The first step to master RPN usage is to know all of its available resources. Understanding the HP 12c RPN stack operation When in normal, 'run' mode, every operation performed in the HP 12c uses the display contents or places results on it.
The display always shows the contents of the X-register. A register is a predefined place in the calculator memory that is able to hold a formatted number with a ten-digit mantissa and a two-digit exponent of ten. The X-register is one of five registers that form the RPN stack, represented in Figure 1 with all contents cleared to zero.
Figure : Stack registers. Anytime a number is keyed in, the X-register is updated to hold this number. It is then available for use. Example 1 What is the most common keystroke sequence to compute the reciprocal of 7. What registers in the stack are used? Solution The most common keystroke sequence to compute the reciprocal of 7. Figure : Calculating the reciprocal of 7.
In this case, simply typing in the number and pressing the related key are enough to compute the resulting value. There are other functions that use only the X-register contents, like or. These are the 'one-number functions', and when they are pressed, the calculator proceeds with the following operation sequence:.
Take a copy of the X-register contents and put it in L-register last-x ;. If a second number needs to be typed in right after the first one to be used with it, they must be separated with the key. For example, to add 3 and 5 together, you would press. Example 2 What is the most common keystroke sequence to enter 2. Solution The most common keystroke sequence to add 2. Figure : Entering and adding the values of 2.
In fact, all of the stack registers have their contents changed during this single addition. However, the real question is that since both numbers must "exist" in the calculator memory before is pressed, "Where do they exist? Based on these facts, it is seen that not only separates two numbers entered in a keystroke sequence, but it actually provides that a copy of the number currently in the X-register is preserved for immediate use, and this copy is kept in the Y-register.
This way, when is pressed in this example, the number that is in the Y-register is the one that was copied there by. This same operational sequence is observed when , , and are used. These are the 'two-number functions'. When the key is pressed, the copy of the number shown in the display is actually kept in the Y-register. This pushes the previous contents of the Z- and Y-registers up to the T- and Z-registers, respectively.
This is called "stack lifting" because the stack register contents are "lifted" or pushed up. Previous T-register contents are lost after is pressed, since they are "pushed" off the top of the stack. Viewing and reordering stack registers contents Example 3 How would you fill the T, Z, Y and X stack registers with the numbers 44, 33, 22 and 11, respectively? Solution The most common keystroke sequence to fill the stack registers with these numbers is:.
The stack registers contents would be updated according to the diagrams shown below:. Figure : Updating stack register's contents. Under certain circumstances, keeping track of whatever is in each stack register is not practical for daily, quick computations. To help viewing the stack contents, two functions are an aid: X exchanges Y contents and roll-down all stack registers contents.
Keeping previous contents as they are, let us try the following keystroke:. Figure : Viewing the stack register contents by making use of the functions. Using Last-x contents in chain calculations The L-register is automatically updated whenever the X-register contents are changed. In this case, the L-register is loaded with a copy of the last value in X prior to executing the function, hence the reference Last x. Whenever possible, using L-register contents in chain calculations avoids numbers or intermediate results to be typed in again.
The L-register's contents can be retrieved to the X-register anytime it is needed with the sequence. Figure : Equation to find the value of y. Solution The shortest keystroke sequence to compute 'y' is:.
Figure : Computing the value of y. When is pressed after 3. Right after , retrieves L-register contents back to the X-register 2 so ln x can be calculated. These are called built-in variables , because they are permanently built into the calculator. Many menus in this calculator work like the example above. The rules for using variables are:. To store a value, key in the number and press the menu key. To calculate a value, press the menu key without first keying in a.
To verify a stored value, press R recall followed by the menu key. To transfer a value to another menu, do nothing if it is displayed that is, it is in the calculator line. A number in the calculator line remains there when you switch menus. To transfer more than one value from a menu, use storage registers. The e key is used to leave the current menu and go back to the previously displayed menu as shown in the previous example.
This is true for menus you might pick by accident, too: e gets you out. The c key is a powerful feature to clear all the data in the currently displayed menu, giving you a clean slate for new calculations.
To see what value is currently stored in a variable, press R menu label. This chapter has introduced some of the built-in menus the calculator offers. Here you define your own solution in terms of an equation. The Solver then creates a menu to go with your equation, which you can use over and over again, just like the other menus in the calculator. The Solver is covered in chapter 12, but here is an introductory example.
Example:Using the Solver. Suppose you frequently buy carpet and must calculate how much it will cost. The price is quoted to you per square yard. Regardless of how you do the calculation even if you do it longhand , you are using an equation. Punctuation and special characters. To type a letter you need to press two keys; for example, 1 is produced by the keystrokes ,-.
Each letter menu has an. The letter menus with just four letters for example, FGHI include a space character! The necessary keystrokes are shown below. Note that the? After an equation is input, pressing E verifies it and creates a new, customized menu to go with the equation. Each of the variables you typed into the equation now appears as a menu label. You can store and calculate values in this menu the same way you do in other menus.
The DSP menu press D gives you options for formatting numbers. To change the number of displayed decimal places, first press the D key. Then either:. Press , to see a number as precisely as possible at any time 12 digits maximum. Changing the number of displayed decimal places affects what you see, but does not affect the internal representation of numbers. The number inside the calculator always has 12 digits. To temporarily see a number with full precision, press shows you the ALL format for as long as you hold down S.
The r function rounds the number in the calculator line to the number of displayed decimal places. Subsequent calculations use the rounded value.
To exchange the periods and commas used for the decimal point and digit separators in a number:. Press D to access the DSP display menu. Specify the decimal point by pressing F or G. Pressing F sets a period as the decimal point and comma as the digit. For example, 1,, Pressing G sets a comma as the decimal point and period as the digit. To help you correct the situation, the calculator beeps and displays a message.
For more explanations, refer to the list of error messages just before the subject index. Beeping occurs when a wrong key is pressed, when an error occurs, and during alarms for appointments.
Pressing - will simultaneously change and display the current setting for the beeper:. Press e when done. Double Space. Then press e. The calculator stores many different types of information in its memory. Each piece of information requires a certain amount of storage space. The amount of memory available for storing information and working problems is about 30, bytes. Units of memory space are called bytes.
The calculator gives you complete flexibility in how you use that available memory such as for lists of numbers or equations. Use as much of the memory as you want for any task you want. To remedy this situation, you must erase some previously stored information. The calculator also allows you to erase at once all the information stored inside it.
If you prefer RPN to algebraic logic, please read appendix D before you read this chapter. The calculator line is the part of the display where numbers appear and calculations take place. Sometimes this line includes labels for results,. Even in this case you can use the number v for a calculation.
Simple calculating was introduced in chapter 1, page Often longer calculations involve more than one operation. Watch what happens in the display as you key it in:.
For example, suppose you want to calculate:. Finding a Percentage. The one exception is when a plus or minus sign precedes the number. Result is. Example: Calculating Simple Interest. How much money will you owe? Some of the math functions appear on the keyboard; others are in the MATH menu. Math functions act on the last number in the display. The power function, u , raises the preceding number to the power of the following number.
Like the other mathematics functions, these functions operate on only the last number in the display. Natural antilogarithm; calculates e x. You can access the MATH menu when another menu is displayed. Just press m , then perform the calculation. Pressing e returns you to SUM. The MATH result remains in the calculator line. Sometimes you might want to include the result of a previous calculation in a new calculation. There are several ways to reuse numbers. When you start a new operation, the previous result moves out of the display but is still accessible.
Up to four lines of numbers are saved: one in the display and three hidden. These lines make up the history stack.
If you hold down [ or ] , the history stack wraps around on itself. However, you cannot roll the history stack when an incomplete calculation is in the display. All numbers in the history stack are retained when you switch menus. Pressing x exchanges the contents of the bottom two lines of the display. Pressing c clears the history stack.
Be careful if a menu is active, because then c also erases the data associated with that menu. Now, suppose you want to multiply Using the history stack saves you time. This lets you reuse a number without retyping it and also lets you break up a complicated calculation. The s key copies a number from the calculator line into a designated storage area, called a storage register. There are ten storage registers in calculator memory, numbered 0 through 9.
The R key recalls stored numbers back to the calculator line. Press s or R. Key in the register number. The following example uses two storage registers to do two calculations that use some of the same numbers. The s and R keys can also be used with variables. For example,. If there is an expression in the display v such number. You do not need to clear storage registers before using them. By storing a number into a register, you overwrite whatever existed there before.
You can also do arithmetic with the values stored in variables. Scientific notation is useful when working with very large or very small numbers. Scientific notation shows a small number less than 10 times 10 raised to a power. In scientific notation, this is 3. For very small numbers the decimal point is moved to the right and 10 is raised to a negative power.
For example, 0. Use - to make a negative exponent. Type in the numbers 4. The business percentages BUS menu is used to solve four types of problems. Each type of problem has its own menu. The calculator retains the values of the BUS variables until you clear them by pressing c. This shows you the value without recalculating it. Each of the four BUS menus has three variables. You can calculate any one of the three variables if you know the other two.
Pressing J , for example, displays:. Store each value you know by keying in the number and pressing the appropriate menu key. Press the menu key for the value you want to calculate. Welcome to ManualMachine. We have sent a verification link to to complete your registration. Log In Sign Up.
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