US2404250A - Computing system - Google Patents

Description

July 16, 1946. ,1. A. RAJCHMAN 2,404,250

Y COMPUTING SYSTEM Filed Jan. 22, 1944 3 Sheets-Sheet l wam @am haw ma /aa /a l lul. el! /ld W /41 /2/ 0% 0 momma mac-'5 /lPdr T0523 INPI/T Tl/BES FMPrmFfmG/d v9/MY orf/e :avr/m rases 7 TOR/VE Y July 16, 1946,.

v.|- A.' RAJCHMAN 2,404,250

COMPUTING SYSTEM Filed Jan. 22, 19514 3 Sheets-Sheet 3 .Maman- INVENTOR. 1b 2707x011/ Y HTTR/VEY Patented July`16, 1946 coMrU'rTNG sys'rEM Jan A. autumn, Princeton, N. J., assigner 'to Radio Corporation of America, a corporation of' Delaware Application January 22, 1944, Serial No. 519,299

6 Claims. (Cl. 235-61) This invention relates to computing systems of a type disclosed in a copending application Serial No. 511,729 flied Nov. 25, 1943. It has for its principal object the provision of an improved computing circuit and method of operation whereby the sum of a plurality ofl numbers is readily derived. The two inventions are dis- .tinguished from one another in that the present invention is directed to the problem of addition, whereas the invention of the copending application is directed to the problem of multiplicaldevices using continuously variable physical quantities, such as voltage, current or phase, as 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 coemcients of the terms are zero or one. These are the-only two digits of the binary system.

In this system, a number is expressed thus.

where the coeiiicients ak are either one or zero. The numbers can be written in the usual digital representation as shown for the first seventeenl numbers in the following table:

.0 0, 1 1 2 10 a 11 4 100 5 101 e 11o v 111 s 1000 9 1001 10 1010 11 1011 12 1100 13 1101 14 1110 15 1111 1s 10000 For any number the first digit from the right, or rst digital position," signifies whether there is a 1-=2 in the number of not, the second digital place whether there is a 2=21 or not, the third 2 whether there is a 4:22 or not, the fourth whether there is an 8:23 or not, etc.

' It is obvious that fractions and fractional numbers can be expressed 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 0 1A; .0010 13g .0011 A .0100 1C .0101 .0110 u 11. .0111 V2 .1000 19s .1001 .1010 H .1011 '.0 .1100 H .1101 "/a .1110 H .1111 1 1.0000 u 11c 1.0001 .1% 1.0010

s 13m/4l 1101.011011 For any number the first digit from they right of the binal point signiiies`whether there is a 1/2=21 in the number or not. the second whether there is a V4=2'', the third whether there is a 35 l/=23 or not, etc.

This system of numeration was chosen -besystem. Under such conditions, no cipherlng or deciphering to or from the decimal numeration is K involved.

All the operation is made in a direct, system in which the binary number is expressed by a system of as manypotentials as there are digits inA 5o it, each potential having one of two definite values V1 and V2 corresponding respectively to the digits zero and one. All these potentials exist simultaneously on a system of conductors each carry-l ing a potential corresponding to one digit of the u number. Thus, for example, to express the first seventeen numbers, ive conductors would be required. The number 9 would be expressed by VrYaViviVs. since it can be written as 01001. In e a device, two or more such systems of potentials are combined and 'a new system of potentiils'isderivediromthem. Theresultofthe computation is the stationary unal value of these output pot'entiais'antl` dependsA only on the stationary value of the input potentials. regardless of the manner in which they were reached. A sudden change in one or more input digits will. ai'ter short transientacause the output potentials to reach their correct stationary values. so that the operation of the direct computing device may be considered as "continuous" It does not involve any `trigger elements with inherently stable states or any other "holding devices, nor does it necessitate any dennite sequence, timing.

or clearing pulses. Therefore. it is not a counterV v of any'sort and does not involve impulses. It is basically the fastest type of numerical device, since no time is wasted in the proper sequencing of operations.

As pointed out above, in the direct binary sysl giocato in any column has an odd number of pairs. an odd numberof groups of four or an odd number of groups of eight. Thus in the above example the operation can be followed by starting from the right column and going through all columns successively as follows: iive ones, write one, carry over one two columns to theleft (since there is one group of four'in five and one is odd) three ones, write one, carry over one to the nex`t column to the left (since there is a pair in three); eight ones. write zero and carry over one three columns to the left (since there is.one group of eight in eight); three, write one and carry over one to the next column; two, write zero and carry over one to the next column; six, write zero and carry over one to the next column and one two columns to the left, one write one. and ilnally one write one. This procedure may Y be summarised by stating that the digits of any one digital position and digits carried over from preceding digital positions to that particular position are added, that is to say the number of ones is merely counted. Then the result of that count tem of computation with xed constraints, the4 output potentials or currents are in direct relation to the input potentials so that for each place or digit of the inputs and outputs there must be provided a conductor.

The sum of two binary numbers A=10111 and B=10110 (A=23 and B=22 in the decimal numeration)A can be made as is done in the usual elef mentary arithmetic.

1 1l carryover 1o111 s v as 10110- B +32 101101 A+B i 4s 'I'his addition proceeds by adding successively thedigitsofAandBofthesamedisitalposition from right to left, taking into account the carry over number which results when the sum of the digits in any digital position is equal I can be calculated by writing the ynumbers in a column and adding as usual. The following is expressed in the binary system, and its lowest digit determines the corresponding digit of the sum. its next digit, determines the carry over to theenext digital position, its further next digit determines the carry over to the further next digital position, etc. of a number in the binary system is obtained by determining whether the number of Vunits in it is odd or even for the lowest digital position, whether the number of pairs of unitsin it is odd or even for the next position, the number of groups oi.' four is odd or even for the further next position, etc. v

This arithmetical process is performed by the computing circuit ci the presentinvention.

Important features xof the present invention. are (1) a plurality of input tubes (one for each digital position of the numbers to be added) each connected to operate as a cathode follower so\ that it is either non-conductive or conducts a standard unit (about 4 ma.) of current. (2) a, plurality of carry overtubes (for transferring vunits of current from lower digital positions to a higher digital position) 'each connected in the same manner as the input tubes, (8) a plurality of carry over control tubes, (4) a resistance network so interconnecting the input, carry over control and carry over tubes as to ensure that the digits oney are carried over to the proper higherdigital positions, and (5) means for registering or indicating in their proper order the various digits of the resulting sum.

The input tubes for any given digital position of the numbers to be added are connected in parallel with one another and. through a common resistor, to a source of plate potential. Also connected in parallel with each digital position group of input tubes and supplied with plate voltage through the same common resistor are whatever carry over tubes that are required to transfer digits one to this digital position'from lower digital positions. To the control grids of the input tubes are applied either --180 (when the corresponding digit is zero) or zero voltage (when the corresponding digit is one). The

f tubes conduct current only when the zero voltexample illustrates the procedure:

nl }carry over digits A Total 11oo1o11 20a This addition proceeds by adding successively AthedigitsofAnAz Asofthesarnedigitalposition from right toleft, taking into account the carry over digits which occur when the sum age is applied to their grids. Each conducting input tube is utilized to represent a digit one and each non-conducting tube is utilized to represent a digit zero.

As the parallel-connected input tubes and the parallel-connected carry over tubes. if any, for

Of course, the expression g a given digital position become conducting one after another, the plate voltage of all these tubes is reduced by discrete steps because all the tubes draw current through the same plate resistor. This voltage reduction in discrete steps is utilized to control the conductivity of the indicator tube and the carry over control tubes for this given digital position. The carry over control tubes, in turn, control the carry over tubes by which digits are transferred to high digital positions. Adjacent the resistors and leads interconnecting these various tubes are legends indicating suitable values which may be utilized in assembling and operating the circuit.

In the operation of the circuit, the indicator and carry over control tubes are conducting when no input or carry over tube corresponding to the' given digital position is conducting. When one of the parallel-connected input and carry over tubes is conducting the indicator tube is biased ot! so that an indication for that digital position is produced. When two of the parallelconnected tubes are conducting. the ilrst carry over control tube is biased off, a carry over tube in the next higher digital position is made conducting, and a potential applied from the cathode of this carry over tube biases of! the indicator tube. Further steps in the operation are hereinalter explained in detail.A At this point, however, it should be noted that (1) the conductivity of the indicator tube for the given digital position is controlled jointly by the parallel-connected tubes and by the higher digital position carry over tubes and (2) the carry over control tubes each include a diode element which enables the grid of the corresponding carry over tube to assume a predetermined voltage.

The invention will be better understood from the following description considered in connection with the accompanying drawings and its scope is indicated by the appended claims.

Referring to the drawings:

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

Figure2isawiringdiagram ofapartofthe circuit of Fig. 1, and

Figure83and4aresimilartol1iga1and2 with the exception that the circuit is so extended as to add six numbers each having six digital positions.

Upon detailed consideration of the circuits of Figs. 1 to 4, it becomes obvious that these circuits are readily extended to deal with any desired number of numbers having any number of digital positions.

The circuit of Fig. 1 includes one group of input tubes Il to i5 to which are applied potentials representative of the various digits of a number A and another group of input tubes Il to 2| to which are applied vpotentials representative of the various digits of a number B. In each of thesefgroups, 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 zero voltage isapplied to one of'these input leads, the digital position which it represents contains a one. When 180 volts are applied to an input lead, the digital position which it represents contains a zero. Switches 40 and 4l (Fig. 2), another computing circuit or any other suitable I 6 means may be utilised to app these digital representative potentials tothe input leads.

The condition of the two l of input tubes Ilto "and Ilto2i is'dete bythedigits 5 of the two numbersto be ad. Each of these tubes is conducting a standard amount of current of about 4 ma. when a potential (0 v.) reptative of the digit -one is applied to its control d and is biased oi'f when a potential 180 v. representative of the digit zero is applied to its control grid. These standard unit currents are supplied through a common resistor 42 and are determined by the fact that each of the tubes is connected to operate as a cathode follower. Under these conditions, the anode potential oi' all the input tubes decreases by a standard amount for each tube that is made to conduct the standardunitsof4ma.andeachofthetubesmay be considered as representing a digit one or a digit zero.

For converting these various digits into a binary number which is the sum of the two numbers, a group of carry over tubes 22 to 26 and a group of carry over control tubes 21 to 32 are provided. The resulting sum is registered or indicated by a group of indicators 22 to 3l 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 Fis. 2.

Fig. 2 shows the details of that part o f the circuit which appears in the heavy lines of Fig. 1. It will be noted that the input tubes Il and II are connected to the same terminal of the resistor 42 as the carry over tube 2l which has its control grid connected to the carry over control tube Il for applying a positive potential when carry over tubes 22 to 28, like the input tubes Il to 2|, are of the cathode follower type so connected as to conduct a standard unit (4 ma.) of current.

It is apparent that the potential at the lower terminal of the resistor 42 is reduced by a predetermined amount when one of the tubes 2l, Il or Il takes current, 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 4I and 44 to the first or control grids of the indicator tube I1 and the carry over control tube 2l. Potential is applied also to these grids from a -150 v. lead through resistorsand. Tothesecondorscreen grids of the tubes Il and I1. potential is applied Connectedinshunettothetubellisaneon.

tube 41 for indicating when this tube is not conducting (a condition existing when a digit xero isin the third digital position of the sum of the two numbers being added).

. The carry over tube 24 of the fourth digital position has the upper end of its cathoderesistor connected through a resistor 4l to the first or control grid of the indicator tube 21. The control grld of the tube 24 is connected to the diode element of the tube Il and through a resistor 4l to the anode of the tube 2l so that the tube 24 conducts current only when the tube Il is biased oil. The purpose of the diode element of the tube 3|) istoestablish atthegrid of theearry overtube 24 a predetermined potential which is intermediatethose ofthe +550 v. and -600 v. leadswhen resented by the input tubes I2 and' I 9. All the f None the tube 30 becomes non-conducting and no Plate current is drawn through its anode resistor by the tube.

The manner in which the circult'operates to convert the digits established by the tubes 25. I3 5 and I9 into a binary number isindicated by the following tabulation:

Input tubes conducting From this tabulation, it is evident that the tubes 30 and 31 are conducting and the tube 24 is biased off when none of the tubes 25, i|2 and I9 is conducting. When one .of the tubes 215, ilv or. I9 is conducting, the potential at the lower end of the resistor 42 is reduced suiliciently to bias of! the tube 31 thereby lighting the lamp 41 and indicating a. digit one in the third digital position of the binary number. When two of the tubes '25, I9 or I9 are conducting, the potential Jat the lower end of the resistor 42 is reduced sufficiently to bias oil the tube 30. This has two results. It makes the tube 24 conducting so that a digit one is carried over to the fourth digital position. When the tube 24 conducts. a positive potential is applied to the control grid of the tube 31 so that this tube takes currentand the lamp 41 is extinguished. When all of the tubes 25, Il and I9 conduct the potential at the lower end fof the resistor is sufficiently negative to bias oil both tubes 30 and 31 so that the carry over tube 244 remains conducting and the lamp 41 is lighted; Under these conditions, a binary number of 1100 is established in the part of the circuit detailed* in Fig. 2. How the complete sum' of two numbers represented by potential applied to all 'the input' leads is established is readily understood yfrom the foregoing explanation.

Figs. 3 and 4 illustrate how the circuit of Figs. 1 and 2 may be extended to produce the sum'oi six numbers each having six digital lpositions, the same reference numerals being fapplied to corresponding parts of all the ilgure's. It will be noted that -this extended circuit in-l cludes a group of input tubes to 55, 55 to 6|, 52 to 61 or 68 to 13 for each additional-number to be added. Since there are six input'tubes |542 |--6 |-91'-13, I4-20-54f-60-60- 12, I3-|9-53-5965-1I, I2|05259A 54-10, I'I--I1-5I--51-63--59 or |0^|6j50 55-52-68'for each] digital position of the num- 5 bers to be added, additional carry over tubes and carry over control tubes are required. Thus a carry over control tube 14 and a carry over tube 15 are required forV transferring 'a digit one to the third digital position when four or more of the rst digital position input tubes |52|`55 5|5113 are conducting. A carry over conf' trol tube 19 and a carry over tube 11 are re-v quired for transferring a'digit one-to the fourthdigital when four-or more o1'- the second digital y position input tubes |42054505512 'or three of these tubes and the' carry over-tubeare conducting.

A carry over control tube 18 and a carry over tube 19 are required to carry a digit one to the iifth digital position when four-and vup tofeight of the tubes 15-25-I3-I9-53--59--55-L-H are conducting and a carry over control tube 50 and a carry over tube 8| are required for vtransferring a digit one to the sixthv digital when all of 1l and 99-I00 function to .transfer a digit one tov higher digital positions is obvious from the f oregoing explanation.

Additional indicatorltubes 0| and |02 are used, together with the tubes 39 to 39, to indicate the sum of the six numbers. A tenth digital position indicator tube |03and .carry .over tube |04 have been indicated in dotted lines for the reason that they may be omitted since the corresponding digit is always zero. This is true because the sum of six numbers of six digits can be at most 101111010A when each of the numbers is As shown more clearlynin Fig. 4, thegcominon anode lead of the. carry over tubes 15 and 25 and the input tubes |3,I9, 53, 59, 55 and 1| is connected through resistors |05 and |05, respectively, to the rst or control grids of the carry over control tubes 18 and 80 (aswell as tothe control grids of tubes and 31'). Potential is also applied to these control grids from a 150 v. lead through the resistors |01 and |00. Potential is applied from a +18 v. lead to the second or screen grid 'of .the indicator tube 31j and from a +45 volt lead 'to the secondcontrol grids 'of the carry over control tubes @0, 10 and 80.' Potential is applied to the anodes ofthetubes 31, 30, 1liv and 00 from a +550 volt lead. IPotential is applied 'to the grids of the carry over tubes 24, 1'9'and 0I from a -600 v. lead respectively through'resistors |09, I|0 and III.

The grids of the tubes 24, 19 and 0| are connected directly to the diode elements of the tubes 30, 19 'and 00 and through the resistors 49, ||2

and I Il to the anodes ofthese tubes. When the tubes 30,19 and 00 are biased off, the correspond- .ing vdiode elelirient functions-to establish a predetermined potential at the grid ofthe tube 24, 19Yor 0|; Adjacent eachyresistor of' the circuit is -a legend indicating a suitable value which may be' utilized inassembling the circuit. p As in the case` of Fig. 2, the input and carry over tubes are oi' the cathode follower type so connected that each is either out oft' or draws a standard unit (about 4 ma.) of current. With theseA connections, the potential at the upper end of the common resistor" is dependent on how mamr of thetubes 15, 25, I9. I9, 53, 59, 65 and 1| are conducting and decreases in equal steps'as one after another= of the ltubes become conducting. I

The values of the various resistors and the applied voltagesare so'ehosen that, when one of the tubes 15, 25, I3, I9, 59, 09, 55 or 1| is conducting, vthe-voltage atv the uppe''termlnal ofthe common resistor 42' is so reduced that the tube ,311s biased'o, lighting the lamp 41 and indicating-a binary number of- 100.

When' twoof these tubes are conducting. the tube SII isbias'ed ofi, the tube 24'becomes conducting thereby transferring a digit one to the next""higher or fourth digital'position, and a voltage"applied from the cathode of the'tube 24 througha resistor I4 to the rst grid of the tube l1 makes this tube conductive and extinguishes the' lamp 41. e

the tube 24 and 100 is registered at the tube 31 making a binary total of 1100.

When four tubes are conducting, the voltage at the upper end of the resistor 42 is reduced further so that the tube 18 is biased of! and the carry over tube 19 is made conducting. A potential applied from the cathode of the tube 19 through resistors H and IIS to the grids of the tubes 31 and 30 makes these tubes conducting so that the lamp 41 is extinguished and the tube 24 is biased ofi. `A binary count of 10000 is now registered in the tube 19.

When ve tubes are conducting, the tube 18 is biased oi, the tube 19 is conducting and the tube 31 is biased ofi. Under these conditions, a binary number of 10000 is registered in the tube 19 and a binary number of 100 is registered in the tube 31 making a total of 10100.

When six tubes are conducting the tubes 30 and 18 are biased oil', the tubes 24 and 19 are conducting, the tube 31 is conducting, a binary 1000 is registered in the tube 24 and a binary 10000 is registered in the tube 19. The total is now binary 11000. In thiscase, the tube 31 is made conducting by potentials applied from the cathodes of the tubes 24 and 19 through resistors I|4 and H5 to its control grid.

When seven tubes are conducting the tubes 31, 39 and 18 are biased on, the tubes 24 and 19 are conducting, and the total binary number registered is 11100.

When all the tubes are conducting, the tube 90 is biased on, the tube 8| is conducting, the tubes 24 and 19 are biased ofi. and the. tubes 31, 30 and 18 are conducting so that a binary 100000 is registered in the tube 9|.

This entire operation may be expressed in" tabulation form as follows:

It is apparent from the foregoing description that an important feature of the carry over system is the resistive couplings controlling the potential of the grids of the carry over control and indicator tubes. This system of couplings operates in such a way that the effective number of voltage steps on any grid is equal to the number of conducting tubes l to 8 (to be converted to the binary system) minus the sum of the products of the carry over digits of higher digital positions by the corresponding power of two. It is evident that such eiective number of voltage steps is precisely the correct binary digit.

From the circuit of Fig. 4, it is seen that the carry over tubes 24, 19 and 89 are at the same D. C. level as the input tubes i3, i9, 53, 69, 65 and 1l so that they are suitable for grouping with the input tubes of the higher digital positions. The same is true of the carry over tube 28 and the input tubes I3 and I9 of Fig. 2.

I claim as my invention:

1. An adding circuit including a separate group of tubes for each digital position of the numbers to be added. means for applying to certain oi said tubes control potentials representative of the digits oi the numbers to be added.

control potentials representative of digits to be transferred from lower to higher digital positions, means for establishing at the anodes of thetubes of each group a potential depending on the number of conducting tubes in that group, and means responsive to the potentials so established ior indicating the sum or' said numbers.

2. An adding circuit including a separate group of tubes for each digital position of the numbers to be added, means for applying to certain or said tubes control potentials representative of the digits of the numbers to be added, and means for applying to other of said -tubes control potentials representative of digits) to be trans- I'erred from lower to higher digital positions, means for establishing at the anodes of the tubes of each group a potential depending on the number oi conducting tubes in that group, and means including a resistance network responsive to the potentials so established for indicating the sum ofy said numbers.`

3. An adding circuit including a separate group of tubes for each digital position of the numbers to be added, means for applying to certain of said tubes control potentials representative of the digits of the numbers to be added, and means for applying to other of said tubes control potentials representative of digits to beltransferred from lower to higher digital positions, means for establishing at the anodes of the tubes of each group a. potential depending on the number of conducting tubes in that group, and means including a plurality of electron discharge devices controlled by the potentials so established to indicate the sum of said numbers.

4. An adding -circuit including a group of input and carry over tubes, means for applying to said input tubes control potentials representative of digits of the same digital position of the numbers to be added, means for applying to said carry over tubes potentials representative of digits to be transferred to said digital position from lower digital positions, means for establishing at the anodes of said tubes potentials dependent on the number of conducting tubes in said group, and means responsive to said potentials for indicating when the number of said conducting tubes is odd.

5. An adding circuit including a group of inputand carry over tubes, means for applying to said input tubes control potentials representative of digits of the same digital position of the numbers to be added, means for applying to said carry over tubes potentials representative of digits to be transferred to said digital position from lower digital positions, means for establishing at the anodes of said tubes-potentials dependent on the number of conducting tubes in said group, and means responsive to said potentials for transferring digits to higher digital positions.

6. An adding circuit including a iirst group which has an electron discharge device for each digital position of a first number. a second group which has an electron discharge device for each digital position of a second number, means for applying to said ilrst group of electron discharge devices potentials representative of said first number, means for applying to said second group potentials representative of said second number, and means for converting said potentials into potentials representative of the sum of said rst and second numbers.

JAN A. RAJCHMAN.

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