US2428811A - Electronic computing device - Google Patents

Description

J. A. RAJCHMAN 2,428,81 l

v ELECTRONIC COMPUTING DEVICE I Filed oct. so, 1943 '12 sheets-sheet 1 Oct. 14, 1947.

Oct. 14, 1947.4 J. A. RAJCHMAN 2,428,811

ELECTRONIC COMPUTING DEVICE Filed Oct. 30, 1945 12 Sheets-Sheet 2 WIUFJH i670? Hire/X VA wm N l u n# n" ew w w V6 7M 0 Z m.. #mw FW mw. a la m6 N ww 0 ma :Snventor X fan GM Gttorneg flo Oct. 14, 1947. l.1..fR/JGHMAIQ 2,428,811

' ELECTRONIC couPuTIuG 'DEVICE Filed oct. 30. 194s 12 sheets-sheet 4 A zzz I -fam/ Suncntor A @Awe ria/:s af y wat mais any Bu www Oct.' 14, 1947. J. A. RJCHMAN 2,428,811

ELECTRONIC COMPUTING DEVICE Filed oct'. so. 194s 12 sneetssneet s F/Ymy) X A F :inventor Gte-meu Oct. 14, 1947.

J. A. RAJCHMAN ELECTRONIC COMPUTING DEVICE Filed oct. s, 1943 12 Sheets-Sheet 6 @rik U01 000| QWO) l Ol (Ittomeg J. A. RAJCHMAN 2,428,811

ELECTRONIC COMPUTING DEVICE Filed oct. so, 1943 Oct. 14, 1947.

PMs/crm# mme/x aufn/r Gttorneg Oct 14 .1947 J. A. RAJCHMAN y 2,428,811

ELECTRONIC COIPTING DEVICE lf'led Oct. 30, 1943y 12v Sheets-Sheet 9 15 'Wfl/X F/X'f) FWS l 46H5 M/rf/rmmq sysrfn A M16 Snoentor lor# 5.7024/7/02 Oct. 14, 1947. J. A. RAJCHMAN 2,428,811

IILECTROVNIGv COMPUTING DEVICE Filed Oc'c..l 30, 1943 12 Sheets-Sheet 10 ffm?) M100 [Mw /4000 ma /00 '/0 l.

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P /Mw' mais INVENTOR a 'Mme/ @5M ATTORNEY 0t- 14 1947- J. A. RAJCHMAN i ELECTRONc COMPUTING DEVICE l 12 sheets-sheet 11 Filed Oct. 30, -1943 ugvErgToR www,

ATTORNEY Oct- 14 l947l J. A. RAJCHMAN 4ELEGTROHI COIPUTING DEVIGE Filed oct. so, 1943 12 shets-sneet 12 :inventor Jv: @jb/zgan Gttorileg A digital position, signiies whether there is Patented Oct. l14, 1947 y ELECTRONIC COMPUTING DEVICE Jan A. Raichman, Princeton, N. 1. assignor tov Radio Corporation of America, a corporation 1 of Delaware Application October 30, 1943, Serial No. 508,343 l (cl. zas-s1) 19 Claims.

This invention relates to computing devices such-as are utilized to generate a -desired function of one or more variables. The function and the variables are represented by systems of electric potentials. It has for its principal object the provision of an improved computing device and method of operation whereby a function of one or more variables may be derived continuously and without appreciable delay as the different variables change fromone value to another.

This improved computing device includes, among other elements, a selector matrix which operates to select a set of values of the different variables, a function matrix which generates certain component functions of this selected set of values, and an interpolator which so combines the various components as to present at its output terminals potentials which are representative of the diflerent digits of a number by which the value of the function is expressed. As will appear, each of these three elements may assume different forms, depending on the conditions under which the device is operated.

All the computations are performed in terms of numbers. The present computing device is therefore of the numerical type, as contrasted with devices using continuously variable physical quantities, such as voltage, current or phase, as the variable of computation. The whole computation is made in the binary system of numeration so that any number is expressed as a sum of powers of two in which the coefilcients of the terms are zero or one. 'I'hese are the only two digits of the binary system. y

In this system, a number is expressed thus:

A=an2n+an12nr1+ ak2k| ao where the coeflicients ak are either one or zero. The numbers can be written in the usual digital representation as shown for'the first seventeen numbers in the following table:

For any number the iirst digit from the right, orzglrxt' a. 1 the number' or not, the second digital place whether there is a v2=21 or not the third whether there is a 4=2 or not, the fourth whether there is an 8=2 or not,l etc.

It is obvious that fractions and fractional numbers can beexpressed in the binary system in a manner similar` to the decimal fractions by using a binal-point" analogous to the decimal point. A table of a few fractions would be:

0 .0000 1% .0001 1A; .0010 1% .0011 41 .0100 .0101 .0110 .0111 1/ .1000 1% .1001 .1010 H .1011 3/4 .1100 ii .1101 .1110 li f .1111

For any number the first digit from the right of the decimal point signiiies whether there is a. l/2=21 in the number or not, the second whether there is a 1/4,=2', the third whether there is a :24 or not, etc.

This system of numeration was chosen because most electronic computations are more easily performed in it than in any other system. This l unusual method of expressing numbers does not involve any practical difficulty so long as the input and output of the computing device are `converted automatically to control somephysical apparatus, such as an'anti-aircraft fire control system. Under such conditions, no ciphering or deciphering from the decimal numeration is involved. I

All the operation is made in a direct system in which the binary number is expressed by a system of as many potentials as there are digits in it, each potential having one of two definite values V1 and Vz corresponding respectively to the digits zero and one. All these potentials exist simultaneously on a system of conductors each carrying a potential corresponding to one digit of the number. Thus, for example, to express the rst seventeen numbers, five conductors would be required. The number 9 would be expressed by the following excitation of the iive conductors: V1VzV1V1V2,' since it can be written as 01001,

In a computing device, two or more such systems of potentials are combined and a new system of potentials is derived from them. The result of the computation is the stationary nal value of these output potentials. 'I'his result depends only on the stationary value of the input potentials, regardless of the manner in which they were reached. A sudden change in one or continuous l v elements with inherently stable states orany other holding devices, nor does it necessitate.

.y 3 A more input digits will, lafter short transients, cause the output potentials to reach their correct stationary values, so that the operation of the direct computing device may be considered as It does not involve any trigger any definite sequence, timing, or clearing pulses.

erated is assumed to be continuous in the mathematical sense.' Such/functions are usually en'- countered when they relateV to physical phenomena, as Afor example the ballistic func- Therefore, it is not a counter of any sort and does not involve impulses. Itis basically the fastest type of numerical device, since no time is wasted in the proper sequencing of operations.

Important objects of the invention are the pro-,-

The invention will be better understood from the following description considered in connec` tion with the accompanying drawings and its1 scope is indicated by the appended claims.

Referring to the drawings:

Figs. 1 and 2 illustrate a function in graphical form, the curved surface representing the function in Fig. 1 and the curves of Fig. 2 represent ing the function for various values of the y coordinate. ,f

Fig. 3 shows the -fu'nctionin tabular form with the variables in the binary system.

Fig. 4 is a wiring diagram ofa selector whic operates yin response to major values of .the variables to select an element corresponding to that particular set of values.

Fig. 5 illustrates a function generator which includes a modified form of selector, a function matrix and an interpolation system.

tions of a gun. 'The function may be in an'explicit mathematical form such as F(,:c, y) :V12-ky matical operations dening the function rather than to use the present device. However, most empirically found functions are not susceptible of being expressed by simple mathematical formulas. They are given in general in the terms of ta'bles or graphs. An example of an arbitrary" function determined in that manner is given here in graphical form (Figs. 1 and y2) and'in tabular form (Fig. 3). Y

Fig. 1 shows the function F0311) [plotted along v the coordinate z, as'a function of the coordinates :z: and y in a rectangular systemfof coordinates f as, il, e. Thus the surface z=F(:c, 11) may be considered to represent the function. Two families of plane curvescan :be obtained byintersecting that surface by a series of v(ar-z) and y-z) planes. y Theselcurves are shown in perspective in Fig. 1. vThe curves (az-z) for differentvalues of y are also plotted in Fig. 2. The surface Z=F(, y) `or the curves Z=F(z)y=con$1;ant.

y represent the function completely for all points.

Figs. 6 and 'I illustrate details in the connecl tions of Fig. 5.

Fig. 8 illustrates an interpolation system which 3 differs from that of.Fig. 5 in that it involves a single carryover system.

Fig. 9 illustrates a function generator adapted to the use of augmentedl interpolating coefficients.

Fig. 10 illustrates the details of the interpolation system forming a part of the generator of Fig. 9, y

Fig; 11 illustrates an expanded scale section of the n function table of Fig. .3,

Fig. 12 is a :function generator adapted for use n of the scale expansion'illustrated by Fig. 11.

Figure 13 is a diagrammatic representation of an adding circuit,

Its

Any table, however large, cannot represent the function for all values of the variables since there is an innnite number of such values. It must therefore give the function for certain values only. yThe table of Fig. 3 gives the value of FCL', y) for 64 sets of values of m' and y. These particular values will be called the "major values and referred to as zo and yo. (The values of the functionl for these points` were yobtained by measuring the Z values in Fig. 1.) The table is in the `binary numeration. The major values of the variable are chosen to correspond to exact yvalues of two, in this case simply thevintegers 1, 10, 11, 100, 101, etc. In each square of the ta'ble, the irstnumber given is the value of the function. Thus, for the point Xn=100 and Yo=11, the value of the function is found in square No. 29 to be 011.1011. point Q of Fig. 1.

To nd the function for values of the variables` other than the major values Xn and Yo, interpolation must be used on the basis of the knowledge that the function F(:c, y) has been assumed to be continuous. The simplest kind of interpolation is the so-called linear interpolation, which is used in the iirst form ofthe invention.

It consists in replacing the actual surface Z=F(:v, y) by little planes for each major area.

. corresponding to the interval between consecu- Figure 14 is a wiring diagram of the circuit of Figure 13,

. Figure 15 is a diagrammatic representation of l amultiplying circuit, and i Figure 16 is a wiring diagram ofthe circuit of Figure 15.

The purpose of the present invention is to It will be explained for the case of 3 generate arbitrary functions bythe direct method of computation operative in the binary system. The device can operate to generate funcp tions of one, two or any number of independent variables. l two variables :r and y as this case includes the complications due to several variables .without 1 ibeing unduly involved. 'I'he function to be gentive major values of the variables, as shown, for example, by the heavily drawn area surrounding the point Pon Fig. 1, the region defined by. :en from to 101 and yo from 11 to 100. It is easy yto see, then, that the value of the function for any set of values 1.', y (represented by the point P) is given approximately by:

I A'.lo This relation is similar to the so-called Taylor series, in which only the rst order termsare taken into account. The values Aa: and Ay, by which the actual values of the variable differ from the major values, will ybe called the minor values. For the sake of simplicity, in the pres# This is also represented by ent example they are the fractional parts of the variables. although in general it is not necessary to make the separation between maior and minor parts just where the binal point is. 'I'he unit intervals Azo and Ayn, differences between y consecutive major values, are thus equal to one.

Therefore the ratios AFz/Ao and AFu/Ayo, which are the rates of change of the function with respect to .1: and y, respectively, are simply numerically equal to AF and AFy. These valas can be seen on Fig. 1.

If the values of AFa: and AFy are known in ad- I dition-to the values of F(:to, yt) for all major points, the value of the function for any other point can be calculatedby the relation (I). This is precisely what is done in the first forms of the invention. The table of Fig. 3 gives the values F(xu, yo), AFJ: and AFy for all the major values.

As an example, consider the point P of coordinates:

Therefore, the value of the function F(:r, y) `at P is:

F(.'E, y) =F(100.1101; 11.1110) =011.1011+ (.0011) (.1101)+(.1011) (.1110) :011.10114- .00101+.10011=100.0111 since (.0011) (.1101)- .00101 and (.1011) (.11.10)-.10011.

As heretoforedndicated, the function generator Aincludes three principal elements or units, namely, the selector which selects a particular point neighboring that at which the function is to be evaluated, the function matrix which makes available values of the function and desired functions at that selected point, and the interpolator which combines these values with the differences of the variables at the desired and selected points, to produce the function inthe form of electric potentials representing its various digits in the binary numeration.

The selector unit is disclosed in two diierent forms (Figs. 4 and 5). In the ilrst of these forms (that of Fig. 4), the major values :ro and yo, which are given in terms of binary numbers, are transformed separately to control an orthogonal network of function matrix input tubes. In the second of these forms (that of Fig. 5), the intermediary step of separate transformation of the major values :ro and yo is avoided. It is to be understood that the network is represented as orthogonal only for convenience of explanation and that the two sets of conductors may have any other convenient arrangement.

`The selector of Fig. 4 is shown as adapted for eight possible major values of :to and the same number of mador values yo. There are therefore 64 possible sets oi values, as indicated by the orthogonal network 0i' tubes I to 64 whichare con- 6 nected in the input leads of the function matrix hereinafter described in connection with Fig. 5.

These values are established through three pairs of conductors 202 and 203 for the yo input anda similar number of pairs 204. 205 and 206 for the zo input. Each pair of these con--v ductors is connected at one end to some ofthe horizontal conductors (201 to 2I4 for the ya input and `others for the :ra input) oi the selector and at the other end to the cathodes of the selector matrix input `tubes 2li to 2I1 for the yo input and 2I8 to 220 for the :ro input. Potential is appli/ed to the grids of the tubes 2I5 to 220 from leads maintained at -610 volts and -500 volts. as indicated in Fig. 4. The application of these potentials to the grids may be controlled by switches 22| to 226 as illustrated, or by another computing device, or any other means which willmaintain these grids at potentials corresponding to the binary numbers of the major inputs. The selector output tubes 221 to 242 have been interposed between the selector input tubes 2I5 to 220 and the matrix input tubes I to 64.

It will be apparent that the switches 2I5'to 220 control the grid potential of the selector matrix input tubes, i. e., set them at Vi=-610 volts or Vz=500 volts. These tubes are merely amplifier tubes so that no appreciable power is drawn in the input circuit, and they are operated as cathode followers.

It willbe apparent that the pairs of y" vertical conductors (left, Fig. 4)

Vwill be excited according to the binary input potentials, i. e`., the left conductor of any pair will be at -610 volts and the right one at 500 volts for the digit 0 and vice versa for digit one. The horizontal conductors 201 to I4 are connected to the grids of the selector output tubes 221 to 234 and are coupled through high resistances (1,000,- 000 ohms) to the certain vertical conductors of the converter.

-The pattern of these couplings is as follows: Each horizontal conductor is coupled to the vertical wire which is at the most negative potential 610 volts) of every pair for the particular combination of excitation of these vertical wires corresponding to its order number. For example, the grid of tube 23| (binary 0II or 3 in decimal numeration) is connected to the left wire of the pair corresponding to the digit 22 (|00), since it is at -610 volts when "0 is set on the switch |00, to the right wire of the pair corresponding to the digit 21 (I0), since it is at -610 volts when 1 is set on the switch I0, and finally to thev right wire of the pair corresponding to the digit 2 (I) since it is at -610 volts when 1 is set on switch I.

It is apparent that the potential of the grid of any one of these selector output tubes will be at -610 volts for the particular combination of excitations of the inputs which correspond' to it, and will be somewhat more-positive (at least by l 33 volts) for any other combination of excitation since at least one of the vertical conductors to which it is connected is at 500 volts. Therefore. one and only one of the selector output tubes will be cut oil, since the cathodes are maintained at 600 volts, and it will be the one correspondwork is at relatively high impedance since it is composed of 1,000,000. impedances. Further- 1 more, the cathode follower driving tends to keep c the cathode at approximately the grid potential Y l independently of the load. -The selector for the :ro variable is shown only diagrammtically on Fig, 4; the coupling megohm resistances are heavy dots and the converter output tubes 235 to t 242 arershown ascircles. This mode of repreis at the low impedance of 50,000 while the netcorresponding to the maior values or nro and ro together and to consider the resulting combinafv tion as one single variable.

sentation will be usedV subsequently in order to simplify the drawings.

The anodes of the selector output tubes 221 to 234 and 235 to 242 are coupled to the grids of the orthogonal network `function matrix input vor double control grid tubes, and they are arof the table of Fig. 3. To each tube lthere correspondsa vertical exciting conductor coming conductor coming from the yconverter. If doutubes I to 6I. These tubes can eitherI be triodes c Therefore, a largerV converter from binary to natural order (having 6 inputs and 64 outputs rather than 3, inputs and a 8 outputs) can replace both converters and the' orthogonal array of tubes of the iirst modifica-V tion. It operates quite-similarly to the converters of Fig.` 4, except that the selected tube is made to conduct rather than tobe cut ofi, as was thecase in the converters. To each of the digits (6 in the present example) of this new variable are assigned two potentials carried on two conductors 2li vto 206 which bear a push-p or conjugate relation to one another, that is to say. for digit` zero one conductor (the left one in Figs. and

` 6) is at the most positive potential V1 (-.i40y

1 ranged in an array corresponding to the squares L i from the :lr-converter and a horizontal exciting -ble grid tubes are used, as shown for tube 53 on Fig. 4, the vertical wire is connected directly to one grid andthe horizontal to the other. It 1 will be apparent that only one out of the 6I tubes of the array will conduct, the one for which both grids are at -340 volts, e., when the corre-l t sponding tube of the zo converter is cut olf (plate t l at 340 volts) and-the corresponding tube of the y converter is cut ofi. For all other tubes, one or the other or both of the grids will be more negative than 340 volts, say at 500 volts. so that they will be cut off,

If triodes are used, as shown for tube 29 in Fig.

l' 4, the single grid of the triode is coupled through a 1,000,000 ohms resistance to the horizontal con.- duotor and through another 1,000,000 ohms to 1 the vertical conductor. It is apparent again that only the particular triade lying in the intersection volts) andthe other (the right one on Figs. 5 and 6) is at the most negative potential V2 (-600 volts) and for digit one the potentials of the two i conductors are interchanged.

o The selector matrix is composedof two sets of orthogonal conductors between which high coupling .resistances (2.700,000 in the present example) are connectedV according toa predetermined pattern. On Fig. 5 the heavy dots on the selector matrix (left)A represent such resistances, which are to be understood as connected between the two conductors on the intersection of which they are drawn. The vertical conductors carry Y the input potentials andthe horizontal wires are of the excited conductors will be conducting.` The i grid of that particular triode will be at -340 3 volts, whereas all other' grids will be mor negative by at least half the potential variation of the converter output tubes,and will therefore be cut off since the cathodes of all the triodes are at 340 volts. It may be noted here, as it was in the case of the converter resistive networks, that i the resistive network of the plate of the coni verters to the grid of the function matrix input tubes has many parasitic connections producing Y extraneous excitations, Here again the operat l tion is as stated in spite of these' because the driving impedances are low (20,000o) and the i coupling resistances are high (1,000,000o).

Whether triodes or double grid tubes are used Therefore, it will ya, one particular horizontal `lead of thev function -mat will be excited. These leads are shown on the right of Fig. 4, or extending above i the tubesi to 6I.

The same result can be obtained with a simple selector built according to the second modiiication. Such a selector is shown at the left of Fig. 5, while Fig. 6 shows the detail of thecircuit.

t The basic idea is to combine the input potentials connected to the grid of the triodes (halves of 6SN7s in the example of Fis. 6) of the matrix input tubes (shown as numbered circles in Figs. 5 and 6). The'push-pull signals are obtained from a, previous computing device, or they may be set in by a series of switches. input tubes 2I5 to 220 (lower left, Figs. 5 and 6) are merely ampliiers, so that no appreciable power is `drawn in the input circuit and they operate as cathode followers, as did the input tubes to the converters of Fig. 4. Y

The pattern of resistances is determined as fcllows: Any one of the-horizontal conductors of the selector matrix which is connected to the grid of a triode of the input matrix tubes (numbered I to 6l on Fig. 5) is coupled through' high (2,700,000o) resistances to the vertical wires Y whichfare at the most positive (Vz=-340 volts) of the two potentials V1 and V: for th'eparticular combination of excitation corresponding to that f selected triode. It is thus obvious that this horizontal grid lead will beat the positive potential Vn 340fvolts) for the combination .of excitations corresponding toit and will be at some pov tential negative with respect to V2 forany other combination.

This results from the fact that for anyother combination'at least yone of the vertical conductors to which that particular triode-grid is coupled will be at the more negative potential V2=600 Volts, S0 that there Will be (l-1) [in the present case o -1=5] connections at V2 (=-600 volts) and one at V1 (=340 volts) and the potential assumed by the lead will `be rthe -(5.340+600) [iig- 383V volts] which is negative with respect 'to V2.

odes, only the tube corresponding to the selected? value represented by the input potentials will conduct and all others will b e cut oi. As an .A example, consider the connection to tube No. 29

for which 10:10() and 210:011; therefore, the new variable has the value 100011, so that the pattern The selector Therefore, with the proper bias 340 volts in the present case) on, the tri of resistances for that lead is RLLLRR, as can be seen on Figs. 5 and 6.

The remark concerning parasitic connections made in connection with the selectors of Fig. 4 applies as well to the selector matrix of Fig. 5. The possible undesirable extraneous excitations do not interfere with the proper operation because the coupling resistances are high (2,700,- 000 ohms), the driving resistances low (50,000w) and the driving circuit isV degenerative (cathode follower).

The purpose of the selector described above is to "select a point :to-yo which corresponds to selecting a certain vsquare on the table of Fig. 3. The purpose of the function matrix is to assign to this square the values of the functions F(zo, y), AF2: and AFy which are'indicated by the table,

The function matrix is represented diagrammatically on Fig. 5 (upper right). The details of the connections are shown on Fig. 6. The matrix is illustrated as composed of two systems of orthogonal conductors, the orthogonal relation being a consideration of convenience and not of,

necessity. The horizontal conductors are connected to the plates of the function matrix input tubes (I to 64 of Fig. 5) which are both thev output tubes of the selector matrix and the input tubes of the function matrix, and the vertical conductors are connected `to the-grids of the function matrix output tubes 243. The state of excitation of these matrix output tubes represents the three functions to be generated. One such tube is assigned to each binary place of the functions. In the example used here, there are three sets of output tubes, the rst for F(o, yo) having seven tubes to take care of the seven places or digits encountered for that function in the table vof Fig. 3,*the second and third each having nine tubes to take care of all significant places encountered in the functions AF and AFy in the table of Fig. 3.

The vertical wires are coupled to thehorizontal wires through high coupling resistances (R=l, 000,000 ohms) according to a predetermined pattern, i. e., certain vertical wires areY coupled to certain horizontal ones, the choice of the wires or the patternl determining the functions to be generated. A resistance is connected between a given vertical wire corresponding to a given set y of major values aro-yo Aand a given horizontal wire corresponding to a. given binary place of the functions when the vdigit of that binary place happens to /be one. The resistance is omitted if that digit happensto-be zero. The function is thus recorded in terms of existing or non-existing resistances. As anV example, consider the square 29 of Fig. 3, and the corresponding input matrix triode No. 29 on Figs, 5 and 6. The values of the three functions are F0120, 11o) :011.1011 AF$=00000.0011

and

Therefore, the potential of the selected horizontal wire becomes negative (in the present case about -200 volts, assuming a current of 10 ma. in the tube No. 29, since the +B is'at 0.5 volt, see Fig. 6). This causes the potential ofi the vertical wires to which this selected horizontal wire iS coupled to Ibecome more negative than the ones to which that wire is not coupled. Therefore, with proper bias (zero in the case of Fig. 6) of the output matrix tubes, the tubes which are coupled will be cut off and the ones which are not coupled will be conducting. Therefore', it follows that the output matrix tubes will be excitedaccording to the predetermined function set in thev function matrix of resistances.

The detail of the connections of the matrix output tube is shown on the lower right portion of Fig. 6.. Consider a typical output tube 243, for example, the one on the lead marked .001 (right) This tube is a pentode 6SJ7.` A neon lamp 244 is inserted in the plate circuit to provide a visible indication of the state of conduction of the tube. This, of course.- is not essential since the functions F(x, yo), AF2: and AFy are to be combined according to .the relation of Equation 1 before the final result F(:c, y) is obtained.- The reason for the different circuit shown for the tube connected to the lead I0 is explained below.

In the function matrix of resistances every ver- 'tical conductor is connected to all horizontal conductors and vice-versa. In fact, there is a connection between any two conductors. Therefore, when the input conductors are excited they produce not only the desired excitation on the desired, outputl leads, but also parasitic excitations on other leads. The matrix is therefore designed in such-a manner as to reduce these parasitic effects to such an extent as to make the ratio of' (9-1-9-|-7=25 in the present case); i the current.

through the driving triodes l to 64 (10 ma, in the present case); Rb their plate resistance (20,000 ohms), Rc the coupling resistance (1,000,000 ohms in the present case) Es the true signal and Ep the parasitic signal on the grids of the output tubes. 'I'hen assuming the worst possible conditions, i. e., the weakest true and largest false signal, the following relations. hold:

Effe-1") Therefore the attenuation, i. e., the ratio of driving signal on triodes to useful signal, depends only on the number N of input elements. In this case N=64 so that the weakest useful'signal on the grid of the output'pentodesv is about volts which is sufficient to cut off the tubes 243. The4 ratio of. true to false signals depends only Aexcept a particular one.

11 1 on the ratio of plates to coupling resistances and the number of outputdeads `p. In the present case this ratio is 1,000,000 I' (zumo-)mp3 assumed worst case when all .the horizontal leads are connected to a given vertical lead. 'Ihis case may well occur. In spite of this the attenuation factor may be reduced to N/2 by the following expedient. The number of coupling resistances' for any one vertical lead may be smaller or greater than N/2. If it is smaller, the attenuation of the signal for that particular signal will be less than N/Z. If it is larger, that means that there are Aatraen the compensating resistances? are different for everyy conductor.

In many applications it is desirable many functions ofthe same variables, as is the case, for example, in anti-aircraft nre computers.

' Itis also the case for a single function if a method f can obviouslybe generated by the same device.

more digits one than digits "zero for that particular vertical conductor. The expedient consists in that case in using a coupling resistance at every place which corresponds to the digit `zero (in-st'ead of one) and omitting it for places correls'ponding' to the digit one (instead of zero). In

this manner the number of resistances on every vertical wire is less (or equal to) than N/Z (32 in the present case) ,so that the maximum lattenuation is N/2. Of course. this expedient requires that the polarity of the signal on the'wires where the resistances have been permuted be reversed. This is shown for the line marked I0 in the lower right part of Fig. 6. An additional phase inverting tube 245 (6SN'7)y is used for the purpose. It

.can be seen that the true signal on the matrix output tubes is now 200/32-6 volts (instead of 3 volts).

'I'he relations (3) andj. (4) mentioned above have been established for the case of maximum attenuation, i.` e., one vertical lead is connected to all horizontal leads (and the corresponding digit is always one) and maximum parasitic signal, when all the matrix is full of resistances In practice, the matrix will be filled in some random mannerso that the useful and parasitic signals will be different for each output conductor and different for every excitation. It could happen therefore that the ratio of the weakest useful signal at some particular conductor to the strongest parasitic signal at some other conductor would not be as great as indicated by relation (4). To bring all conductors to a standard condition of attenuation equal to N/2 the vertical leads are coupled to the plate supply of the input tubes (+0.5 volt in our example) through compensating resistances Rd which are adjusted for each conductor so as to make the loading uniform. (See Fig. 6.) For example, the value of the resistance for lead marked |00 is` 200,000 ohms. This value was obtainedby considering that the maximum number of' coupling resistances on any one vertical lead is 32, and that the number of resistances on that lead is 27,: therefore, a loading corresponding to five coupling resistances in parallel' is necessary to bring that lead to the 32 loading, standard condition.V

Therefore the corresponding compensating resistance is 1,000,000/5=200,000 ohms. Qi goutte,

of interpolation more refined than linear is used.;`

Any number of functions of the same variables It suffices merely to connect their "function" matrices to theflrst function matrix. It amounts l to increasing the numberp of vertical conductors. This can be done without further changes in the device as long` asthe parasitic signal does not become unduly large. However. it is seen from relation (4) that asp increases, the ratio of true to false signal tends toward unity. By using a large Rc/Rb ratio the number of usable places can be fairly large. There is a method by which there is no limitto the number of functions which can be generated. It consists of using a degenerative drive of the matrix, using two tubes instead of one for every input place of the matrix.

Fig. 'I shows one typical driving arrangement for'any input (horizontal) conductor. The output of the selector and input of one function matrix are two separate tubes (rather than'a' single one). The output of the selector is con' nected as before. 'I'he input of the function matrix is derived from the cathode rather than the plate. The tube 241 is connected as a cathode follower so that the potential of the cathode is` approximately equal to that of the grid regardless` of the load. This means, therefore, that, the

parasitic signals will be suppressed all together since the potential of all the non-excited horizontal leads of the function matrix will be forcibly maintained at +0.5 volt, in spite of parasitic effects while only the excited lead will become negative.

The function table as described has two matrices of resistance, the selector matrix, which determines which values of the major parts of the variables .are assigned to which values of the function, and the function matrix, which deter--v mines the nature ofthe function. vBoth of these are arbitrary, that is to say, the pattern o f.

resistances can be chosen t'o express any desired function.

A particularly convenient method of mounting the large number of resistances consists in holding them in holes drilled in a-,Bakelite board.

The board is drilled according to the desired pattern and the resistances are inserted and soldered in piace with the two sets of conductors on opposite sides of the board. If the generator is` installed in someV computing device whereit is desirable to change. frequently the nature of the function, as may be the case in computers for re control when types ofv guns or shells are changed, the board of resistances may be provided with jacks and may be plugged in and out with-y out disturbing any permanent connections.

When the function F620, iin) and the interpolating coeilicients AFa: and AFV are known, it sumces to make the two multiplications and the two additions indicated in relation i) to obtain the de-v sired function F(, y). Means for doing this are shown diagrammatically on Fig. 5. The squares 256 and 4201 symboli multiplying and adding devices operating by the direct method. 'I'he upper sides are the terms ofthe product, the

lower right side the result.

to generatel In a first form, the adding and multiplying device is simply the one tube device such as is disclosed in the aforesaid copending application serial No. 496,746. The inputs to the-e1ectronic calculating tube are direct without any coupling tmpedances, as explained in that application. Of course, it must be kept in mind that the different inputs must be on the same D.C. level, which means that the minor parts of vthe variables Aa: and .Ay must be brought to the same level as the interpolating coefiicients 'AF and AFy.

In a second form, the adding and multiplying devices are the direct multiplier and adder described in my copending application Serial No. 511,729, lled Nov. 25, 1943. As previously mentioned, the various multiplications and additions required to combine the major values x' and yo, the minor values Aa: and Ay'and the interpolating coefficients AFa: and AFy, as indicated by the squares and legends at the lower right-hand corners of Figures 5, 9 and v12, may be performed by devices of the type disclosed by myl copending application Ser. No. 496,746. Thus in the case of the square 256 of Figure 5, for example, the AF.: leads are connected to the multiplicand leads of Figure of the copending application, the Am and vForo, ya) leads are connected respectively to the multiplier and the input B leads and potentials representative oi' the value of Az,

are produced at the output leads bearing the numerals 25, 26, 2'I and 28. The square of Figure 5 indicated the numeral 251 is a second device which is similar to that of the copending application and functions to derive the'product Ay, AFy and to add this product to the output Az, AF+F(xo, yo) of the device 256. 1

The various additions involved in deriving the value of the function also may be performed by the adding circuit which is disclosed in my copending application Ser. No. 519,299 (Patent No. 2,404,250) and was made prior to the iiling date of the present application.

This adding circuit is disclosed in Figures 12 and 13 of the present application.

Figure 13 is a diagrammatic representation of a computing circuit arranged in accordance with the invention for adding two numbers (A and B), of six digital positions, circles being used to indi- 1 cate the electron discharge devices involved in the various connections. Y

The circuit of Figure 13 includes one group of input tubes 3|0 to 3|5 to which are applied potentials representative of the various digits of a number A and another group of input tubes 3|6 to 32| to which are applied potentials representative of the various digits of a number B. In each of these groups, the lowest digital position is at the top and highest digital position is at the bottom. This is indicated by the binary numbers placed above the various input leads. When -180 volts are applied -to an input lead. the digital position which it represents contains a zero. When zero voltage is applied to one of these input leads, the digital position which it represents contains a one. Switches 340 and 34| Y ard amount for each tube that is made to conduct the standard units of 4 ma. a'nd each of the tubes may be considered as representing a digit one or a digit zero.

For converting these various digits into a ybinary number which is the sum of the two num'- bers, a group of carryover tubes 322 to 326 and a group ofl carry over control tubes 321 to 332 are (Fig. 14), another computing circuit or any other digits oi' the two` numbers to beadded. Each of provided. The resulting sum is indicated by a group of indicators 333 to 339 which may include a, neon lamp or the like. The manner in which these results are accomplished will be more easily understood-in connection with Figure 14.

Figure 14 shows the details of that part of the. circuit which appears in the heavy lines of Figure 13. It will be noted that the input tubes 3|3 and 3|9 are connected to the same terminal of the resistor 342 as the carry over tube 325 which has its control grid connected to the carry over control tube 332 for applying a positive potential when a one is to be transferred from the second digital position to the third digital position which is representedby the input tubes 3|3and 3l'9. All the carry over tubes 322 to 326, like the input tubes 3|!! to 32|, are of the cathode follower type so connected as to conduct a standard unit' (4 ma.) of current. y

It is apparent that the potential at the lower terminal of the resistor 342 is reduced by a. predetermined amount when one of the tubes 325, 3|3 or 3|9 takescurrent, by twice this amount when two of these tubes take current and by three times this amount when all three of these tubes take current. These different voltages are applied through the resistors 343 and 344 to the first or control grids of the indicator tube 331 and the carry over control tube 330. Potential is applied also to these grids from a v. lead through resistors l'345 and 346. o the second or screen grids of the tubes 330 and 331, potentia1 is a'pplied from a +45 v. lead. l

Connected in shunt to the tube 331 'is a neon tube 341 for indicating when this tube is not conducting (a condition existing when a digit zero is lin the third digital position of the sum of the two numbers being added). l

The carryover tube 324 of the fourth digital position has the upper end of its cathode resistor connected through a resistor 348 to the first or control grid of the indicator tube 331. The control grid of the tube 324 is connected to the diode element of the tube 330 and through a resistor 349 to the anode of the tube 330 so that the tube 324 conducts current only when the tube 330 is biased off. The purpose of the diode -element of the tube 330 is to establish at the grid of the carry over tube 324 a predetermined potential which is intermediate those of the +550 v. and' -600 v. leads when the tube 330 becomes nonconducting and no plate current is drawn through its anode resistor by the tube.

The manner in which the circuit operates to convert the digits established by the tubes 325,

.From uns tabulation, it is @violent that the and 3I9 is conducting; When one of the tubes 325, 3| 3- or 3 I3 is conducting, the potential-atthe lower end of the resistor 342 is reduced suiliciently to bias oif the tube 331 thereby lighting the lamp 341 and indicating a digit one in the third digital Aposition of the binary number. When two of the tubes 325, 3I3 or 3|9 are conducting, the potential at the lower end oi.' the resistor 342 is re- I tubes 330 and 331 are conducting and the tube 324 is biased oil when none of the tubes 325, 3|3` duced sufficiently to bias oil the tube 330. This has two results. It makes the tube 324 conducting so that a. digit one is carried over to the fourth digital position. When the tube 324 conducts, a

coincidence effect is utilized to produce the terms AaBx. However. additions of intensities are utilized foi` the summations. although this could beaccomplished in other ways.

,The two systemsof potentials representing ranged, as shown in Figure 15, in an orthogonal network whose intersections constitute the ele- -ments of a. matrix corresponding to the terms AxBr. A vacuum tube 436 on each of these intersections is made to conduct only if there is coincidence of excitation of the two wires at such iny tersection, and therefore give a value to Aix only when A1 and Bx are both one. All the coefilcients A1Bk corresponding to the power 2l+k are located on diagonal lines,l vertical on the Figure 15.

Therefore, if all the plate currents of the tubes on these lines are added, the total current will be proportional to the coeiilcient of the 21+k term, provided that each tube, when conducting, contributes a standard amount of current. 'The system of potentials assumed by the plates is already a representation of the product, but it is not in the binary"system, vsince the c'oeillcient'of each positive potential is applied to the control grid of the tube 331 so that this tube takes current and thelamp 341 is extinguished. When all of the tubes 325, 3| 3 and 3|! conduct the potential at the lower end of the resistor is sufilcently negative to bias oil both tubes 333 and 331 so that the carry over tube 324'remains conducting and the lamp 341 is lighted. Under these conditions, a binary number of 1100 is established in the part of the circuit detailed in Figure 14. How the complete sum of two numbers represented by potential applied to all the input leads is established is readily` understood from the foregoing explanation. How the carry over system of Figures 13 and 14 is extended to produce the sum of numbers having a higher number of digits will be understood readily from consideration ofthe multiplying circuit of Figures 15 and 16, since this multiplying circuit employs the samecarry over and indicating system as that of the adding circuit. y

'Ihe multiplying circuit of Figures 15 and `16 may be utilized to perform the various multiplications required to produce thevselected valueof the function. By this multiplying circuit, the product of two binary numbers is obtained in the form of potentials representative of the digits of such product.

The product of two binary numbers :c and y power of 2 may be larger than one. To obtain the answer-in the binary system, the Si current steps appearing in the i row of each 2p+2frows must be revalued into binary number places to excitethe proper carry-over and indicating` tubes. This can -be done in several different-ways.

It has been found that the -most convenient manner is as follows: Let

Si=Ci+2Di+1 .YL 2"DH It is apparent that if there are m carry-over tubes located on the rows (j+1), f

(J+2) (v+m) which are excited when the corresponding coef-r ilcient D is one, the proper carry overs will be obtained provided that the circuit of each carryover tube, added to the circuits of the proper row, will contribute the same standard amount of current as the tubes of the matrix. 'I'his is so bethe 2p+2 rows which win be excited when-'tho where A1 and Bk are equal to one or zero, can be scales the number of answers in the basic multiplication table of digits is always greater than the n radex. In accordancewith this invention. that of the orthogonal network because the current cause any one of the coeillcients DHA multiplies the power 2H* and is added .precisely tothe row corresponding to the (i4-Mm power, as herein-k after explained in detail. To'obtam thoresulafit suffices merely to provide an indicator on each of corresponding coeillcient C; is equal to'one. The carry-over tubes 455 and 483 and indicator tubes 484 to 495 for the case of p=5 are shown on Figure 15. 'lhe thirty-six tubes 435 of the matrix and the carry-over tubes 455 to 483 all contribute a standard current when conducting. The tubes 436 contribute no currentwhen there is no excitation from one of the corresponding leads. Auxiliary amplifying tubes 496 to 5I3 are used in one modification of the invention.

'I'he basic part oi'- the multiplier is the circuit which will produce the signals to excite the indicator and carry-over tubes, according to Equation, 4. This circuit is repeated on each one of the (2p+2) rows, with various degrees of comwill .be readily understood from a few examples.

There can, of course, be no carry-over from the tube 435 at the lower corner (diagonal No. l)

I. and y are carried by two systems of wires ,ar-

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