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Fourier Analyzer and Two Fast-Transform Periph- Erals Adapt to a Wide Range of Applications

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Fourier Analyzer and Two Fast-Transform Periph- Erals Adapt to a Wide Range of Applications JUNE 1972 TT-PACKARD JOURNAL The ‘Powerful Pocketful’: an Electronic Calculator Challenges the Slide Rule This nine-ounce, battery-po wered scientific calcu- lator, small enough to fit in a shirt pocket, has log a rithmic, trigon ome tric, and exponen tia I functions and computes answers to IO significant digits. By Thomas M. Whitney, France Rod& and Chung C. Tung HEN AN ENGINEER OR SCIENTIST transcendental functions (that is, trigonometric, log- W NEEDS A QUICK ANSWER to a problem arithmic, exponential) or even square root. Second, that requires multiplication, division, or transcen- the HP-35 has a full two-hundred-decade range, al- dental functions, he usually reaches for his ever- lowing numbers from 10-” to 9.999999999 X lo+’’ present slide rule. Before long, to be represented in scientific however, that faithful ‘slip stick’ notation. Third, the HP-35 has may find itself retired. There’s five registers for storing con- now an electronic pocket cal- stants and results instead of just culator that produces those an- one or two, and four of these swers more easily, more quickly, registers are arranged to form and much more accurately. an operational stack, a feature Despite its small size, the new found in some computers but HP-35 is a powerful scientific rarely in calculators (see box, calculator. The initial goals set page 5). On page 7 are a few for its design were to build a examples of the complex prob- shirt-pocket-sized scientific cal- lems that can be solved with the culator with four-hour operation HP-35, from rechargeable batteries at a cost any laboratory and many Data Entry individuals could easily justify. The photograph of the calcu- The resulting nine-ounce prod- lator on this page shows how uct surprises even many who are the keys are arranged. Numbers acquainted with what today’s enter the display, which is also large-scale integrated circuits called the X register, from left can achieve. to right exactly as the keys are The HP-35 has basically the pressed. Entry is entirely free- same functions and accuracy of field, that is, digits will be dis- other HP calculators, and it is played exactly as they are en- portable. It is a close cousin to tered, including leading or trail- the many four-function elec- ing zeros. tronic calculators which have The enter-exponent key, EEX, appeared in recent years, ini- is used for entering numbers in tially from Japan and now from scientific notation. For example, many US. manufacturers. However, three features the number 612,000 may be entered as 6.12 EEX 5 or set the HP-35 apart from four-function calculators. 612 EEX 3 or -0612 EEX 7 as well as 612000. The First, none of the four-function calculators has change-sign key, CHS, changes the sign of the man- PRINTED IN U.S.A. 2 @ HEWLETT.PACKAR0 COMPANY, 1972 tissa or, if pressed immediately following EEX, the Answers greater than 1O1O0 (overflow) are dis- sign of the exponent. Mistakes during data entry played as 9.999999999 X loee, and answers smaller can be corrected by use of the clear x key, CLx. A than are returned as zeros. These are the special key is provided for entering T- HP-35's 'closest' answers. Improper operations, such as division by zero or the square root of a Display negative number, cause a blinking zero to appear. The dispIay consists of 15 seven-segment-plus- decimal-point light-emitting-diode (LED) numerals. Single-Operand Function Keys Answers between 1010 and will always be dis- The function keys operate on the number dis- ed as floating-point numbers with the decimal played in the X register, replacing it with the func- point properly located and the exponent field blank. tion of that argument. The trigonometric functions, Outside this range the HP-35 displays the answer in sin, cos, tan, arc sin, arc cos, and arc tan operate in scientific notation with the decimal point to the degrees only. For inverse trigonometric functions right of the first significant digit and the proper the function key is preceded by the arc key. The power of 10 showing at the far right of the display. angle obtained will be the principal value. To make the display more readable, a separate digit The functions log x and In x compute the log- position is provided for the decimal point. arithm of x to base 10 and base e respectively, The The display is always left justified with trailing exponential function ex is also provided. Other sin- zeros suppressed. For instance, the answer to 3 + 4 gle-operand functions are the square root of x, appears as .75 instead of 0.750000000. and the reciprocal of x, llx. - Arithmetic Keys: Two-Operand Functions The arithmetic functions, +, -, X, and +, and the power function xy,operate on the X and Y regis- Cover: Our thanks to Dr. ters, with the answer appearing in X. Numbers are Dennis R. Clark of the Stan- copied from X into Y by use of the ENTER?' key. "I ford University Department Thus to raise 2 to the 7th power the key sequence Iof Pharmacology for allow- is 7, ENTER?, 2, xy and the answer 128 is displayed ing us to photograph him at immediately after xy is pressed. This is a general work with his HP-35 Pocket principle: when a key is pressed, the correspond- Calculator. ing operation is performed immediately. E Although raising x to a power can be accom- plished via the formula xy = ey In and in fact is done this way internally, the single-keystroke op- eration is much more convenient. The power, y, can In this Issue: be any positive or negative integer or fraction, while x must be positive. The 'Powerful Pocketful': an Elec- tronic Calculator Challenges the Slide Registers and Control Keys Rule, by Thomas M. Whitney, France Five registers are available to the user. Four of these, called X, Y, Z, and T, form an operational Rode, and Chung C. Tung. , . , . Page 2 stack. The fifth, S, is for constant storage. (For Algorithms and Accuracy in the HP- clarity, capital letters refer to the registers and 35, by David S. Cochran. page 10 lower-case letters refer to the contents of the registers .) Packaging the Pocket Calculator, by Five keys are used to transfer data between regis- ters. The ENTER? key pushes the stack up, that is, Edward T. Liljenwall.. , . , . page 12 x is copied into Y, y into Z, z into T, and t is lost. New Capabilities in Digital Low- This key is used as a separator between consecu- tive data entries, such as in the power example Frequency Spectrum Analysis, by just described. Roll down, R&, is used to view the Stephan G. Cline and Norman D. contents of X, Y, Z, and T. Four consecutive opera- Marschke. page 14 tions of this key return the registers to the original state with no loss of data. 3 3 in display (X register) \ 3 duplicated into Y register by ENTER+ 4 in display. Product (12) appears in X and stack drops. Automatic ENTER? pushes 12 into Y. Display shows 5. ENTER+ pushes y into 2, x into Y. x is unchanged. 6 in display. Product (30) appears in X and stack drops. Sum (42) appears in X and stack drops. Fig. 1. HP-35 Pocket Calculator has a four-register opera- tional stack (last-in-first-out memory). Here's how the stack works to solve (3 X 4) -I- (5 X 6). Answers appear in display register X, in floating-point or scientific notation, Fig. 2. Instruction panel on back of calculator answers to 10 significant digits. most frequently asked questions. The contents of X and Y can be exchanged using semiconductor/large-scale-integration) circuits: cy;this is useful if the operands have been entered three read-only-memories (ROMs), an arithmetic in the improper order for xy, -, or +. The constant and register circuit (A&R],and a control and timing storage location, S, is accessed via the two keys circuit (C&T).The logic design was done by HP and store, STO, and recall, RCL. the circuits were developed and manufactured The operational stack is automatically pushed up by two outside vendors. Three custom bipolar cir- for data entries following any operation other than cuits are manufactured by HP's Santa Clara Divi- ENTER'?, STO, and CLx. This saves many uses of the sion: a two-phase clock driver, an LED anode ENTER? key. The stack automatically drops down driver/clock generator, and an LED cathode driver. following any two-operand function (+, -, X, +, Fig. 3 is a block diagram of the calculator. xy).For example, to do the problem (3x4) + (5x6) The HP-35 is assembled on two printed circuit the key sequence is: 3, ENTER?, 4, X, 5, ENTER'?, boards (see Fig. 4). The upper board contains the 6, X, + (see Fig. 1).ENTER? is unnecessary be- display and drivers and the keyboard. The lower tween X and 5 because the answer to the first term, and smaller board has all the MOS logic, the clock 12, is automatically transferred to Y when the 5 is driver, and the power supply. entered. Also, no RCis necessary after the second X The calculator is organized on a digit-serial, bit- since the first term, 12, is automatically transferred serial basis. This organization minimizes the num- from Z to Y after the multiplication. ber of connections on each chip and between chips, The clear-all key, CLR, clears all registers includ- thereby saving area and cost and improving reliabil- ing storage.
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