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)