calculator to add 1 to the minutes
value and subtract 60 from the seconds. Entering a DMS
number whose minutes part is 60 or greater causes the
calculator to add 1 to the degrees value and subtract
60 from the minutes. For instance, 1 degree 60'/90"
becomes 2 degrees 1' 30".
Because DMS notation expresses a number in subdivisions
of 60ths and 3600ths, you can use a DMS number for
hours/minutes/seconds calculations.
Angle Conversions Each example includes changing the angle units setting
3rd [DRG>] to the destination units after typing the
conversion. If the setting is not adjusted, the units
indicated along with the result do not match the
calculated value.
Polar/Rectangular Converting rectangular coordinates to polar results in
Conversions coordinates with a positive radius and an angle that
depends on the quadrant of the point.
-> In the positive y quadrants, the angle is positive.
-> In the negative y quadrants, the angle is negative.
This causes a point you may enter at 270 degrees to
have an angle of -90 degrees.
(br/all-12/12/94)