By Richard J. Nelson
rnelson@educalc.com
The HP 48 calculator is the most advanced scientific calculator available for the 90's. It is called a calculator, but it is not like any calculator presently available because of its thousands of features and functions many of which are unique. This Technical Note will provide facts and obversations regarding the HP 48 to help prospective buyers determine that the HP 48 is optimum for them.
Choosing an advanced scientific calculator is not an easy task. As a consumer you tend to ask your dealer: "What does this machine do?" This approach is not the best way of going about the task. To describe the HP 48 in any reasonable detail, either on paper, or verbally, would require a great deal of time. The details are extensive and mind boggling.
First ask yourself: "What are the problems or tasks I need to perform?" If you have difficulty answering this question you may not need a top-of-the-line product. It is not reasonable to compare the HP 48 with any other calculator, or to compare any other calculator with the HP 48. The HP 48 is so beyond every other calculator on the market that it has no peers. It is reasonable to compare HP 48 graphics features to another machine and vice versa. That makes sense. There are several unique groups of features that, if you need one or more more of them, the choice is clear, you need the HP 48.
If you need any one of these features your search is over. The only choice remaining is between an expandable GX or non-expandable G version.
The HP 48 is a classic state-of-the-art product that uses integrated circuit memory. In order to recover development costs a large number of machines must be sold. It is better for HP to sell a more powerful machine than the user may presently require than to make many models of assorted smaller groups of functions. The surveyor may never use the higher math functions, but the large screen and memory of the HP 48GX is just what is needed for survey work.
Who needs the HP 48? Advanced high school students, surveyors, college students, engineers, programmers, and technicians all use the HP 48. When portability is important the HP 48 is the tool of choice. The HP 48 is needed by any user who has advanced math problems to solve and plot or any user who needs a customizable machine.
The HP 48 is the computational heart of Opinion Polling devices you may see at many US Post Offices. It is used for remote data aquisition, as a navigation computer, or production line monitor. The HP 48 is a super powerful, versatile, and adapable machine that has more supporting third party products than any calculator from any manufacturer. Following in the footprints of the famous HP 41, the HP 48 is ten to fifty times more of anything you may specify for the HP 41. The HP 48 is becoming the standard of the handheld world for custom applications.
Do you need an HP 48G or would an HP 24S or TI-82 be better? To help you answer this question you need to have a good idea of what you will do with the machine for the next few years. Do you need a graphing calculator? If the answer is yes your choice is the TI-82, TI-85, HP 48G, or HP 48GX. As mentioned above the TI machines are eliminated if you need the features listed before.
Another important consideration when making the decision as to the best calculator is to ask what model are your peers using? If you are a student and the teacher and most other students are using model 'S', then that model should be at the top of your list. If you are a sales person (real estate, insurance, etc.) and your fellow sales people are using a particular model 'B' then you should strongly consider that model. The reason for this is the built-in training and help resource your fellow users provide.
What we are talking about is the user interface. The logic system of the machine that you use to communicate the problem to the machine. In the "old days" manufacturers used to advertise that you entered your problems into the machine the same way you solved them on paper. The implication was that you would not have to think (and understand?) how you solved the problem. This was, of course, a marketing perspective, and no machine made today, or in the past, works exactly as you write the problem down. All advanced machines today have a similar user interface so the issue is unimportant.
I divide calculator user interfaces into four types. The first is Arithmetic. This interface is found on a typical desktop adding machine. The machine has no intelligence and 1 + 2 x 3 = 9. The second type is Algebraic. This means that the machine recognizes the algeberaic hierarchy rules we learned in Algebra class. Algebra uses parentheses and sometimes machines, usually financial calculators, that allow parentheses are inaccurately called algebraic.
The example problem solved on such machines is: 1 + 2 x 3 = 9. This clearly does not follow algebra rules which state that multiplication must be performed before addition. A machine that uses the Algebraic hierachy solves the problem as: 1 + 2 x 3 = 7. I use this problem to test the logic system of an unknown machine. This seems strange to the average person. Two machines have the keys labeled exactly the same, yet pressing exactly the same key sequence produces two different answers.
RPN avoids this confusion. The first Scientific Pocket Calcuator, the HP 35 introduced in 1972, used RPN. The example problem has to be explicitly expressed as: (1+2)x3 or 1+(2x3) to be perfectly clear. The underlying concept here is vital to the difference between a calculator and a computer. A calculator is designed with a key per function, a computer has no restrictions. So keystroke counting is vital to evaluating the efficiency and ease of use for calculators. RPN avoids confusion by executing all operations when the key is pressed. This idea scares and confuses most people. When you press the + key on an RPN machine an addition is immediately performed. When you press the x key a multiplication is performed. There is never confusion as to what is happening or what the rules are. What is interesting is the fact that Algebraic machines use RPN internally, and that extra memory and program instructions are required to make them work.
The implication of RPN logic is that you must give the machine the data (numbers) first and then perform the operation. The problem: 1 + 2 x 3 is impossible to solve on an RPN machine. It must have the parenthesis around the two numbers and operator to be performed first to insure that either 7 or 9 results. Associated with RPN (historically) is a key marked ENTER. This is the key that saves the first number until the second number is keyed.
The fourth type of user interface is called Command Line. This is typical of the usual computer (DOS) input. You type a series of data and commands on a single line and press ENTER (also labeled ENDLINE or RETURN on older machines). The machine accepts the input, digests it and accepts it if you didn't make a mistake. If you made a mistake it returns the line with an approximate indication of the error.
Which is the best user interface? To answer this question you must first define the class of problems you are required to solve. This is always implied, never explicity defined, and is what causes the most confusion. The HP 48 is Algebraic, RPN, and Command Line entry all in one. This may be difficult to understand, especially for TI, Casio, and Sharp users. RPN uses a stack, a series of storage registers ordered, for visual convenience, like a stack of boxes where numbers are stored. Historically the bottom of the stack is what you see in the display. With multiple line displays it is possible to see many levels of the stack at the same time. The characteristic of the HP 48 that gives it a multiple user interface capability is that it is an object oriented system. An object is what you place on the stack. Each level will accept one and only one object. The HP 48 uses 31 different object types. The most common ones are: Real Numbers, Complex Numbers, Strings (text), Programs, Arrays, Lists, and Algebraics. Each is identified with a special symbol or delimiter. Real numbers have no delimiter, complex numbers use ( , ), etc. Algebraics use ', tic, marks. The example problem above is solved two ways, as an RPN problem, or as an Algebraic problem. Press these keys to solve the problem 1+(2x3)=7:
RPN: Press 2,ENTER,3,*,1,+ 6 Keystrokes Algebraic: Press '1,+,2,*,3,EVAL 7 KeystrokesThe extra keystroke is to define the object as an algebraic. EVAL is evaluate and used as an equal key. The Algebraic expression may be as complex as you wish. Either sequence is entered into the HP 48 command line. The HP 48, like all graphics calculators, uses a command line entry system.
There is one other feature of HP machines that makes them different. They are consistent. No matter what number you enter - within the dynamic range of the machine - and no matter what operation you perform, you will be given a numerically and mathematically correct answer - within the dynamic range of the machine. Other calculators have restrictions on their operations. These restrictions are usually listed in the Owner's manual. It is OK to use small or large numbers for the SIN function, but not too small, or too large. If you do, the machine will either lock up or show an error. This does not happen on HP machines. If it is a twelve digit machine with an exponent of -500 to +500 you may use any number within this range without restrictions. TI, Casio, and Sharp have restrictions. From a mathematical correctness or learning perspective you may safely bet on the HP!.
Not many years ago it was possible to buy a scientific calculator and learn to use it by spending a few hours skimming the Owner's Manual while watching TV. The machine had 200 functions. The HP 48 has 2,300 functions by HP's count. If you spend just one minute on each function a work week of your time is required. As an HP 48 user you will need more than a few weeks to master such a high performance machine. You do not have to master every feature and function, but you must understand the basic philosophy of the machine. I can tell if a user has a fundamental grasp of the HP 48 by listening to three sentences. If the word object is not used I suspect that the most basic and important concept isn't understood.
Is the HP 48 too complex to learn and use? It is more complex than the machines of ten years ago? Too complex for you? If you think it is, you may not need to solve equations, plot functions, solve matrices, or perform complex math operations. Your peers are using the HP 48. You either acquire the skills of using the tools needed to get the job done or you are not competitive. If the HP 48 is your first machine you will have an advantage. Fortunately there is a great deal of information available to help you.
HP's technical support team cannot save you from reading the User's Guide. You must study it yourself. To reach them call (503) 715-2004. Some users complain that they have to pay for the call. Think of this situation as being able to ask a highly trained and experienced expert any question. You cannot find such an expert anywhere else. If you have read the User's Guide, tried the procedure on the machine and you still can't get an answer, it is important to get help. And if it is important you should have no problem justifying the cost of the call. Gone are the days when you call an 800 number and have someone spend the time to teach you how to use the machine on the telephone. Call with a specific question.
There are bulletin boards supporting the HP 48. One is called Nybble's Bytes in the Chicago area at (708) 304-0666. Brian Walsh is the system Operator. There are several others that have HP 48 sections, too many to list here. There are also FTP sites on the Internet that collect and maintain HP 48 software. All of the HP 48 Goodies Disks are on several FTP sites.
The EduCALC catalog has more Accessories, Cables & Interfaces, Peripherals, Software, Programming Aids, Bookware, and Support Services than any other source. If you can't find what you need in the EduCALC catalog it probably is not being offered in the market place. And, it is EduCALC policy to cross over the line dividing pre-sale technical support (How do I select the product I need?) and post-sale technical support (I have turned it on, now what do I do?) further than any other dealer. Remember, the manufacturer is the expert on the product. Of course it is vital to have a specific question, rather than ask "Will you explain to me how the solver works". This is true no matter where you call.
The EduCALC catalog has over 17 pages dedicated to the HP 48. Within these pages are the products of 32 third party suppliers. Included are over 50 plug-in applications cards for the HP 48GX/SX. The Accessories section includes Memory Cards, extra HP manuals to replace those lost or provide a duplicate copy for work, overlays, protective bags for harsh environments outdoors, hard environmental case, assorted soft cases and stands.
The Cables/Interfaces section includes cables, adapters, and file transfer programs from HP and other suppliers. The Peripherals section has the IR printer and Sparcom portable 3-/2" disk drive. The Software section of the EduCALC catalog is the largest, 56% of the total space. Programs are available for students and professionals. The largest professional group of users is surveyors, and programs are available on floppy disks and plug-in cards. Sparcom is the largest supplier of program cards with a very strong student collection, especially for Mathematics, Electrical Engineering, Chemistry, Mechanical Engineering, and Physics. There are two game cards with some games in their second or third generation.
The next HP 48 section in the EduCALC catalog is the Programming Aids section. This includes programs and books. There are three levels of programming on the HP 48. User code or User RPL, System RPL, and Assembly or Machine code. User code is described in HP's User's Guide. System RPL offers greater functionality and speed. There is a fair amount of information published and available from other sources on System RPL. Assembly programming information is in very short supply in the commercial market place. If only one person in 100 programs in User code, only two people of 100 programmers will dabble in System RPL programming, and one in 250 programmers will become proficient in Assembly programming.
The last HP 48 section is Bookware. Books are always needed when you have a question on either the machine or an application. What most people want is an approximately equal mix of both. Yet there are few books that achieve this mix. First it takes an experienced person in a specific application. This person should have the skill and desire to write a book. At the same time this creative, experienced, person should have a special interest in the machine to master it well. If these unique ingredients come together in one person there is one last requirement. The person must take at least a year of his or her life to actually put this knowledge to writing the book. See page nine for an example of one of these "gems".
Third Party "Products" are not limited to commercial products. They may also be services such as Technical Notes and Goodies Disks. These are available because a large number of dedicated HP 48 users give their time and expertise freely to their fellow enthusiasts. I use the term enthusiast instead of user, because the average user expects to have his or her hand held if they are given a program. The Goodies Disks have a long history in the HP community going back to the mid 70's. Joseph Horn spends an average of 400 to 500 hours preparing each Goodies Disk. The average person doesn't spend 500 hours on any one activity in a year, let alone ten such activities. This is a true labor of Love.
There are nearly 200 products in the HP 48 section of the EduCALC catalog. It takes a bit of study and reading of product descriptions to decide which product comes closest to meeting a specific requirement. Some questions, however, are asked again and again. Here are a few specific recommendations to answer the most common questions.
When it comes to using the HP 48 there are five general needs. They are:
The first is connectivity. Any time you trust valuable and important information, either programs or data, to battery maintained memory you are at risk. You need some means of protecting what you have by making a backup copy and storing that copy in a physically safe place. This is usually done by connecting the HP 48 to a computer and copying your important programs and data to a floppy disk. You may buy a cable only or cable with software. EduCALC offers the official HP serial cable, #F1015A, or a third party version, #2609, that saves $2. I favor the #2609 cable because it does not use an adapter that is provided with the universal HP version. The #2609 cable is mechanically more stable. Kermit is built into the HP 48 and getting a copy from a friend is legal. This approach is the lowest cost means to connect the HP 48 to a desktop for backup purposes.
If you want to buy the Serial Interface Kit the HP version is the lowest cost - surprise! The alternate is the nearly identical Sparcom CalcWare Link - #2953 for DOS/Windows or #2954 for Mac's.
The second need is memory expansion. Memory is used to run programs and store data. HP 48 memory is of two types, system memory - 32K in the HP 48G/S/SX, and 128K in the HP 48 GX - and port memory. RAM cards, when plugged into one of the two GX (or SX) ports may be merged or kept independent as port memory. Most beginners merge their memory cards. I do not recommend this because once merged you cannot remove the card. Perhaps one merged card is justified when using the HP 48SX because it only has 32K of system memory. Once the card is more than half full the tedious steps to move objects to port zero so the card may be freed usually ends in something being lost. Look to the future and buy the proper sized memory you need. If the HP 48GX card is larger than 128K it must be used in port two.
The third need is a printer. The ideal printer is the #82240B infrared, IR, printer. This is sometimes called the whistle printer because it looks like a giant whistle. The IR printer has 24 columns. The HP 48 printer functions are designed to print to a 24 column printer. Any serial printer could be connected to the HP 48 serial port to print, but still the output would be 24 columns. A user written program could format the output to as many columns as desired. Because there are so many printers on the market there is very little HP 48 software designed to work with a serial printer. The HP IR printer is great with either text or graphics. Large HP 48 graphics objects are automatically printed in strips that may be taped together for a larger sized printout.
The fourth need is books to help understand the machine, program it and use it. Of the nine programming books in the catalog, the most important are:
The price is high. For the first three, and this is only the minimum, the total is nearly $66. I bought two sets, one for home, the other for work.
There is only one book on graphics and it is very good. Ray Depew, the author, has two versions. HP 48SX Graphics, #2417, $9.95, and Graphics on the HP 48G/GX, #2928, $19.95. This is highly recommended. It includes two chapters not related to Graphics - Equation Writer and Solver. Some users may justify the book for these chapters alone.
There are three good Calculus Books on the HP 48. Calculus on the HP 48G/GX is promised for October 1995 by Grapevine. Based on previous Grapevine books this is expected to be very good. The book just below this level is Algebra and Pre-Calculus on the HP 48G/GX. This is a very good HP 48 algebra book.
Discovering Calculus with the HP 28 and the HP 48 by Smith and Minton, #2647, $17.95. This is our oldest calculus book, several others have come and gone.
An HP 48G Calculus Companion is by Mathews and Eidswick, stock #3227, $25.95. The Calculus subject is slightly better covered here than the others. Overall this book may be the best of the lot. It is very popular amd works equally well with the HP 48G and GX.
My personal view is that scientific calculators are VERY specialized devices. Users can not expect extensive information about them to be available. The HP 48 is exceptional in this regard. There are a few serious dedicated users that communicate technical details. The HP BBS and Internet are the primary sources for advanced information from these users. The manufacturer, HP, is in the tool business not the education business. When I am involved with a problem that requires a question to be answered it is usually late in the evening or on a weekend when I can't call someone for help. I turn to my library. My criteria for book selection is simple - buy every book available for the model I am using. This is not practical for the average HP 48 user because there are over 15 books with a total catalog cost over $300. The above recommendations are provided to illustrate the depth of third party support for the HP 48 and not to be a complete review of every book.
There are more than 50 application cards available for the HP 48. At an average price of $100 each (the range is $30 to $460) a complete software card library would cost over $ 5,000! While the cards may seem expensive they cost as much as some college text books. Having all the equations and programs related to a complete course on a business- sized-plug-in card is a great help.
Joseph Horn gathers HP 48 programs and articles and puts them on high density disks as a public service. EduCALC makes them available for an order processing charge of $4.95 each. At this time (9/95) there are ten Goodies Disks and I am sure that there will be at least two more. Goodies Disks are an unbelievable source for programs at an average cost of pennies per file. Please remember, however;
Goodies Disks are provided "AS IS" without support of any kind. |
After Joseph spends hundreds of hours preparing the disks without compensation of any kind, he cannot be expected to provide technical support. The Goodies Disks contain some of the most powerful and advanced software you will ever see for the HP 48. The primary criteria for selection is math programs, hacker tools and techniques, video games, and specific recommended applications. Most HP 48 bugs (and fixes) are documented on the Goodies disks. Users must look at the Goodies Disks as new territory to explore and study. If you are calling around and asking a lot of questions because you haven't taken the time examine the complete disk, you just might be given the advice, "The best solution to your problem is to delete the file in question from your disk".
At present there are ten Goodies disks. GD10 is a Hackers Disk with a special option. GD10A is a 5-1/4" disk, GD10B is a 3-1/2" disk, and GD10C is a ROM card of selected Hackers Tools. Most Hackers Tools MUST be run in a non-banked switched port (Port 0 or Port 1). The GD10C cost is the same as an OTP card in the quantity of 2 to 8, presently $39.95. A 41 page User's Manual is included.
Clearly the Goodies Disks are not for everyone. The first time user should order the most recent disk because it has a cumulative index of all previous disks. An included search program allows you to find what you need.
The fifth need is software. HP 48 programs are available on application program cards and floppy disks. The following cards are especially outstanding and represent the best in their category. Sparcoms Math*Pro, #2960, $99.95. This is a greatly improved Math Applications card #2324, $89.95. With nearly three times the equations and faster, this is an excellent pre-calculus card. Sparcoms Calculus Pac, #2691, $89.95 is the next math level and it is very good.
The top-of-the-line math card is John Holland's Engineering Mathematics Library card, #2694, $139.95. This is a very advanced card with half of the 715 functions probably not recognized by the average four year college graduate in Engineering Mathematics. The "Owner's Manual" is a formal hard bound text book. This card is not for the beginner. You should be very familar with the HP 48 to use this card effectively. The Bringslid math cards could use more examples in their rather sparse owner's manuals. The Bringslid products are written in Norway for Norwegian students. They are good, but a little different. The user interface is not well explained and requires a little study.
Sparcoms most popular card is their General Chemistry Applications card, #2294, $89.95. This includes the Periodic Table omitted by HP when they included their Solve Equation Library card in the G series machines.
One of the most exciting features of the HP 48 is its ability to perform limited symbolic math, especially algebra. This means that you may expand and simplify algebraic expressions and perform operations on algebraic expressions and equations. The symbolic math capability also extends to differentiation and integration but not to matrices.
Students want to solve their Algebra problems (especially factoring and simplifying) a specific way. A student wants intermediate answers and answers in standard form. This expectation is unfulfilled with built-in HP 48 functions. There is a solution, howwever. There is a unique quality of HP machines that inspires their users to explore them and document the machine itself. The resulting community knowledge of the internal workings of the machine results in advanced software. Two programs, ALG48 and ALGB provide an algebra capability that every student would "kill" for. And these programs are free, just dial up your favorite BBS and get your very own copy.
An example of comparing native HP 48 symbolic capability with ALG48 is printed in the box on the next page. An HP 48 program was written to produce the outputs. A simple expansion problem is "solved" using the 48 EXPAN command and comparing it with the ALG48 RSIM library command.
EXPAN is repeatedly applied to the expression (x-y)^5 ten times - until it doesn't change. One of the problems with using the RULES of HP 48 algebraic commands is the "mess" that often results. ALG48 RSIM produces a consistent answer in standard form as illustrated by the ten examples. The HP 48 EXPAN command is often faster than RSIM, both use faster System RPL and Assembly code, but RSIM puts order to the output. If you always finish an algebraic operation with RSIM the output will look "right".
ALG48 is a "living" program, it keeps getting better and better as users world wide provide feedback to the two authors Claude-Nicolas Fiechter and Mika Heiskanen. In the examples the expression (x-y)^5 is expanded one to ten times using the HP 48 EXPAN command in the hopes it will give a meaningful answer. It produces an increasingly messy expression. After each expansion ALG48 RSIM and FCTR is run on the EXPAN results to show the versility of these two commands. FCTR is the "inverse" of RSIM. Execution times are calculated for each of these three operations in each of the ten examples.
In the worst case (x-y)^5 is expanded ten times. The nine lines of x's and y's are hardly recognizable as related to the input expression. The HP 48 EXPAN command took 11 seconds to produce the "mess" while RSIM made it right in 5.3 seconds. Factoring the "mess" created by ten EXPAN's takes 11.3 seconds. FCTR usually takes longer than RSIM. Here is how the ALG48 documentation (version 2.1) describes itself.
"ALG48 provides a number of commands to do advanced algebraic (symbolic) calculations on the HP 48, including polynomials and rational functions simplification and factorization, and symbolic matrices manipulation"
"ALG48 differs from other mathematical packages for the HP48 in two important aspects:
The second improvement many users want for the HP 48 is more speed. Many operations seem to take a long time (a few seconds is a long time in many situations) and users want to know how to speed up the machine. I get calls all the time asking for the ROM that makes the 48 faster. There is no such ROM. There are good operating habits that keeps the speed from decreasing. Keeping the stack clear of "garbage" helps. Large numbers of key assignments will make the machine very sluggish in USER mode. A hackers trick is to convert each key-assigned-object to a code object - see CODE program on #GD10C. This speeds the machine up if you have large numbers of key assignements.
Do You Need An HP 48? The answer is yes if you need any of the unique HP 48 features listed on the top of page two. You will only find these features on the HP 48. Can you get by with the non-expandable HP 48G? Yes, if you are sure that no future growth is anticipated. Most users who need an advanced Graphing Programmable Scientific Expandable Calculator will grow as they learn the machine. The two card slots of the HP 48GX are a hedge against obsolescence, which is rapid with the electronics technology used in todays products. EduCALC does NOT have an HP 48G trade in program.
The HP 48 continues the long history of exciting advanced machines from Hewlett-Packard - the HP 65, 67, and 41. Users are so enthralled with high end HP machines that they are dissected, and analyzed. This results in high performance software. Some of these are accomplishments well beyond those envisioned by the designers. The symbolic math Library ALG48 described above is only one example. Many HP 48 support products are produced by individuals or small companies who are inspired by the machine. Some products are done as a "second business" not requiring a profit for survival.
Now that HP has reduced the price on both versions of the HP 48 G series price is not a restriction - assuming, of course you need this class of machine.
RN REV B 960925