Manual / Guide · c. 1968
HP 9100A Training Manual
Hewlett-Packard's training manual for the 9100A.
Manual / Guide · c. 1968
Hewlett-Packard's training manual for the 9100A.
HEWLETT-PACKARD CALCULATOR Model 9100A raining JOHN KEITH C A L C U L A T O R T R A I N I N G M A N U A L _Title Chapter MARKETS KEYBOARD . I •• . .II INSIDE THE CALCULATOR Ill PROGRAMMING IV COMPETITION V ENGINEERING MATHEMATICS VI STATISTICS VII INPUT/OUTPUT . . .VIII CHAPTER I M A R K E T S ROM 1 Reliability The Future Type of Customers Competition Hardware Integrated Circuits Specials OEM Lease I 1 2 5 6 6 7 7 7 Peripherals Accuracy Dynamic Range Training Service Reliability 7 8 8 8 9 9 Illegal Operations Environment . 9 . . 10 " The -hp- Calculator was developed in the Corporate ~hp- Laboratories in conjunction with Loveland Division engineers. The Calculator represents a combination of three basic ideas--a new type of memory for storing constants or subroutines, a new set of algorithms or logic used to define the set of trigometric functions, and a unique electronic organization or logic. This new type of memory is a read-only memory, abbreviated ROM, and is used for storing the keyboard subroutines. The ROM gives us a major competitive advantage because it enables us to store a large number of information bits (32, 000) in a relatively small box and at a much lower cost than could be done using conventional memory systems. A read -only memory constructed from, diodes would require about 10, 000 diodes, be in a separate box about the size of the Calculator, and increase the selling price by $2, 000 - $3, 000. ROM Reliability is also a feature of the -hp- read-only memory. It is an entirely passive device; and once it has been tested at the factory, it should last for the life of the instrument. There are no diodes to fail and no magnetic levels to change. This, of course, is quite a customer benefit. Until our competitors develop a similar type ROM, they will not be able to offer a calculator that will directly compete with the 9100A. Rather, our future competition may offer fewer keys but different key sets and allow their customers to choose the key set which best fits their need. RELIABILITY It is very important for us to capitalize on our existing competitive advantage. Olivetti and other firms which have not yet entered the calculator field are working on more advanced models. Therefore, we probably enjoy a greater competitive advantage at this time than we ever will in the future; and it is very important for us to penetrate those new calculator markets where the -hp- name is not well known. It will never be easier! We, of course, are also working on more advanced models as we feel our objectives are far broader than the 9100A. Briefly stated, our objective is to make and maintain -hp- as a leading supplier of electronic, calculators. Our immediate goal is to expand the peripheral equipment such as printers, plotters and interface boxes for the existing 9100A Calculator. Beyond that, we are working on the design of the calculators for the:1970!s. We would very much like to receive your comments about what you would like to have to sell five years from now. Or rather, what you think the market will need in five years. THE FUTURE TYPE OF CUSTOMERS Seventy percent of your calculator customers will be people who have not previously talked with an -hp- field engineers. Of these, one-half will work for companies -hp- has not called on. Two significant points stand out with regard to our present customers: We will not learn of their needs in the normal test instrument call. In some cases this represents a substantial increase in the amount of time required to visit the additional departments. For example, at Chrysler we call on only 2 of the 28 engineering groups who might buy calculators. The fact that 35% of the customers are from companies or businesses that we do not call on at all, further demonstrates the need for additional coverage. BUYING HABITS As many as 20% of your customers will desire to lease rather than purchase. The civil engineer usually always leases his equipment. You should be familiar with the current -hp- lease plans. The majority of people who now own calculators also have a service contract. This appears to be a strong carry-over from the days of mechanical calculators and could change as they realize that an electronic calculator is more reliable. Most service contracts are sold for 6 - 7% of the cost of the equipment. Generally the customer expects faster service on his calculator than on his test equipment. He may have several voltmeters and so could get by without one,but he probably has only one calculator and depends on it. GENERAL COMMENTS Initially almost all sales will require a demonstration. A good demo takes about 30 minutes followed by 15-20 minutes for customer questions and solving specific customer applications. The degree of research and engineering as measured by both dollars and number of people is a good indicator of how many calculators a firm might buy. The specifier in a company is usually appointed because of his background and experience rather than position. In some cases this may be the computer center, accounting department or even the department manager. Generally one individual is considered the authority on calculators and most people are aware of who he is. COMPUTER CENTER People from the computer center are not good contacts, There are several characteristics which often show up. They may be defensive about any device which will take work from them. Even if they like it, they feel it should be in their area. Usually, they believe that larger computers are the best way to go. Computer center personnel have a vested interest in pushing a trend to buy larger computers rather than smaller. They don't appreciate or understand why we consider our calculator easier to program; after all, everyone knows Fortran! Most computer people feel that the large computer is available to anyone who wants it and since the computer is a fixed expense, it is more economical than a calculator. They don't like the idea of engineers writing inefficient programs, maybe getting one-half way through and then needing help. Of course, the engineers in their labs don't share these feelings. Most engineers complain about long turnaround times and programmers who don't understand their problems. For example, at one account, the director of the computer center told us that they would never buy a calculator for their labs because their 6500 was available to everyone. Yet, less than a month later, IME sold their engineers a calculator. People working with large computers generally consider the calculator a toy. They are not aware of the type of "calculator" problems that actually exist in their engineering labs, and don't have much influence over the labs they serve. The computer people do use calculators for testing algorithms and checking programs. They are potential customers, and many will buy calculators. But, they are not apt to give you good leads to other departments. Most groups are aware of Time Share systems, but believe that they cost only $100/month. This is true of even the companies that have one. In reality most terminals cost $700-$!, 000/month. TIME SHARE We found very few users of either Programmable Calculators or Time Share that made extensive use of fixed program libraries. Generally they had all modified the programs for their applications or in most areas written their own. You will have to be a proficient programmer to take maximum advantage of our library by modifying it for specific customer applications. Customers in the electronics industry seem to be able to make the fullest use of our keyboard subroutines. Of course, this is the area in which our test equipment sales give us the most contact. In addition, our present customers in this area are also better prospective customers for calculators than customers in other fields. In the mechanical field, for example, users of electronic instrumentation are not normally also users of calculators. ELECTRONICS Although most electronics companies have bought service contracts for the presently owned calculators, several doubted their economics. Our electronic customers will probably represent the largest group that does not buy service contracts. CHEMISTRY The analytical chemist will not be a major customer for the 9100A. He usually has simple calculations requiring a very simple calculator or a very large computer with lots of data storage. However, the chemical engineering field is very attractive. Many chemical engineering problems involve statistics, molecular weights, percentage concentration, etc. which are easily solved using the 9100A. TRANSPORTATION EQUIPMENT Companies in the transportation equipment business make extensive use of computer terminals. You should prime yourself on the relative place of desk calculators and time sharing before making a big pitch to automobile or airframe manufacturers. This area may require a sizeable increase in the number of calls required to sell calculators. The mechanical departments have greater potential than the electrical ones. There are a number of small job shops related to the automotive industry that could use calculators. AEROSPACE Aerospace companies consolidate purchasing requirements with the purchasing department playing a large role in evaluation and negotiation. Many companies have an engineering facility group which is very helpful in getting you connected with specific engineering departments. A wide variety of engineering disciplines are represented. It is hard to get to see all the people interested in calculators. One technical group is not very helpful in referring you to the next group. While they have larger computers, perhaps more than any other industry, these computers are not readily accessible to the people with problems. So accessibility and availability are good selling tools for the calculator. CONSULTING ENGINEER Consulting engineers seem to have the greatest need for a formatted output. They typically use a lot of data and need a permanent record. Also, there are special purpose computers available to them with a formatted output. This is probably the easiest group to reach by direct mail because most civil engineers are registered. Consulting engineers can make the most effective use of a prepared program library. Their problems tend to use the same equations over and over; more so than any other area. They will require a lot of hand holding. At least they seem to have problems with the Calculators/Computers they are now using. They expect and seem to get assistance from salesmen now selling them competitive equipment. Since this group is found in smaller offices, the ratio of engineers per calculator is higher; but the opportunity for repeat sales is small. Most of the smaller offices have ties with a computer center either in a university or a larger office. So the fact that we can't solve their larger problems is not necessarily a deterant to a sale. A calculator for office use with the computer center for back-up, may be the best and most economical solution for them. Only one out of three engineers in a consulting engineer's office do the type of work that requires a calculator. Others are involved in proposals, drafting, etc. Contractors who buy calculators are usually larger firms. The smaller firms usually do not do their own engineering. The data processing man is the primary contact with contractors and is more receptive here than in most places. CONTRACTORS University professors do a lot of funded research which requires use of calculators. Since very little equipment is shared; the ratio of calculators to personnel will be higher in this area. There are usually 10-15 departments in each school with a potential of several units each. You will usually deal directly with the end user who is also the specifier of calculators. He commonly has money set aside in a grant for computations. This money can be spent to buy calculators. Student problem solving is another big university application. Several schools have calculators available in a central area for students. UNIVERSITIES The following questions illustrate good answers to the most common questions of a casual nature. Q. What features does your calculator have that your nearest competition lacks ? A. Olivetti--Speed, dynamic range, total addressing capabilities, ability to correct program steps, 175 decades more dynamic range, transcendental functions, simple programming language. Wang — Speed, unlimited qualifiers, mag card, 3 register display, completeness and accuracy of transcendental functions, self contained unit. Small computers— Less expensive, simple man-machine interface. COMPETITION Q. What is the difference between this machine and a computer? A. Traditionally, a computer has not had an input console which contains the English and algebraic keys as is found on the calculator. Input to a computer is not keyed in by the user—it is prepunched on tape or cards. The fact that we have a device that will allow a human in the control loop is the thing that sets a calculator apart from a computer. COMPUTER We feel that it has the physical features normally attributed to a calculator even though its insides are structured like a computer; most people identify it by its physical features and not by its operating characteristics. Q. Compare your calculator to a time share terminal. A, The calculator and time share can stand on their individual merits. We offer portable, silent operation and a sense of "total ownership" that is unattainable on a time share terminal. Most everyday operations are performed much more efficiently on the calculator than on time share—finding the arc tan of a number requires 125 operations and six minutes on time share, the calculator requires 2 operations and milliseconds. We offer an accuracy that is not characteristic of time share. Q. A. List the ways in which your 9100A Calculator will outperform some computers. 1. Portability, size, cost 2. Ease of operation 3. Convenient man/machine interface 4. Accuracy, broad dynamic range 5. It is unnecessary to learn a special computing language. HARDWARE Q. I understand that you have a read-only memory. Would you comment on this. A. The know how in the ROM design and manufacture we consider proprietary. Q. Do you use multilayer boards in the calculator? A. Yes, the conventional "back panel" wiring is a multilayer board. Q. Do you use epoxy transistors? A. We use both metal and epoxy case transistors. Q. Do you manufacture your own? A. Keys Case CRT Multilayer boards INTEGRATED CIRCUITS YES IT IS CAST ELSEWHERE YES YES Q. I understand that you did not elect to use integrated circuits. Why? A. Much of the circuity such as core drivers conduct currents that exceed the upper limits offered by I. C. 's. We use unique circuitry not currently available in I. C. packs. The power requirements of the IC's considerably exceeds that of the discrete circuitry used. The power saving shows up in two ways--a smaller power supply and no fan is required. The package would be considerably larger if IC's were used. Q. Will you redesign the calculator to use in-house 1C technology? A. When 1C technology allows us to obtain a substantial savings -without loss of performance we will consider a redesign. Q. How does the cost divide up in the system? A. We had originally estimated that the core, logic (including ROM), and supporting hardware (case, keyboard, CRT, power supply, etc.) would each share 1/3 of the cost. It turns out that this estimate held true. Q. How many man years went into developing the calculator? A. 700 man months over a 2 1/2 year period. Q. Will you redesign the calculator for special purposes—for instance, the hyperbolic functions may be of limited value to civil engineers, while degree, minute, second-to-decimal conversions would have a great appeal. Can you accomodate such changes? A. We can accomodate such changes. However, they usually represent a major effort and the merits of each must be thoroughly evaluated. SPECIALS Q. Can you make a stripped down version? A. Yes, but the selling cost will not decrease as rapidly as the loss of calculating power. Q. Will you offer the calculator or parts of it as an OEM item to systems house ? A. We would certainly like to discuss such applications in detail. OEM Q. Will you lease the machines or offer lease/buy contracts. A. Yes, there are a number of lease options. LEASE Q. You have no printing mechanism. Isn't that a serious liability? A. No, many applications do not require a printer. However, for those who have a printing requirement, a small silent printer is in development and will be available in 1969. Q. Have you any other peripherals in the offering? A. We are working on an X-Y recorder for plotting functions. We have an input/output connector in the back with allows I/O devices to be connected to the calculator. The PRINT and FORMAT keys are specifically designed for I/O equipment. Q. You have mentioned a printer and an X-Y recorder as peripherals. How much will they cost? A. Prices have not been established. We estimate they will be in the neighborhood of $1, 000 and $2, 500 respectively. PERIPHERALS ACCURACY Q. What is the accuracy of the machine? A. Many of the functions are non linear in nature and require graphs or tables to extract the absolute error. However, in almost every case the calculated f(x) is bounded by the true values for f(x) as x is allowed to vary between plus or minus one count in the tenth significant digit. DYNAMIC RANGE Q. You have a 10 digit display. Some of your competition has 15 or 20 digits. Isn't this a serious liability. A. Most of the competitive calculators do not operate as true floating point machines. (There is some confusion between automatic decimal positioning and floating point.) The dynamic range of a non-floating point machine is limited to the register size. If one considers all problems, it can be shown that the effective register length (the length at which no loss of accuracy occurs) on a non-floating machine is limited to one-half of the register length. Q. Why in the world do you need such a broad dynamic range? A. Although the factors associated to almost all physical phenomena are well within the dynamic range of the calculator, some intermediate products and quotients involve very large numbers which can overflow machines having a narrow dynamic range. TRAINING Q. With all of the complex functions, it must require a considerable training period to master the device. How long does it require to become proficient? A. A prime feature is the ease with which one can1 learn to use the instrument. The basic calculator operations (+, ~, x, ~, etc.) can be mastered in minutes. The same applies to the complex functions, provided the user understands what the function means. If the user has had any experience in computer programming, then an hour is adequate for learning the programming commands. If he has never programmed, then it requires a few hours to learn the concepts of looping, branching, initializing, etc. Q. What types of training manuals will be used? A. The instrument will be supplied with all necessary training and operating supplies: -A comprehensive operating and programming manual -A quick review pull out card attached to the instrument -A comprehensive library containing ready to use programs and program techniques • -Programming cards Q. Will you maintain a programming service? A. We will maintain and distribute programs submitted by users or developed at Hewlett-Packard. A regular publication, THE KEYBOARD, is sent to all users to keep them informed of, new programs and applications. Q, How much will additional program cards and coding sheets cost? A, The following are furnished with the calculator; replacements are available at: Program Library $30. 00 Operating Manual 2. 50 Program Pads 10. 00 (5 pack- 500 sheets) 10 Mag Cards in Flip Top Box 10. 00 Diagnostic Card 2. 50 Dust Cover 5.00 Q. How will the instrument be serviced? A. Each user is given a diagnostic program which automatically tests each operation that can be executed. If this fails to run, the machine will be serviced on a major subassembly replacement basis. If the customer has a service contract, the calculator will be serviced on his premises; if there is no service contract, it will be serviced by returning it to an -hp- service center. SERVICE Q. What do you expect for a mean-time-between-failure? A. We are offering a standard one year warranty, which is considerably longer than the typical 90 day warranty offered by the competition. This is made possible by taking such measures as preageing each transistor for 100 hours and testing it before use in the calculator. Q. Do you offer a service contract after the 1 year warranty? A. Yes. Q. Can you ruin the machine by pressing the keys in a random order? A. No, you may set it to calculating a problem that will take eons for a solution; however, it can always be stopped by pressing the STOP key. RELIABILITY Q. How can I tell if it is making a mistake? A. If any of its active circuity is out of commission, it will almost invariably show up by an odd looking display. The diagnostic program provided with each calculator will exercise and check all keys. It is doubtful that the diagnostic would run and yet have the machine working improperly. Q. Does the calculator have error detecting or error correction circuitry? A. We have a warning light that detects illegal mathematical operations— many calculating errors result from illegal operations. Hence, if the warning light lights during an operation, an error has occurred. If there is any question on reliability, the diagnostic routine should be run. ILLEGAL OPERATIONS •iViVil f M f ENVIRONMENT ft m H Q. What are the environmental conditions under which the calculator will operate? A. It passes the environmental specifications of 0 to 55C, and 95%relative humidity at 40C. Q. Can the calculator be operated from a field battery source? A. It would require an inverter capable of delivering 70 watts. Q. How much abuse can a mag card withstand? A. Certainly it must not be placed in a strong magnetic field; however, 1 have rubbed the card several times over the calculator top without loss of information. Since most cards receive little abuse in their protective case, I can see little concern for losing information by rough handling. The cards are recorded in a NRZ saturated mode which offers excellent noise immunity. 10 CHAPTER II K E Y B O A R D General Description Diagnostic Program 11 11 Accessories Keyboard Data Entry Display Registers Arithmetic Keys Storage Recall Function Keys Vector Keys Range of Arguments Calculator Function Times Calculator Error Function Error Error Summary 12 12 14 15 16 18 18 19 21 23 23 24 24 26 iii The Hewlett-Packard 9100A Calculator is a scientific desk-top calculator. Trigonometric and logarithmic functions are calculated with a single keystroke. The Model 9100A is programmable ; conditional branch instructions provide complete programming capability. In addition, two programs can be recorded on each magnetic card supplied with the 9100A. GENERAL DESCRIPTION The Calculator has two memory systems. One is a unique HewlettPackard Re ad-Only-Memory. It contains the subroutines necessary to execute the keyboard instructions and to calculate the trigonometric and logarithmic functions. The 9100A also contains a magnetic core memory which adds the storage and programming features. There are 19 accessible registers in the magnetic core memory; three are displayed, two are only for data storage. The 14 program registers can accommodate up to 196 program steps or can be used for additional data storage. Three registers are displayed on the cathode ray tube; they are designated X KEYBOARD, Y ACCUMULATOR andZ TEMPORARY. The format of the display can be selected on the keyboard. With Floating Point notation, the contents of the registers are displayed as a ten-digit number and a two-digit exponent, indicating the power of ten multiplier. This display mode allows simultaneous presentation of very large (up to 10") and very small (down to 10"9a) numbers. With Fixed Point notation, the contents of the registers are displayed in decimal format, with the number of digits to the right of the decimal (0 to 9) set by the decimal thumbwheel. A magnetic program card loaded with the Diagnostic Program is shipped inserted in the rear pocket of the Program Library. To enter the program: DIAGNOSTIC PROGRAM PRESS: Be sure magnetic card is fully inserted in the card reader with the printed side of the card towards the user. PRESS: PRESS: 11 Execution of the program (indicated by a flashing display of X = 3, Y = 2. 000000 and Z = 1) ensures that the 9100A is operating correctly. ACCESSORIES The accessories and equipment supplied with each Model 9100A are listed in Table 1. TABLE 1 Accessories/Equipment Supplied PART NO. QUANTITY DESCRIPTION 09100-90001 2 09100-90002 09100-90003 09100-90004 1 1 1 4040 - 0350 5060 - 5919 1 1 8120 - 0078 9320 - 1157 1 1 Operating1 and Programming Manual Program Library Program. Pad Magnetic Program Card Loaded with Diagnostic Program Dust Cover Magnetic Program Card Container with Ten Program Cards Power Cord Pall-out Instruction Card contained in the bottom of the 9100A KEYBOARD OFF [ DEGREES PROGRAM] | ON RADIANS: RUN, Switches ac line power to the Calculator. Application of ac line power lights the register designators at the right of the cathode ray tube. Selects the entry and display units for the trigonometric functions. Selects the mode of operation. RUN: used to perform calculations, address the program coun- PROGRAM: used to enter and verify a program manually. ter, execute a program, and enter the-mag card. Selects the mode of display FLOATING DECIMAL POINT: the display consists of a ten-digit number and a two-digit exponent, indicating the power of ten multiplier. NUMBER 12, 345. 67898 = 1. 234567898 x 10' 12 DISPLAY I.S3H 551 B3B Of FIXED DECIMAL POINT: the number is displayed with the decimal point correctly located. The decimal wheel sets the number of places to the right of the decimal point. The least significant digit is rounded. If the number overflows to the left of the decimal point, the display for the overflowed register reverts to floating decimal point. DECIMAL WHEEL SETTING DISPLAY 1531S.S1B3B _/ 3 3 15.512 Leading Zeros Last Digit Blanked Rounded .Number too large for this setting- automatically shifts to floating decimal point. The error light indicates an illegal operation such as division by 0. V^X sin-lX (|X| > 1), In X {X < 0). An illegal operation during program execution will not stop the program. Clears the X, Y, Z, e and f registers (0.-> X, Y, Z, e andf). Clears the FLAG and clears the ARC and HYPER conditions. Clears the X register (0. -* X). Clears the ARC and HYPER conditions. It is not necessary to press CLEAR X before each entry. Changes the sign of the contents of the X register. Changes the sign of the exponent if ENTER EXP was pressed preceding CHG SIGN. Sets the decimal point. It is not necessary to enter the decimal point when entering integers or when using the ENTER EXP key. G Clears the exponent and causes the next digit entries (0 to 99) and CHG SIGN to affect only the exponent. The exponent digits are entered in a serial manner, with each new digit entry becoming the least significant digit of the exponent. " a. a. 3. DO DO 10 Pressing ENTER EXP after any keyboard operation, except digit entry, will enter 1. 0 for the number in X. To restore control to the mantissa, press the DECIMAL key. 13 DATA ENTRY All keyboard entries are displayed in the X register. SET: ENTER: 126.78 [CLEAR! Q©©Q0© 30©©0© ENTER: -39, 800 = - 3. 98 x 104 (ClEARl X I I CHG { SIGN D0©©© CHG I SIGN J /ENTER \P SET: SET: Decimal wheel to 4 4 1 r" © (LzJ U a a. .0031 Q©©00 14 SET: SET: Decimal wheel to ENTER: 128.0167 00©©Q©0©0 SET: Decimal wheel to 3 SET: Decimal wheel to 8 SET: ENTER: -4xlO~ 1 2 (CLEAR) X I / CM G \ I StG A \l I CHC i / H 1 HJ L±J IHJ IS LU 0. a. -i. oa aa -IS These keys reposition the contents of the display registers as required for succeeding calculations, x, y and z refer to the contents of X, Y, and Z. DISPLAY REGISTERS Duplicates the contents of X to the Y register and shifts the contents of Y to the Z register. Loses the contents of the Z register. Duplicates the contents of Z to the Y register and shifts the contents of the Y register to the X register. Loses the contents of the X register. 15 Shifts the contents of X to the Y register, shifts the contents of Y to the Z register and shifts the contents of Z to the X register. Shifts the contents of Z to the Y register, shifts the contents of Y to the X register and shifts the contnets of X to the Exchanges the contents of the X and Y registers. The contents of Z are unchanged. ARITHMETIC KEYS The arithmetic keys operate on the X and Y registers, entering the result of the calculation in the Y register and leaving the X register unchanged. Adds the contents of the X register to the contents of the Y register. The sum appears in the Y register and the X register is unchanged. + 4 = 12 7 + 4 = 17 Y Y ©m0©0© n. v. 16 Subtracts the contents of the X register from the contents of the Y register. The difference is entered into the Y register and the X register is unchanged. Q 17 - 9 = 8—*-Y 00m©0 00m©©Q©0©0 Multiplies the contents of the X register by the contents of the Y register. The product is entered into the Y register and the X register is unchanged. 0 9 x 7 = 63—^Y a S3. 7. 3 x 5 x 4 + 8 = 7. 5 Dm©©0e a. isa oo Divides the contents of the Y register by the contents of the X register. The quotient is entered into the Y register and the X register is unchanged. 36 4=9 a H. 3.0 17 EXAMPLE ( 3 x 4^~ ) +1 i (6 - 9) . _— ^ Qy . . ^-^ Y (8 x 2) - 6 STEP KEY STEP KEY 1— 3 44 7— 9 9— 8 1— X 10— 5— 6— 6 + 11 — 2— 3- . STORAGE 12- * 2 X The Storage and Recall Keys provide access to the 16 storage registers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e or f. It is not necessary to clear a register before storing; a number; the new number is written over the previously stored number. Stores the contents of X in the register indicated by the following keystroke: 0, 1.-2, 3, 4, 5, 6, 7, 8, 9, a,, b, c, d, e, or f. The contents of the X register are unchanged. Stores the contents of Y in the register indicated by the following keystroke: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, or f. The contents of the Y register are unchanged. RECALL Press a, b, c, d, e or f to recall the contents of the register to the X register. The contents of a, b, c, d, e, or f are unchanged. The yt( i key must be used to recall the contents of the numeric registers. Pressing only 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 will not recall the contents of that register to the X register, but will enter that number in the X register. Recalls the contents of f and e to the X and Y registers. The contents of f and e are unchanged. 18 Exchanges the contents of Y with the contents of the register indicated by the following keystroke: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, or f. This is the only instruction that recalls the contents of a numeric storage register. © Selects the entry and display units for the trigonometric functions. With DEGREES selected, an entry in degrees cannot be converted to radians by selecting RADIANS. Inverse trigonometric functions are calculated for the principal value of the function. FUNCTION KEYS 9 sin'Sc; - 90° to + 90° (- 7T/2 to -f- TT/2 radians) 9 cos ~TC; 0° to 180° (0 to + 7T radians) g tan~ 1 X;-90° to +90° {- 7T/2 to +7T/2 radians) EXAMPLE: sin 135° = +.7071; sin' 1 f .7071 = 45» tan -1000 =+5. 671 tan '* + 5. 671 = 80° Replaces the contents of the X register with the Sine of the contents of X. Replaces the contents of the X register with the Cosine of the contents of X. Replaces the contents of the X register with the Tangent of the contents of X. © Prefix used to calculate the inverse trigonometric or hyperbolic functions. The answer is placed in the X register. 19 [hyper Prefix used to calculate the hyperbolic (sinh, cosh, and tanh) functions. The answer is placed in the X register. EXAMPLE: sinh"1 2 = 1.4436 CORRECT INCORRECT —A /—~\ 1 | arc ] [hyper] (hyper) [ arc j f alnx] sinh. 2 X sin 2 X ERROR LIGHT Replaces the contents of the X register with the logarithm to the base e of the contents of X. Replaces the contents of the X register with e raised to the power defined by the contents of X. Replaces the contents of the X register with the logarithm to the base 10 of the contents of X. Replaces the contents of the X register with the square root of the contents of X. Integer x- Eliminates the decimal part of the contents of the X register. Leaves the integer into the X register. Absolute value of Y. Sets the contents of the Y register positive 20 Enters pi in the X register. Conversion from rectangular to polar coordinates will calculate the angle, 0, in the range: VECTOR KEYS - 180° < 0 < +180° - Trradians < 9 < +TT radians Changes rectangular coordinates consisting of an x component in the X register and a y component in the Y register to polar coordinates. Angle (0) = Tan'1 y/x —*-Y DEGREES Changes polar coordinates consisting of a radius (R) in the X register at an angle (0) in the Y register to rectangular coordinates: y component = R • sin 0 —»-Y x component = R • cos 0—*-X a. -I.QOQQ -t.oaaa ACCUMULATE -K Adds the contents of the X and Y registers to the contents of the f and e registers respectively. The sums are entered in the f and e registers, f and e are cleared with the CLEAR key. f + Xe + Y- © 21 ACCUMULATE -: Subtracts the contents of the X and Y registers from the contents of the f and e registers respectively. The differences are entered in the f and e registers. f —X- e —YRecalls the contents of the f and e registers to the X and Y registers respectively. The contents of f and e are unchanged. X •Y EXAMPLE: Vector Addition (2x + 3y) + (4x + 5y) - (3x - 6y) = 3x + 14 y STEP KEY STEP KEY STEP 1 CLEAR 6— 5 11 2— 3 3— f 7— 8— * 4 4-—- P 9— ACC 4- 5— ACC + 10— 6 12— 13— 14 15— KEY CHG SIGN -t3 ACC — RCL 2 EXAMPLE: Multiplication of complex numbers (j = -1) (3 + J4) (-2 + J3) * - 18 + jl STEP KEY STEP 1— CLEAR 7 STEP 13 — KEY !„* 2— 4 s— 3 1*1 3— t 9— t 15 — RCL 4— 3 10— 2 16— e* TO POLflH 11— CHG SIGN1 In* 12 TO POLAR 5 6— 22 KEY ACC + 17 ACC -f TO RECT" Range of arguments for trigonometric, hyperbolic, logarithmic and exponential functions. RANGE OF ARGUMENTS [XI <. I x l O 10 IXI < 1 sin X, cos X, tan X; sin-1 X; cos'1 X; tan'1 X; sinh X; any X IXI < 230.25 IX! < 230.25 IXI < 230.25 any X IXI > 1 IXK 1 X > 0 X > 0 -227.95 < X < 230.25 cosh X; tanhX; cosh'^X; tanh-1X; InX; logX; ex Range of the 9100A: 1 x 10SS to 1 x 10 -98 ,-99 Even though 1 + 10" 3 may be entered and stored in the calculator, the calculator's lower range is 1 x 10"98. To demonstrate this enter 2 x 10"50and 5 x 10"50 into the X and Y registers and multiply. The Y register will overflow and read zero. Range 1. •i- or 2. MPY 3. DIV 4. SQRT 5. SIN, COS, TAN 6. ARC SIN, ARC COS 7. ARC TAN 8. EXP 9. LN 10. TO RECT 11. TO POLAR 2ms 2-22ms 4-2 7ms 4-2 Oms 240ms (1st quad 330ms (1 circle 140ms 80ms 110ms 50ms 280ms 200ms Average Time CALCULATOR FUNCTION TIMES 12ms 18ms 19ms 280ms 23 CALCULATOR ERROR A solution may be in error for the following reasons: 1. Approximate nature of physical law or principle upon which the solution is based. 2. Truncation error--this is caused by using a closed form expression of an infinite series such as: sinX = X - X 3! X 5! 7! Here we have truncated all powers of X higher thai: X . 3, Round-off errors — causes error in numerical computation due to the use of finite number of significant digits. This is the limiting factor of the 9100A. 4. Mathematical errors in computation. The accuracy of algorithms used in the Calculator is limited to the number of significant digits inputted and used in each calculation. The displayed digits, guard digits, and exponent digits give 12 significant digits and two digits for the exponent. Usually analysts are interested in magnitudes of numbers and the first few significant figures. Thus you can readily see the advantage of our scientific notation (floating point) and carrying 12 significant digits and exponent over competitive fixed point machines. One quickly recognizes magnitudes by looking at the exponent... and the added advantage of a range 10~98 to lO 9 9 . 24 CALCULATION ERROR The calculation error may be briefly explained in the following manner. FUNCTION ERROR The transcendental function error may be explained in the following way. Consider the function shown below The two guard digits are carried along in all calculations extending the accuracy of the Calculator. In fixed display the least significant displayed digit is rounded. In floating point the least significant displayed digit is not rounded. Let AX represent the smallest increment or the limit of the Calculator's resolution to describe the independent variable X. In the Calculator this would be the 12th digit or least significant guard digit. Assume the value of the function in the region A to B is desired. A AX change causes a small change AY, However, if the value of the function in the region B to C is desired, aAX change causes a much larger change AY. The size of the error region, AY, will increase as the average slope of the function in that region increases. If the function rises exponentially, the error will increase quite rapidly as X increases. The function error may be summarized as follows: The calculated estimate, f(x), lies between the exact value of f(X + AX) and the exact value of f(X - AX); stated mathematically; f(X - AX) < f(X) < f(X +AX) AX is one count in the 10th place* This is valid for anyX within the range of the function's argument. Estimates of these upper and lower tolerances may be obtained by using calculated values i(X) at plus one count in the tenth place (+AX) and minus one count in the tenth place (- AX). This may be stated mathematically: f(X -AX) < f(X) < f(X +AX) Graphically the calculated value lies in the regions shown below: I [estimated Itolerance I region tolerance region for f(X) 1 i(X +AX) (calculated value) 'f(X +AX) (exact value) ?(X) (calulated value) f(X -AX) (exact value) i(X -AX) (calculated value) Here is an example: EXAMPLE f (X) = sin X X = 3 6 0 000 003 00 AX = 1° X + A X = 360 000 003 1° X -AX = 360 000 002 9° f(X) = .500 000 000 000 i(X + AX) = . 514 978 232 099 f(X +AX) = . 515 038 074 910** ?(X) = .499 818 609 118 f(X -AX) == .484 809 620 246** T(X -AX) = .484 504 290 825 *It is necessary to specify the tenth rather than the twelvth because of the calculation error. **The exact values are from National Bureau of Standard's "Handbook of Math Tables." 25 Absolute error = [f(X) - f(X)] = .0001814 Relative error = — ERROR SUMMARY civ\ .036% The following is a summary of maximum calculator function errors. They are expressed as absolute errors unless relative error is noted. Absolute error = [ f(X) - f(X)[ r, i *• error = Relative f(X) = exact value f(X) = calculated value Note: a) One visible count is one count in the tenth digit. b) "No. of decades of circles" refers to the number of integer circles divided by 10. I. ADD(-h-) ± 5 x 10-H x 10(larger addend exponent) II. MPY ± 1/2 visible count HI. DIV ± 1/2 visible count IV. SQRT ± 1/12 visi