Historical Document · 1968
Wang's logarithm method, filed 22 September 1964 and granted 17 September 1968: stored logs of 10, 2, 0.9, 1.01, 0.999 and 1.0001, factors of the form 1 +/- 10^-n applied by shift and add, with worked tables for ln 2.10 and the antilog of 4.23845.
Sept. 17, 1968 AN WANG 3,402,285 CAL CULATING APPARATUS Filed Sept. 22, 1964 "-e 47-O (5)4(3)(5)(6) DEcir?t point A Al-O (O-46(2)(3)(9) a -62) GO-4 a-09 O-6 afa (, /. 727 4 -2 PTTTTT a 44 '64 w W A2 W1 27 - NPUf 4. M Nitt 3 LHAA Year" i. D /6 in SEF to 94 t A. /2 2. A 22 /04 24? 42 < /4 (DC) 14 (5% ()h CD44 O O O"C) 47 '76 47 '6% United States Patent Office Patented Sept.3,402,285 17, 1968 1. 2 stants. The selected constants are preferably related to 3,402,285 the radix of the natural number in the form 1-1/RA, CALCULATING APPARATUS R is the radix and A is an integer. Use of such An Wang, Lincoln, Mass, assignor to Wang Laboratories, where constants enables each multiplication operation to be Tewksbury, Mass., a corporation of Massachusetts 5 performed by a shift and single addition step. Means are Filed Sept. 22, 1964, Ser. No. 398,254 24 Claims. (CI. 235-160) ABSTRACT OF THE DISCLOSURE A calculator includes an input register and a log reg ister, each having adder circuitry coupled to it. Ten manual control buttons are provided for entering numer ical values 0 through 9 into the input register. The cal culator also includes a store of logarithmic values of the following constants: 10, 2, 0.9, 1.01, 0.999 and 1.0001 and a sequencer. Operation of the sequencer is initiated by a single manual log control button. The sequencer then automatically controls, in a series of steps, the selection of constants and the operation of the input register and log register adders to generate in the log register a logarithmic value of the quantity stored in the input register. museum provided to sense the size of the natural number as it is varied in the multiplication operation, and in response to each sensing of a predetermined numerical condition, the value of the constant is changed. With the present day O logic technology, the invention enables the generation of the logarithm from a base number in less than fifty The generation of antilogarithms is accomplished through modified control of the same circuitry. Logarith 5 mic values are stored in digital form available for imme diate and direct manipulation or for transfer to auxiliary temporary storage, as desired, in accord with the nature of the mathematical operations being performed. Appa ratus incorporating the invention enables performance of addition, subtraction, multiplication, division, expo nential manipulations (involving the use of logarithms of milliseconds. logarithms (log log) for example) may take the form of a compact desk type of calculator. Other objects, features and advantages of the invention This invention relates to calculating apparatus and more will be seen as the following description of a preferred particularly to calculating apparatus that include the capa 25 embodiment thereof progresses, in conjunction with the bility of manipulating data on a logarithmic basis. drawing, in which: Current commercial and scientific procedures demand FIG. 1 is a diagrammatic view of the control panel that increasingly large masses of data be processed, and of a calculator constructed in accordance with the inven such processing frequently involves or is an integral part 30 tion; and of mathematical analyses. Such mathematical analyses FIG. 2 is a logic block diagram of apparatus employed encompass, in addition to addition and Subtraction, multi plication, division and even more complex manipulations, e.g. those employing exponential values. While digital com puters of conventional logic organization can perform such manipulations, the techniques that are employed frequently involve complex, circuitous and time-consum in that calculator. There is shown in FIG. 1 a diagrammatic indication of the control panel 10 of a desk type calculator. Display is provided on the face of the control panel for three registers-an accumulator register 12, an input register 14 and a log register 16. These displays may be of the ing operations to obtain the desired results or solutions electronic type, employing a cathode ray tube or Nixie to specific problems. tubes, for example. The logarithm is a well known tool for simplifying 40 Positioned on the control panel adjacent the register such operations. However, the techniques for utilizing displays are a series of controls. A first group of controls logarithms in calculations have, in general, employed for entering numerical values in decimal form into input either mechanical devices (analog computers) in the register 14 is located in the center area 30, the ten control nature of slide rules or similar but more sophisticated buttons being designated 30-1-30-0, as indicated. In devices, or stored tables of logarithmic values (e.g. a pre addition there is provided a series of computation con set relay matrix) in a digital computer type of device. 45 trols-addition control 32, subtraction control 34, multi The analog devices, in addition to the speed and accuracy plication control 36, division control 38, square control limitations inherent in such devices, have characteristics 40, reciprocal of the square control 42, square root con of inflexibility relative to available processing techniques, trol 44, and reciprocal of the square root control 46. while the stored table technique requires tremendous stor 50 A third group of controls enable the transfer of data age capacity which result in large and expensive computer between registers 12, 14, and 16. Depression of control equipments. button 50 will convert the quantity stored in the word Accordingly, it is an object of this invention to provide register 14 into its logarithmic form and store it in reg a novel and improved calculating apparatus which enables ister 16 (actually in the same manner as the multiplica more expeditious performance of mathematical manipu 55 tion control 36); depression of control button 52 will lations. convert the logarithm value stored in log register 16 into Another object of the invention is to provide a compact its natural (base) form and store it in the accumulator calculating device capable of performing complex mathe register 12. Button 54 controls the transfer of the con matical manipulations. tents of log register 16 to word register 14 directly (that Still another object of the invention is to provide a 60 is, without any logarithmic conversion), and button 56 novel and improved computer capable of performing com controls the transfer of the contents of accumulator reg putations on a logarithmic basis. ister 12 to the log register 16 without a logarithmic Another object of the invention is to provide novel and conversion. improved apparatus for generating logarithms. In addition, there is provided a decimal point control Still another object of the invention is to provide novel 65 60 which is used to indicate the position of a decimal and improved apparatus for converting logarithmic point in the data being entered into the word register and numbers into their natural (base) number form. a series of controls enabling transfer between the log Apparatus constructed in accordance with the inven register 16 and auxiliary storage registers, buttons 62 tion includes means for generating logarithmic values by controlling transfer to auxiliary registers from the log successively multiplying a value in natural number form 70 register and buttons 64 controlling transfer from the by selected constants and correspondingly modifying a corresponding auxiliary registers to the log register. logarithmic value by the logarithms of the selected con The calculator as shown in logical block form in 3,402,285 3. FIG. 2 includes the three shift registers 12, 14, and 16, 4. It will be noted that the last four constants are in the form 1-1/RA where R is 10 and A is successively the each of which has a corresponding number of stages 70. integers 1, 2, 3, and 4. With respect to logarithm genera Coupled to each shift register is a decimal adder circuit 72 which may be of conventional design, and control 74 tion operations, the operation of the programmer 90, a coupled to the decimal adder 72 which determines whether 5 sequencer or counter, is initiated by the manual log con trol button 50 via OR circuit 104 and the sequencer is an addition or subtraction operation is to be performed stepped automatically under the control of the contents by the adder circuit 72. As the calculator operates on of input register 14 to control the sequence of steps in numbers in the decimal radix, each stage 70 includes four flip-flops together with controls for storing signals the generation of a logarithm. Each logarithm read out in an appropriate binary coded decimal form. In an () of memory 92, as controlled by the output of the pro grammer 90 on line 98, is applied over a line in cable addition (or subtraction, depending on the condition of 100 through converter 94 to the adder 72 to modify the control. 74) operation of the accumulator register 70, an input train of BCD signals on line 76 is serially added contents of register 16 in an addition or subtraction oper ation, also as controlled by programmer 90. Programmer to the contents of the shift register as transferred from 90 also causes the contents of register 14 to be modified the least significant stage 70-L, and each resulting Sum digit is placed in the most significant stage 70-M and then in multiplication operations by the constants. Flip-flop shifted with the other signals stored in the register. Upon 102 and OR circuit 104 control the stepping of pro completion of the shift of the word through the register, grammer 90, and the flip-flop is actuated in response to a change in the value of the quantity stored in either the result (sum or difference) is stored therein. Transfers from the register to other registers are over line 78 20 register 14 or register 16. These modification operations, while coordinated, may be performed in various manners, under control of gating units 68. It will be obvious that a variety of adder circuitries, both serial type and parallel for example, at substantially the same time or one modi type, may be employed in the practice of the invention, fication operation may be completed and the other then commenced and performed as a function of the first. and the transfer control may likewise take a number of forms. Data is entered into the word register 14 from keyboard converter control 30 or from a separate input device, 25 After a number has been loaded into word register 14, the button for the selected operation is depressed. ASSume a direct logarithmic conversion is to be made and log register 16 is clear. Button 50 is depressed and a pulse such as a tape (which input data may include programmed is applied through OR circuit 104 to step programmer control instructions) through addresser 80 which channels the entry of data over lines 82 into the respective stages 30 90 which generates control signals for the first step of the logarithmic conversion operation. That first step is to 70 of register 14. Addresser 80 includes a counter and gate logic which indicates the next ordinal position in adjust the decimal place, as necessary for the operation, register 14 that is available for data entry. The first so that the value stored in word register 14 is between digit (converted into appropriate binary coded form by 0.1 and 1.0. This is done in a shifting operation (utilizing conventional means in control 30) is thus entered in the delay circuit 96, for example). An effective shift of one most significant stage, the next digit in the immediately order to the left multiplies the quantity by a factor of ten and a similar shift to the right divides the quantity adjacent stage, etc., under the control of addresser 80. by ten. In this embodiment concurrent with each shift, a Decimal point button 60 controls the stepping of decimal point storage register 84, a counter which stores an corresponding subtraction (or addition) of the log to the indication of the decimal point position. That register is 40 selected base of ten is made to the contents of the log register 16. stepped upon entry of each digit by a signal on line 86 from control 30 until button 60 is depressed, which The modification operations are continued with each modification changing the contents of decimal point regis operation provides a signal over line 88 that terminates the stepping operation. The contents of register 84 then ter 84 by ONE (line 106 from sensor 108) until register 84 goes to ZERO at which time an output is produced on indicate the decimal places in the number entered into and displayed from word register 14. (The decimal point line 110. That output is applied over cable 112 to set position may also be displayed if desired.) If the number flip-flop 102 and the transition is passed through OR cir cuit 104 to step programmer 90. Alternatively, the modifi to be entered in register 14 is less than one, the decimal point button 60 is depressed before any entries are made cation operations may continue until most significant stage 120 of register 14 contains ZERO and the next stage 122 through control 30, and then the digits of the number, contains a value other than ZERO. When that condition is including all the zeros, are entered Serially. The calculator also includes a programmer 90 which detected, a signal over line 124 and cable 112 will set flip flop 102 and step the programmer 90 to Step Two. The is responsive to the control buttons 32, 34, 36, 38, 40, next output signal from programmer 90 over line 126 42, 44, and 46; a logarithmic constant store 92; and a logarithm converter circuit 94. In response to the depres 5 5 will clear flip-flop 102 in preparation for the next pro grammer stepping pulse. sion of a computation control button, the programmer 90 determines the nature of the operation to be performed When the contents of register 14 have been properly ad justed, that value is then multiplied by TWO. This op and operates the add subtract control circuitries 74 asso eration (Programmer Step Two) is accomplished by ad ciated with registers 14 and 16; a delay control 96 associated with register 14 and optionally the converter 60 ding the contents of register 14 to itself. As soon as the most significant stage 120 of the word register 14 contains circuit 94 to modify the contents of both registers 14 a value other than ZERO, an output is produced on line and 16. 124 which steps programmer 90 to Step Three. Concur Memory 92 stores the logarithmic values of pre rently with each multiplication of the contents of register established constants which are related to the radix of 14, the logarithmic value of two is subtracted from the the number system to be employed in the calculator, in contents of log register 16. this case the decimal system. Those logarithms may be The programmer in Step Three mode effects a multipli to any desired base, for example the base e, and in this cation of the contents of the word register times the con calculator are as follows: stant 0.9 with corresponding addition of the logarithm of Constant: Log 0.9 to the contents of log register 16. This multiplication 10 ------------------------------ 2.302.585093 operation (x0.9) can be performed in a single adder op 2 ------------------------------- 693.47 181 eration involving the subtraction of one-tenth of the quan 9 ------------------------------ 105360516 tity stored in the word register from that quantity. The 1.01 ---------------------------- .009950331 one-tenth value is obtained by a shift of one order as controlled by delay 96 and inserting the delayed quantity 999 ---------------------------- .001.000500 1.0001 -------------------------- 00009.9995 through adder 72 in a subtraction operation. When the 3,402,285 5 contents of stage 120 change to ZERO, the output on line 124 steps programmer 90 to Step Four. The modification operation is continued in similar man Programmer Step ner, multiplying by the constants 1.01 (1--Ao?); 0.999 (1-540°) etc. until the contents of register 14 equal ONE 5 to a preestablished accuracy. (When the constant 0.99999 (Step Seven) is reached, the difference between the con tent of the word register 14 and ONE may be added di rectly to the contents of the log register 16.) At that time the quantity stored in log register 16 is the logarithm of O the value originally stored in word register 14. An example of this operation is indicated in the follow ing table in which the steps to generate the log to the base e of the number 2.10 by this apparatus are set forth. 5 Programmer Step Constant 2 2 2 3 3 3 3 3 4. 5 5 6 7 7 7 7 X2 X2 X2 X.9 X.9 X.9 X.9 X.9 X, 0. X .999 X.999 X1.0001 X.99999 X .99999 X .99999 X.99999 X. i Register 14 2.100000 210000 420000 840000 1, 680000 1.52000 3608 22472 . . 102248 .992024 1.001944 1,000943 .99994.3 000042 000032 1000022 100002 1.000002 Register 16 0.00000 2.30259 160944 91629 .22314 32850 43389 53922 ... 64458 74994 .73999 74099 74.99 .7489 7490 74.191 ,7492 74193 1. 2 2 2 2 3. 3 3. 3 3 3. 4. 4 4. 4 4. Constant 0.1 0, 0.9 0,9 0.9 0.9 1.01 10. 0. 1.01 1.01 1.0 0.999 0.999 0.999 0.999 0.999 Register 14 Register 16 1000000 1.000000 000000 4.23845 1.93586 99.63327 900 81 729 656 66266 669.287 675970 .682.738 689565 696.460 695764 695069 , 69.4374 693680 692987 99,73863 99.84.399 99.94935 00.05471 00.04476 00,0348 00.02486 00, 01491 00.00496 99.995O1 99.99601 99.99701 99.99801 99.99901 000000 Decimal Point 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 The antilogarithm is 69.2987. It will be observed that the logarithm of a logarithm may be taken by transferring the contents of register 16 20 to register 14 and then performing a log generation trans fer. The process may be reversed in similar manner to generate antilogs. Natural numbers may be added (or subtracted) in conventional manner through the use of the accumulator register 12. (A time shared adder may 25 be used in place of the three adders if desired.) As in dicated above, in addition to manual input control, pro grammed control from a tape for example may be em ployed to control the calculator in the performance of a complex series of manipualtions. Also raw data may be 30 entered into the calculator from a tape or other record for performance of a series of calculations. While the apparatus has been described in conjunction with the decimal radix, it will be obvious that the inven tion is not limited thereto and provides calculating mech 35 anisms which may operate in any desired radix to per form multiplication, division, and other complex mathe matical calculations through the use of logarithms which The next quantity is then loaded into word register 14 also may be to any desired base. The storage capacity re via input control 30. If multiplication is to be performed, quired for the calculator is small, as only selected log the logarithm of this quantity is generated in the same manner as described above and thus that quantity is added 40 arithmic values (seven in the disclosed embodiment) need be stored. The simplicity of the logic enables the calculator to the log value already stored in the log register 16, to be a compact device suitable for desk type use and whereas if division is to be performed, the steps of gen enables accurate calculations to be performed with facility erating the logarithm of the second number are performed in complement sequence so that that quantity is effectively heretofore impossible except with much larger and more subtracted from the value stored in the log register 16. 45 complex devices. The logic operated through programmer If a number is to be squared, control circuit 94 is oper 90 in response to instructions from the input buttons con ated in response to the corresponding control button to trols, in addition to logarithmic conversions, addition and subtraction operations (performed by transfers between double all the log values transferred from storage 92. Similarly, a square root may be directly taken by halving input register 14 and accumulator register 12 via transfer each of the log values that is transferred from memory 50 control units 68), as well as similar transfer to auxiliary 92 to register 16. storage registers (not shown) in response to input buttons 62. Thus, the calculator is equipped to rapidly perform When it is desired to obtain the natural number from a logarithm (antilog), the transfer steps are reversed with a wide variety of operations in response to manual input the word register 14 being set initially to the value 1.0. of data and under manual program control. If desired, a The log register 16 contains the logarithm of the value sequence of operations, specified by an input tape which to be set into word register 12. First the exponent (first controls programmer 90, can be performed on the cal digit) of the log is sensed and adjusted to a value less culator. Thus, the calculator also has the capacity to per than ZERO, effecting a multiplication (or division) by an form complex mathematical computations. It will be ob integral multiple of ten. An output on line 130 from the vious that the base of the logarithms stored in memory most significant stage of register 16 steps programmer 90. 60 92 may be any suitable value and that computations may The location of the decimal point is stored. be performed in radixes other than decimal. The contents of the word register 14 are then multiplied While a preferred embodiment of the invention has by 0.9 and the corresponding log value is added to the been shown and described, various modifications thereof contents of register 16 until the contents of the log regis be apparent to those having ordinary skill in the art, ter exceed ZERO. At that time the programmer 90 is 65 will and therefore it is not intended that the invention be lim stepped and cause the contents of the word register to be ited to the described embodiment or to details thereof and multiplied by the quantity 1.01 and the log of that con departures may be made therefrom within the spirit and stant to be subtracted from the contents of log register 16. scope of the invention as defined in the claims. This manipulation is repeated until the contents of log What is claimed is: register are less than ZERO, at which time programmer 70 1. Apparatus for performing a logarithmic conversion 90 is stepped. When register 16 contains ZEROS in all the comprising storage means for storing logarithmic values significant stages, word register 14 stores the value whose of a selected group of constants in the form 1-1/RA log was initially stored in register 16. where R is the radix and A is an integer, The following is a step-by-step example of the conver means for modifying a first number of radix R to pro sion of the number 4.23845 to its antilog. vide a product of said first number and one of said 3,402,285 8 7 said first number and a shifted value thereof to pro constants by adding said first number and a shifted vide a product of said first number and one of said value, programmer means for controlling said modifying constants, Second modifying means coupled to the other storage means to act on the results of each modified number register for modifying a logarithmic value by ac produced by said modifying means including means 5 cumulating signals transferred from said storage responsive to the modified numbers for causing said means representative of the value of the logarithm programmer means to change the value of the con of each constant utilized by said first modifying stant used by said modifying means, and means, and means responsive to said programmer means for ac cumulating a logarithmic value by transferring to 10 programmer means for controlling said first and second modifying means to act on each result produced by adder means signals representative of the value of the said modifying means including means responsive to logarithm of each constant utilized by said modify said results causing said programmer means to ing means. change the value of the constant used by said modi 2. The apparatus as claimed in claim 1 and further in fying means. cluding means for doubling the signals transferred from 9. The calculator as claimed in claim 8 wherein said said storage means to said logarithmic accumulation programmer means controls said modifying means to means to accumulate a logarithmic value equal to the utilize a series of constants, the constants of said series logarithm of the square of said first number. differing from one another only in the value of A and A 3. The apparatus as claimed in claim 1 and further in cluding radix point control means including means to shift 20 in said series of constants being a series of successive integers. said first number and to correspondingly transfer signals 10. The calculator as claimed in claim 8 and further representative of logarithmic values of a predetermined including radix point control means including means cou constant from said storage means to said logarithmic ac pled to said first modifying means to shift said first num cumulation means in an accumulation operation until predetermined orders of said first number contain pre 25 ber, and means coupled to said second modifying means to ac determined values. cumulate signals representative of logarithmic values 4. Apparatus for performing logarithmic conversions of a predetermined constant until predetermined comprising first modifying means for modifying a first constant until predetermined orders of the number in number of radix R by adding said first number and a said first modifying means contain predetermined shifted value thereof to provide a product of said first 30 values. number and one of a selected group of constants in the 11. The calculator as claimed in claim 8 and further form 1-1/RA where R is the radix and A is an integer, including means for modifying the signals accumulated second modifying means for modifying a logarithmic by said second modifying means to accumulate a value by accumulating signals representative of the value of the logarithm of each constant utilized by 3 5 logarithmic value equal to the logarithm of a power of said first number. said first modifying means, and 12. Apparatus for performing a logarithmic conversion programmer means for controlling said first and second comprising first and second registers, modifying means to act on each result produced by an adder coupled to each register, said modifying means including means responsive to said results for causing said programmer means to 40 storage means for storing logarithmic values of a se lected group of constants in the form 1-1/RA where change the value of the constant used by said modify R is the radix and A is an integer, ing means. input means for entering signals representative of a 5. The apparatus as claimed in claim 4 and further number in said radix R in said first register, including radix point control means including means cou for modifying the contents of said first register pled to said first modifying means to shift said first num 45 means to provide a product of the contents of said first ber, and register and one of said constants by adding the con means coupled to said second modifying means to ac tents of said first register and a shifted value of its cumulate signals representative of logarithmic values contents together, of a predetermined constant until predetermined programmer means for controlling the successive modi orders of the number in said first modifying means fication of the contents of said first register includ contain predetermined values. ing means responsive to the contents of said first 6. The apparatus as claimed in claim 4 and further register for causing said programmer means to change including means for modifying the signals accumulated the value of the constant used in modifying the con by said second modifying means to accumulate a loga tents of said first register, and rithmic value equal to the logarithm of a power of said means responsive to said programmer means for cor first number. respondingly modifying the contents of said second 7. A calculator comprising two storage registers, register by transferring signals representative of the storage means for storing logarithmic values of a group value of the logarithm of each constant utilized to of selected constants, modify the contents of said first register from said 60 programmer means for successively multiplying the con storage means to said second register through the tents of one of said storage registers by selected adder coupled thereto to generate a logarithm of said ones of said constants and modifying the contents number entered in said first register. of a second storage register by the logarithm of the 13. Calculating apparatus for performing mathematical selected constant in a corresponding operation, and means responsive to the contents of one of Said 65 operations comprising an input register, an accumulator register, registers for controlling said programmer means. a log register, 8. A calculator comprising two storage registers, adder circuitry coupled to each said register for con storage means for storing logarithmic values of a Se trolling the modification of the contents of the cou lected group. of constants in the form 1-1/R^ where 70 pled register, R is the radix and A is an integer, storage means for storing logarithmic values of a se input control for entering signals representative of a first number of radix R in one of Said storage registers, first modifying means coupled to said one storage 75 register for modifying said first number by adding lected group of constants in the form 1-1/R^ where R is the radix and A is an integer, input control means for entering signals representative of a first number of radix R in said input register, 3,402,285 10 programmer means for controlling the adder circuitry fying means, and programmer means for controlling coupled to said input register to modify said first said first and second modifying means including number by adding said first number and a shifted means responsive to said results for causing said pro value thereof to provide a product of said first num grammer means to change the value of the constant ber and one of said constants, for controlling the used by said modifying means, adder circuitry coupled to said accumulator register a single manual control button for initiating the opera to add a number transferred from one of the other tion of said logarithmic means, registers to the contents of said accumulator register, and output means for displaying the logarithmic value and for controlling the adder circuitry coupled to generated by said logarithmic means in multidigit said log register to accumulate signals transferred 10 decimal form. from said storage means representative of the value 19. The calculator as claimed in claim 18 wherein said of the logarithm of each constant utilized in the first modifying means includes a first register and adder modification of said first number in said input register circuitry coupled thereto and said second modifying means to control a logarithmic conversion, and includes a second register and adder circuitry coupled means responsive to said programmer means for con thereto, and means responsive to an output from one of trolling the transfer of signals representative of num said registers as a function of the numerical values stored bers between said input register, said accumulator therein for controlling said programmer means. register, and said log register. 20. The calculator as claimed in claim 18 and further 14. The calculator as claimed in claim 13 wherein said including storage means for the logarithmic values of said programmer means controls said adder circuitry to utilize 20 selected group of constants and means responsive to said a series of constants, the constants of said series differing programmer means for applying signals representative of from one another only in the value of A and A in said the logarithmic values of selected constants to said Second series of constants being a series of successive integers. modifying means from said storage means. 15. The apparatus as claimed in claim 14 and further 21. The calculator as claimed in claim 18 and further including radix point control means including means 25 including means responsive to a manual control button for coupled to said input register to shift said first number, modifying the signals applied to said second modifying and means for accumulating a logarithmic value equal to the means to accumulate in said log register signals repre logarithm of a power of the number stored in said first sentative of logarithmic values of a predetermined modifying means. constant until predetermined orders of the number 30 22. The calculator as claimed in claim 18 wherein said in said input register contain predetermined values. programmer means is a sequencing device and includes a 16. The apparatus as claimed in claim 15 and further first output for selecting one of said constants, a second including means for modifying the signals accumulated by cutput for transferring a logarithmic value of said selected said log register to accumulate a logarithmic value equal constant to said second modifying means, and for con to the logarithm of a power of said first number. currently actuating said first modifying means to modify 17. A calculator comprising input means having a the number stored in said first modifying means by a plurality of control elements including ten manual control shifted value of that number corresponding to said selected keys representing numerical values from 0 through 9, constant, and means responsive to an output from said input register means for accumulating a numerical value first modifying means indicative of a predetermined 40 entered by said control elements, in the number stored in said first modifying means logarithmic means for generating the logarithmic value change for actuating said programmer means to select a different of the numerical value in said input register means, one of said constants. a single manual control button for initiating operation 23. The calculator as claimed in claim 22 and further of said logarithmic means, including means responsive to an output from said second and output means for displaying the logarithmic value modifying means indicative of a predetermined change in generated by said logarithmic means in multidigit the number stored in said second modifying means for decimal form. actuating said programmer means to select a different one 18. A calculator comprising input means having a plu of said constants. rality of control elements including ten manual control 24. The calculator as claimed in claim 23 wherein said buttons representing numerical values from 0 through 9, constants are in the form 1-1/RA where R is the radix input register means for accumulating a numerical value and A is an integer. entered by said control elements, logarithmic means including first modifying means for References Cited modifying a first number of radix R stored in said UNITED STATES PATENTS input register means by selectively adding or sub 5 5 tracting a shifted value thereof to provide a product 3,099,742 7/1963 Byrne -------------- 235-150 result N where N is a product of said first number and one of a selected group of constants, second modify 3,141,963 7/1964 Zuhlsdorf----------- 235-164 ing means for providing a logarithmic result by ac MALCOLM. A. MORRISON, Primary Examiner. cumulating signals representative of the value of the 60 V. SIBER, Assistant Examiner. logarithm of each constant utilized in said first modi U.S. DEPARTMENT OF COMMERCE PATENT OFFICE Washington, D.C. 20231 UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3, 402, 285 September 17, 1968 An Wang It is certified that error appears in the above identified patent and that said Letters Patent are hereby corrected as shown below: Column 6, in the table, third column, line 10 thereof, ": 675970" should read -- . 675979 - -; same table, third column, line 13 thereof, '6964.60" should read -- . 696.460 - -. Column 8, lines 28 and 29, cancel "until predetermined constant --. Signed and sealed this 10th day of February 1970. (SEAL) Attest: Edward M. Fletcher, Jr. Attesting Officer WILLIAM E. SCHUYLER, JR. Commissioner of Patents