US2444042A - Electrically operated calculating apparatus for converting numbers from binary to decimal form - Google Patents

Description

June 29, 1948. G c HARTLEY ET AL 2,444,042

ELECTRICALLY OPERATED CALCULATING APPARATUS FOR commune NUMBERS FROM BINARY TO DEGIMAL FORM Fi ed J y 1943 7 Sheets-Sheet 1 650 c F150? m M gus 6w f LESL 15 Sal v55 Mme/l.

A Aitor June 29, 1948.

Filed July 12, 1943 G. C. HARTLEY ET AL ELECTRICALLY OPERATED CALCULATING APPARATUS FOR CONVERTING NUMBERS FROM BINARY TO DECIMAL FORM '7- Sheets-Sheet 2 START HU D5 [VI/017025 GEORGE uF (wok mum:

ttorney n 1943- G. c. HARTLEY ET AL 2,444,042

ELECTRICALLY OPERATED CALCULATING APPARATUS FOR CONVERTING NUMBERS -FROM BINARY TO DECIMAL FORM Filed y 1 1945 7 Sheets-Sheet 4 i i a f i i iA/a 8/6 5/6 #79 6//o H/9 I3 J/5 /5 11 HO! HR/ MRI MR2 MR3 MR4 2 i Aitorne;

June. 4 G c. HARTLEY ET AL 2,444,042 ELECTRICALLY OPERATED CALCULATING APPARATUS FOR CONVERTING NUMBERS FROM BINARY TO DECIMAL FORM Filed July 12, 1945 7 Sheets-Sheet 6 LESLIE BA/NES MQ/GH.

31 Aitory June 29;

ELECTRICALLY OPERATED CALCULATING APPARATUS FOR CONVERTING NUMBERS FROM BINARY T0 DECIMAL FORM Filed July 12, 1945 '7 sheets-sheet '7 L w 2 Rt 2 Q O u g Q 0 m i \r (\l L 5 R E E *0 ELF] (9 Elk, g 8 0 INVENTORS (I) G C. 1 /46 745) 4531/5 5. x/n/ax/ 1 J R 00010 E Q A TTOH/VEY 7 ZQW A;

Patented June 29, 1948 ELECTRICALLY OPERATED CALCULATING APPARATUS FOR CONVERTING NUMBERS FROM BINARY TO DECIMAL FORM George Clifford Hartley and John Ridd Gould, London, England, and Leslie Baines Haigh, West Orange, N. J assignors to Standard Telephones and Cables Limited, London, England,

a British company Application July 12, 1943, Serial No. 494,283 In Great Britain July 21, 1941 9 Claims. 1

This invention relates to electrically operated calculating apparatus. 7

In copending applications, Serial Nos. 494,282 and 492,960, filed July 12, 1943, and June 24, 1943, respectively, there have been described forms of such apparatus for performing calculations on on'numbersexpressed in radix two and the results of the calculation were obtained as a number expressed in radix two. In application, Ser. No. 494,281, filed July 1-2, 1943 now Patent No. 2,411,549, there is described a form of electrically operated calculating apparatus which automatically converts a number expressed in radix ten into a number expressed in radix two.

Radix .ten is the ordinary system of numbers based on the number 10; radix two is a system of numbers basedon'the number 2. No-digit in any number ofradix two is ever greater than 1. A succession of numbers may beobtainedin radix two by adding '1 to the preceding number in each case, but, whenever the addition of 1 produces 2, ()"is entered for the digit and 1 is carried over to thenext left position. For example, numbers in radix two corresponding to 1 to 12 of radix ten'are as follows:

Radix ten Radix two, Radix ten Radix two Mi ioi-owin The present invention relates to means for obtainingin radix ten the equivalent of a number expressed inradix two. According to the present invention there is provided calculating equipment comprising means for entering'thereinto a number expressed in radix two, electrically operated means for computing automatically the number expressed in radix ten which is' equivalent to said first mention-ed number, and means for rendering the computed number availble.

The nature of the invention will be better understood from the following description of three difierent enibodiments thereof taken in conjunction with the accompanying drawings in which Fig. renews a ei-i'cu-it ior'converting a number expressed-m radix two into a number expressed 2 in radix ten where the latter is known not to exceed two digits;

Figs. 2 and 3 taken together form a complete circuit diagram, with 2 on the left of Fig. 3, of a calculating equipment into which numbers expressed in radix 2 are entered digit by digit.

Both in Fig. 1 and in Figs. 2 and 3 there are shown electrically operated means, operative in a plurality of stages for computing the number expressed in radix ten which is equivalent to a multi-digit number expressed in radix two which is entered into the equipment.

Figs, 4, 5 and 6, taken together, show yet another form of circuit for converting a number expressed in radix two into a number expressed in radix ten, and in this case the computation is performed in a single stage.

Fig. '7 is a circuit diagram of -a subtracting circuit shown in Fig. 1. in the several figures a pluralityof relays are shown, these being designated by a letter or letters, followed by a slanting line and a number, the number representing the'number of contacts which are physically controlled by the relay. These contacts are designated with the letter or letters of the relay to whioht-h'ey belong followed by a number which distinguishes the contacts of a particular relay from one another. In order to eliminate confusion of wires in the diagram and to make it easier to understand the operation of the circuits, the contacts have been shown in the circuits which they control, rather than adjacent the relays-which operate them.

Referring to the drawings, Fig. 1 shows a circuit in whichthe' magnitude of a number expressed in radix two entered therein is automatically expressed as a sum of a series of lesser magnitudes, the circuit including registering means for registering the lesser magnitudes. There are also shown circuits closed :by said registering means for rendering available the number in radix 'ten which is equivalent to the number entered. The means for expressing the magnitude of the number entered as a sum of predetermined lesser magnitudes comprises means for performing an attempted series of subtractions of numbers expressing said lesser magnitudes. In the circuits shown it is assumed to be "known that the radix ten number tobecomputed'doesnotpossess more than twodigits.

Such a number consists of the (Wef- INK- trout and [Mlfiont if both IM and IN are operated and over INA back and lM l back if either [M nor IN is operated and over 1N3 d [ME front if llVi is operated and !N is I seated. The wires marked a: and respectively leadto the circuits" for performing subtraction in denomination-2 and for indicating on wire er the value of the digit (i. e. whether 1 or appearing in denomination 2 in the result. The circuitsin denominations '2 2 and 2 are exact duplicates-of those in denomination 2 As will eppearpresentiy, for the arrangements shown in Fig. 1, the maximum remainder that can appear is nineteen, i. e. 1%011 in radix two andthus no wire a has been shown in that figare. The arrangements for giving a digit in denomination '2 of the remainder have accordingly been omitted in Fig. 7. The contacts of relays 5 M and 5N for extending round to wire b2 could also have been omitted.

The "first operation after the relay DA operates is the closing of the contacts DAE DAl'Z so that acombination cf the relays IA- -IG can be operatedby' the grounds on'the input lead a3-g3. Su pose that the min'iiend entered be 1160011, the radix two equivalent or ninety-nine. When the relay DA operates in the example given, relays IA, IE, 1T (not shown) and IG will be operated since the-grounds representing the number 110601 1. puts grounds on leads a3, 223, f3 and g3. This closes contacts IAZ, [B2, |F2 (not shown) and IG2 which connect grounds to relays 6M, 5M, EM and 0M and operate them.

relay DA also acts to enter the number eighty, i. e. 1 010009, radix two, as the subtrah'end by applying grounds to leads al and cl through contacts DAS" and D'A i, respectively. Thiscperates relays 5N and 4N.

The remainder 10011, which is the radix two equivalent of 19, is indicated by ground applied to wires-c2, f2, and g? as follows; ground through 0371 front, to wire 9'2 ground throug h llvi'i front, TN! back, to wire f2; ground through 1N3 back, 1M Trent, 2N4 back, 2M4 back, 3N4 back, ill/I l back, Ki/T2 back, 4N! front, to wire 02.

No grounds a pear on the wires 32 and d2 because neither relay in each of these denominations is operated and there is no ground on the wire The circuit for wire b-L includes 5N5 back, all/2 front, through 5N4 back to open contact at 5M4 back and also through M l back to open contact at 4N4 back. There is therefore he ground on lead 19 2.

Becaus'eo f the operational? relays 5M, 6M, and *gidt'in'fi is applied at 5N3 back, 51M4 front, fiNd 'rro'r'it, from, to line 0. line it has no ground and the circuit can "be traced through front, 6 front, 5M3 front, to open contact to 5N2 front.

Wires 62-{172 are connected by contacts to relays 'RB-RG, (three only of which are shown), which relays this store the remainder temporarily. In the example given, since the remainder is nineteen, represented by 11101 1 in radix two, relays RC, RF (not shown),

and operate.

In this case the remainder is positive, and ground a pears on the wire "p, as already ex- The ground-on'th'e wire is operates relay K through XXA front, and at contacts Xi, just below and to the right of the relay RG, completes locking circuit for such of the relays as are operated. At contacts (er;- treine right of the -figure) ,a circuit is completed ier relay 'sa over from contacts DAIS, front iii contacts X3, front contacts XXI to ground. Relay SA operates to record that subtraction was possible and looks over contacts SAl to ground on the start lead ST. At contacts X2v the circuit for relay XX is broken. This relay is shunted by a condenser and a resistance so that it has a delayed release time which is accurately controlled. The release of relay XX releases relay SA at XXl front. When relay XX has released, the condenser QA, (upper left of figure), which is in a charged condition, having been connected to battery through front contacts XX2, discharges over back contacts XXZ, front contacts DAl, and one winding or relay DB. Relay DB operates its contacts DB! and thus connects second winding to the ground on the start lead ST and operates fully, opening at DB2 the circuit of the relay DA, which releases, and at contacts DB3 preparing a circuit for the opera-- tion of relay DC. At contacts DA5-DAI2 the original circuits for the input relays LA to IG are broken. The operation of relay X also removes the locking circuit for relays IAIG at Xi and X4 back and also puts ground on the operat ing circuit at X4 front for a new combination of these relays to be operated, which combination is determined by the relays RB--RG which are operated. Such of the relays which are not to be in the new combination, (these being IA and 113), release, and the relays which are to be in the new combination either operate or hold over the new circuit. The relays IF and IG hold over RF2 (not shown) and RG32, while relay IC operates over RC2. The original combination of the M relays in Fig. 7 then assumes a new setting, representing a new minuend, to correspond with the combination or relays IAIG which are operated. Thus, since relaysIC, IF, and IG are 0pera'ted, their contacts directly operate relays 4M, 5M and 0M, While 6M and 5M are released. Relay XX in releasing breaks the circuit of relay X, by opening front contacts XX l. The release of this relay is delayed by a condenser and resistance in shunt to its winding, for the purpose of all-owing time for the contacts DA5-DAl2 to open and relays IAIG to release before the ground is put back on their locking circuits at back con tacts X4 and X5 The relays IB--IG act to store the remainder. Thus, in the example chosen, relays IC (not shown) IF (not shown), and IG are operated. There is no need to provide a relay for the digit of the remainder correspondng in denominational value to that registered by relay IA, since such digit should not appear in the remainder. When relay X releases, relay XX is reoperated.

The relay DB at contacts DB5- and DB8, shown at the right of subtracting circuit S, now applies ground to the wires hi and (11, in order to subtract or attempt to subtract the number 1(31000 which is the equivalent in radix two of the number forty. Grounds on these wires operate the relays 5N and 3N in the circuit of Fig. 7, and relays 5N and 3N release because of the release of DA. Relay X or relay Z will be operated according as the subtraction is, or is not possible. In this particular example, the subtraction was not possible and relay Z operates while relay X does not operate. SB is not operated because relay X is not operated and the previous remainder remains stored on relays IA-JG. The operation of relay Z releases relay XX at 2! backwhich in turn releases X at front, it having been prepared for operation through front contacts DB3. This releases relay DB and grounds are removed from relays 5N and 3N at contacts DB5 and DB6 and these relays release. At the next stage relay DC at contacts D05 and D06 applies ground to the wires cl and el respectively, which operates relays 4N and 2N, so that an attempt is now made to subtract 10100 the radix two equivalent of twenty. The release of relay Z operates relay XX again over 21 back and D04 front. Subtraction is not possible, relays N and 2N being operated and ground being extended to wire 11. to operate relay Z over 2N3 front, 2M3 back, 3N2 back, 3M3 back, 4N2 front, 0M3 front, N2 back, 5M3 back, 6N2 back, 0M3 back, and XX3 front to the Z relay. A similar sequence of operations takes place, relay XX releasing when relay Z operates, and relay DD is operated. The operation of relay DD releases relay DC and applies ground to leads all and ii through contacts DB4 and DDS. The release of relay DC releases relays 4N and 2N and the operation of relay DD operates relays 3N and IN to attempt a subtraction. With relays 5M, 1M, and 0M still operated, and relays 3N and IN operated for a subtrahend of 1010, a subtraction is possible and a remainder of 1001 the radix two equivalent of 9, is registered by the application of ground to wires d2 and 92. Ground is extended to wire d2 over 1N4 front; 2N4 back, 2M4 back, 3M2 back, and 3N! front. Ground is removed from lead 2 by the operation of relays 1M and IN. Ground is removed from lead C2 by the release of 0N. The removal of grounds from oil and f2 releases relays RC and RF and the ground on (12 operates relay RD. Relay 0M remains operated to hold relay RG operated.

1he release of relay XX also releases relay Z and the release of relay Z reoperates relay XX. Ground is also extended to wire p to indicate that subtraction was possible from 4N3 back, 4M0 front, 5N0 back, 5M4 back, 0N4 back, 6M4 back. This ground operates relay X over XX4 front and thus when relay DD has operated over contacts DC3 front in the same manner as described above, relay SD operates over DD5 front, X3 front, XXI front to ground and looks over SD! front to the ground on start wire ST. After this sequence of operations, on the release of relay XX, relay DE operates and locks to the start lead ST, and releases relay DD at DEE back. The remainder registered on relays P,BRG will be a four digit radix two number less than ten. The relays SA, SB, SC, SD form a set of storage elements, one for each of the magnitudes eighty, forty, twenty and ten, each of said relays being placed in operated or non-operated condition to register the presence or absence of its corresponding magnitude in the series of magnitudes of which the number entered is built up. The front contacts DEA close circuits for the indicator lamps I over contacts of the relays SA-SD for the tens digit and relays RD-RG for the units digit to display the number in radix ten which is the equivalent of the original number entered in radix two. The relays RD, RE and RF for temporarily storing digits of the successive remainders are not shown but certain of their contacts are shown in the circuits of the lamps I for indicating the value of the final units digit. Thus in the example given in which relays SA and SD were operated and also remainder relays RD and RG, ground is extended over DEA front to the lamp 9 in the tens array over SA2 front and SD5 front, and to lamp 9 in the units array over RD3 front and RG1 front, indicating that the original to compute automatically numbers of more than two digits. In the case where it is known that the result will be a number in radix ten of not more than three digits, the experimental subtractions are first made with 1100100000 (eight hundred), 110010000 (four hundred), 11001000 (two hundred) and 1100100 (one hundred), followed by the attempted subtractions described above, and similarly the circuit may be extended to deal with large numbers of digits. r

The same process may be extended to the conversion of decimals with the exception that the result must, in general, be an approximation. By working to an appropriate number of significant figures, however, it is possible to achieveany desired degree of accuracy. The process in this case is to start by attempts to subtract the radix two equivalents of the radix ten numbers 0.8, 0.4, 0.2 and 0.1. These are to ten significant figures .1100110011, then .0110011001, .0011001100, and .0001100110. With decimals it will not be possible to read a radix ten number directly from the remainder expressed in radix two. It will, therefore, be necessary to continue to subtract .08, .04, .02, .01, etc, until the remainder is negligible in the standard of accuracy required in the answer.

In the circuit shown in Figs. 2 and 3 means is provided for transforming each digit of the number entered into an equivalent number in radix ten and for computing from said equivalent numbers the number expressed in radix ten which is equivalent to the number entered.

The numbers in radix two are entered, digit by digit commencing with the digit of highest denomination. A pair of keys is provided for this purpose and is shown in the bottom left hand corner of Fig. 2, one key for each of the two possible digital values 0 or 1. These keys can clearly be replaced by the contacts of coupling relays or multi-position switches arranged to connect the circuit to any kind of device which represents a digit of a radix two number by grounding one of two wires.

At the left hand side of Fig. 2 is shown a set of sequence relays controlling the sequence of computing operations, which latter are carried out by means of relay circuits shown on the right hand side of 2 and in Fig. 3. Provision is made for as many denominations in radix ten as may be required for the radix two numbers that are to be converted, i. e. one denomination for radix two numbers up to and including 1001, two denominations up to 1100011, three denominations up to 1111100111 etc.

The value of a digit entered in radix two is recorded by operating one of two relays PA and PB; PA for the value 0 and PB for the value 1. It will be observed that the equivalents in radix ten of the radix two numbers 0 and 1 are the same numbers 0 and 1, respectively. The operation of PA or PB thus represents the value 0 or 1, respectively, in radix ten also.

As soon as the first digit 1 of a radix two number to be converted is keyed, the equivalent radix ten number 1 is entered, from contacts of PB, into the units denomination of the calculator, and stored therein. (If the first digit 0 is keyed in error, there is no change in the calculator because none of the regular calculating relays are operated by the entrance of a 0 before a 1; only sesame the incidental sequence relays atthe left of Fig. 2 are operated and released in their predetermined sequence.) The second ,digit of theradix two number is then keyed and "calculation begins.

Considered in radiX two, the keying of this second digit implies that the number so far keyed has become, by that ,keying action, a twodigit number, with the first digit transferred from denomination 2, which ,itlprevicusly occupied, to denomination 2 and the second digit placed indenomination 2, i. e. a number havinga total value equal to 2;timesthe value of its first digit plus the value ofits second digit.

,Now, the equivalent of the two number 10 in radixten is thenumberZ. Itfollcwathera fore, that the radix :ten fi llivalentof the twodigit radix two number keyed isequal .totwice the radix ten equivalent of the first digit keyed, plustheradixten equivalent of the second digit keyed, i. e. to twice thefirst-digit keyed,,plu s.the

second digit keyed. Similarly, when the third digit ,of theradixtwo number is keyed, the radix ten equivalent of thisis equal tot'wice the radix ten equivalent of the two-digit number previously; keyed, plusthe third digit keyed, .andso on.

Thus, the conversion or" a number expressed in radix two intoa number expressed'in radix ten can .b ca ried out y ,a Jpmces e re at d doubling and adding. For example, thelradix ten equivalent of the radix two number 1011101 maybe computed as shown in Tablel.

operated condition of any IA relay represents the value 1 in the denomination concerned, of a 2A relay the value 2, a 4A relay the value 4, and a 5A relay the value 5.

A plurality of indicator lamps are shown along the lower edge of the figures. These are arranged to indicate the numbers -9 in each of the thousands, hundreds, tens, and units denomination. They are controlled by contacts of the A relays i, 2, 4 and in each denomination in a manner to be hereinafter described.

When anumber stored on the A relays is to be doubled, calculation takes place in two stages. First, the numberlstoredis transferred from the a relays ,to the ,corresponding'B relays. Second, the holding circuit of the A relays is opened, and the latter immediately re-operate in a new combination, representing the number which is the double of that previously stored, directly determined by contacts of the B relays. Carry over from one denomination to another (which, it will be observed, can never exceed value 1 when a number is doubled) is determined by contacts of the 5B relays acting in the next higher denomination.

When the value ljis to be added in the units denomination, this calculation takes place concurrently with the doubling process. The value 1 is treated as a carryover of lfrom a lower denomination, not provided, to the units denomination, and the change is effected by contacts of the keying relay PB, acting in the units denomination in the same 'way'as the abovementioned contacts of the 5 B relays'a'ct in the other denominations.

The doubling'process may be repeated for any number, of radix two digits, subject only to the capacity of the calculator. i

The following Table 2 shows the relays operated in any denomination, when each of the ten possible stored numbers is doubled'with and without the addition of ,1 carried over from the next lower denomination.

Table 2 Stored num- Number stored B relays operated gg ggfigg A relays operated a gi g? A relays operated tied over 0 None 0 -None 1 1A 1 TB 2 2 3 1A. 2A 2 2B 4 4A 5 5A 3 "2B 6 1A 5A 7 2A 5A 4 AB 8 1A 2A 5A. 9 4A 5A 5 5B 10 None 11 1A 6 113 '5B 12 2A. 13 1A 2A 7 2B 5B 14 4A 15 5A. 8 .,2B 5B 16 1A 5A 17 2A. 5A 9 4B 5B 18 1A 2A 5A. 19 4A 5A 'Ihecircuit is arranged-.to-carry outsuchcom- Detailed circuit operation @putations rapidly and. automatically,

-"-In'- each denominationw-there-is a set of 1 four aggregate relays,. IA, 2A,: AAand 5A (iTI-IA-etc,

in the thousands denomination, lHA,,.' etc, ,(not shown), inzthehundreds; I'TA, etc, ino ihettens,

ancl IUA, etc.=,in: the-units), and. a set-,of-v four aggregate-retaining e ayS QB nd'.-.5B,

(lTI-lIB, etc., in the thousandsadenomination the etc,- in'the tens, and lUB, -etc., in-the units). The

11 back contacts of the 5A, iA, 2A and lA relays in each denomination.

The operator depresses key i for the first digit. PB operates and locks to PBl, over back contacts M2 and Ti and front contacts STZ). AP operates over MI back, PBB front ALI back STI front, to ground and locks to APi and T2 back and the same ground. C operates through APZ front. Display ceases, open at Cl.

lUA operates from ground on C2 front, o-ver iUB2 back, 2UB2 back, and PB2 front. M operates over C4front, PBB front, ALI back, STl front, to ground, and locks to Ml front. Relay T is a slow acting relay and now operates through CI front, slowly enough to allow IUA time to operate before T.

AP, open at T2, releases. iUA holds over IUAI front, AL2 back, STZ front, AP3 back, to ground. C, open at AP2, releases. T, open at CI, releases.

PB, open at C5 releases, as soon as key I is allowed to restore, lUB operates to C3 back over IUAf. front. The units lamp l and lamps i! in the other denominations light in circuits from ground on CI back, over 8T4 front, 5UA3 back, lUAZ-i back, iiUAt back, IUA3 front, lamp I to battery for the unit digits and similar circuits for lamps ii in the other denominations and display the number 0001, the radix ten equivalent of the radix two number so far keyed (stage I in Table 1). M releases as soon as BBO opens.

It will be observed that, as a consequence of the operation of. PB, AP, C and T operated and released again in turn in self-timing circuits, that while C was operated the value 1 was entered into the calculator, and that when C released again the new number 1 was displayed.

On observing this number, the operator depresses key 6 for the second digit. PA operates and locks to PAI, over back contacts M2 and TE, now closed and STE front to ground. AP operates to PAZ and locks to API, followed by C, and display ceases. IUB holds over lUBl front, AP3 front, to ground. IUA, open at C2 back, releases. ZUA operates to C2 front, over EUBQ front and 2UB3 back. M operates over C4 front, PAL front, ALI back, STi front to ground and looks over M I front to the same ground. T operates over CI front, slowly enough to allow ZUA time to operate.

AP, open at T2, releases, followed by C and T. EUA holds to AP3 back. PA, open at C5, releases as soon as key is allowed to restore. IUB, open at C3 front, releases. 2UP operates to C3 back, over EUAE front. The units lamp 2 and lamps 0 in the other denominations display the radix ten number 0002 (stage II), units lamp 2 being energized over iUAfiz back, 2UA3 front, :ZUAS back, UA3 back, STA front, Cl back, to ground. M releases as soon as PA2 opens,

It will be observed that, as a consequence of the operation of PA, AP, C and T once more operated and released in turn, that while C was operated the number 1 previously stored was doubled, and that when C released again, the new number 2 was displayed.

The operator depresses key i for the third digit. PB operates and locks. AP operates and locks, followed by C, and display ceases. 2UB holds to AP3 front. 2UA, open at C2 back, releases. 5UA operates to C2 front, over 4UB2 back, 2UB2 front, IUB3 back and PB5 front. M operates by the closing of C4 and looks over MI. T operates, slowly enough to allow 5UA time to operate.

AP releases, followed by C and '1. 513A holds to AP3 back. PB releases as soon as key I is allowed to restore because of the opening of C5. 2UB, open at C3 front, releases. 5UP operates to C3 back, over 5UA2 front. The unit lamp 5, and lamps 0 in the other denominations, display the number 0005 (stage III), lamp 5 of the units being lit over 2UA4 back, IUA5 back, 4UA4 back, 5UA3 front, ST4 front, CI back, to ground. M releases as soon as PB6 opens. I

It will be observed that, as a consequence of the operation of PB, AP, C and T once more operated and released in turn, that, while C was operated, the number 2, previously stored, was doubled, and the number 1 entered was added to the product, and that when C released again, the new number 5 was displayed.

The operator depresses key I for the fourth digit.

PB and AP operate and lock, followed by C, and display ceases, 5UB holds to AP3 front. 5UA, open at C2 back, releases. IUA operates to C2 front, over 4UB2 back, 2UB2 back, and PB2 front. ITA operates to C2 front, over 4TB2 back, 2TB2 back and 5UB2 front. M operates and locks. T operates, slowly enough to allow IUA and ITA to operate.

AP, C and T release. IUA and ITA hold to AP3 back. PB releases as soon as key I is allowed to restore.

SUB, open at C3 front, releases. IUB: and ITB operate to C3 back, over IUAZ and ITA2, respectively. The units lamp I, the tens lamp I, and lamps 0 in the other denominations, display the number 0011 (stage IV). M releases as soon as PBS opens.

It will be observed that, as a. consequence of the operation of PB, AP, C and T once more operated and released in turn, that While C was operated the number 5, previously stored, was doubled, and the number 1 entered was added to the product, that carryover of 1 from the units to the tens denomination was effected automatically, and that when C released again the new number 11 was displayed.

The operator depresses key I for the fifth digit.

PB, AP, C, M and T operate and display ceases. IUB and ITB hold to AP3 front. ITA, open at C2 back, releases.

IUA, although open at C2 back, holds to C2 front over 4UB2 back, 2UB2 back, PB2 front. ZUA operates to C2 front over IUB-2 front and PB3 front, 2TA operates from ground on C2 front over ITB2 front and 2TB3 back.

AP, C and '1 release. IUA, ZUA and ZTA hold to AP3 back. PB releases as soon as key I restores, followed by M. ITB, open at C3 front, releases. IUB, although also open at C3 front, holds to C3 back, over IUA2 front. 2UB and 2TB operate to 03 back, over 2UA2 and 2TA2, respectively. The units lamp 3, the tens lamp 2, and the lamps D in the other denominations, display the number 0023 (stage V).

The operator depresses key 0 for the sixth digit. PA, AP, C, M and T operate, and display ceases. IUB, 2UB and 2TB hold to AP3 front. 2UA and 2TA, open at C2 back, release. IUA holds to C2 front, over IUBZ back, 2UB2 front, IUB3 front and PB2 back. 5UA operates to C2 front over 4UB2 back, 2UB2 front and IUB3 front. 4TA operates to C2 front over 4TB2 back, 2TB2 front, ITB3 back, and 5UB5 back.

AP, C and '1 release. IUA, 5UA and 4TA hold to AP3 back. PA releases as soon as key 0 restores, followed by M.

TUB and 2TB, open at C3 front, release, IUB holds to C3 back over lUAZ. 51113 and 4TB operate to C3 back over EUAE and GTAE, respectively. The units lamp 6, the tens lamp i, and lamps ll in the other denominations, display the number 0046 (stage VI). The circuit of the units lamp -6 may be traced over 2UA5 back, iUAE front, 'fiUA l back, sons front, 6T4 front, Cl back, to ground. The circuit for the tens lamp :1 map be traced over fiTAS front, tTAt back, STE front, CI back, to ground.

The operator depresses key 1 for the seventh and last digit. "PB, AP, 0, M and T operate, and display ceases.

lUiB, EUB and 4TB hold to APE; front. UA, open at C2 back, releases. lUA holds to C2 front, over 4UB2 back, 2UB2 back'and PB2 front. ZUA. operates to 02 front over HUB Z front and PBS front. ETA holds to C2 front over lTBt front and "-5UB4 front. STA operates to C2 front over 4TB; front.

AP, C and T release. lUA, 211A, iTA and tiTA hold to 'AP3'back. 'PB releases as soon as key I restores, followed by M. SUB, open at C3 front, releases. 61113 and TB'hold, and EUB and 5TB operateto 'CS-back, over lUAE, iTA'Z, ZUAZ and STAE, respectively. The units lamp 3, the tens lamp e, and lamps ll in the other denominations, display the number 0093, the radix equivalent of the complete radix 2 number keyed, (stage VII). The units lamp 3 operates over lUA i front, "Z-UAB 'frontJlUASback, EUAB back, 5T4 front, and Cl back, to ground. The tens lamp 3 operates through lTAQ front, iiTAt front, S 54- front,-Cl back, to ground.

It will be observed that while 0 was last op- "erat'ed, the number 46, previously stored, was doubled,and the number 1 entered was added to the product, and that carry-over of 1 from the units to the tens denomination was again effected automatically.

'It 'h'asbeen'shown in the above example how the values 1,-2 and 3 in oneor other denominationare doubled Without the addition of 1 carried 'over from the next-lower denomination, and how thev'alues '1, 2, 4, 5 and 6 are doubled, with '1, carried over from the next lower denominati'on,- added to the product. The manner in "which the'other possible values of a digit of a "number expressed inradix ten are alsondoubled by thecircuits shown will be apparent from the drawing and it-' is not thought necessary to describe such operations :in detail.

l 'igs l; 5-and'6 form a circuit diagram of circuits for automatically calculating the number -expressed in'radix ten which is equivalent toany nurnb'er having up to twelve digits in radix two. "lhe tliree figures form one complete circuit dia- -='gram;di'fferent contacts of the several relays appearing in eachof the three figures, identified by 'reference characters which indioatethe relay to which they belong. Thadigits' of the radix two number are entered-simultaneously intothe calculat'or-by app-lying ground tosuch of the wires H 'a'-l, to;p-of Fig. 4, as represents digits having the value 1. Relays A--L are thereby energised to represent the: digital values 1 in the respective denominations.

A number expressed in radix two and having n digits is equal 130 (a) +(b) 2" -l-(c) 4- Y "etc where a; b, 0, etc, are the values of the respective digits and can be 0 or 1. Thus the successive digits that have the value 1 in a twelve digitniifnber are equivalent to 2948, 1024,5112,

the embodiment of the invention shown in Figs. 4, 5 and 6 each digit of a number expressed in radix two is transformed into an equivalent number in radix ten and the number expressed in radix ten which is equivalent to the number expressed in radix two is computed from the said equivalent numbers. Figs. 4, 5 and 6 show circuits by means of which such of the numbers 2048, 1024, etc., as correspond to the several denominations of the radix two number are added to produce the result of the addition in radix ten.

The circuits may also be considered as comprising means for automatically expressing the magnitude of the number entered as a sum of a series of predetermined lesser magnitude, relays A-L constituting registering means for registering the particular series of magnitudes 2048, 1024, etc., that are contained in the number entered. Circuits are closed by these relays to render available (by display on a series of lamps) the number in radix ten which is equivalent to the number entered.

The contacts of the relays AL form chain circults for carrying out the addition of the numbers or magnitudes that they represent, carry over relays being provided to carry over values from one denomination to another that arise as a result of the addition.

Consider first the circuits for the units lamps shown at the bottom of 6. Since each of the relays AL represents by its operation a number having a units digit of value other than Zer contacts of all the relays AL appear in the circuit. Since the order of addition of the magnitudes is immaterial, the order of connection of the contacts of the relaysis altered from the order in which the relays are connected to the wires al in order to effect economy in carry over relays, as will be apparent later.

When all the relays AL are in unoperated condition, a circuit is completed for the lamp displaying digital value 0. Each of the relays AL, other than relays A, E, I and B has live sets of contacts in Fig. 6, the moving contacts of which are connected by five incoming leads to the contacts shown next above in the figure.

The operation of relay L, representing 1 in the units column, changes over the connection of its five incoming leads from lamp 3 to lamp l, 2 to 3 and soon. A ground appearing on one of these incoming leads will therefore light a lamp representing an even value if L is not operated, or an odd value if L is operated.

The operation of relay K representing 2 in the units column changes over'its five-incoming leads from 0 to 2, 2 to 4, etc., if L is unoperated or from 1 to 3, 3 to 5, etc., if L is operated. Thus the OD- eration of relay K adds 2 to the conditions represented by the operation of other relays. The contact setK5 should change over from 8 to 10. This is'done by causing it to change over from 8 to O and at the same time causing the operation of a relay TK inserted in series in the circuit.

Relay 'J represents 4 in the units column and has contacts connected to changeover from each contact of K to the next set but one which gives the effect of adding 4 to the number represented by the conditions of the contacts shown above it. Similarly contacts of relay G representing, when operated, the number 32 which is 2 in the units column and contacts of relay C representing when operated 512 which is also -2 in the units column, are connected so that each adds 2 to the number represented by the contacts shown above it. Relay J in representing a change over from 6 to -10 tacts J operates a relay TJ. In like manner relays G and C in representing a change over from 8 to by contacts G5 or C5 respectively operate a relay TC.

Considering now the part of the units chain from and including contacts of relay C to the lamps, whatever combination occurs in the operations of relays C. G, J and K the sum of the units digits represented by these relays cannot exceed ten so that the figure carried over to the tens column by their combined operation cannot exceed 1. The same relay TC therefore is caused to be operated by contacts C5 and by contacts G5 and the operation of either TC or TJ is caused to operate TK which by its operation indicates a carry over of 1 to the tens denomination for all the four relays C, G, J and K.

Relay H represents 16 and therefore changes over the connections to the next but two sets of relay C contacts. There are three change overs which may necessitate a carry over of 1 to the tens denomination, viz. from 4 to 10, from 6 to 12, or from 8 to 14, and accordingly there are three windings included in the circuits which effect these change overs, two windings of relay THA and one winding of relay TH.

Contacts of relay F which represents 64 are wired similarly to contacts of relay J, and include in the circuits completed by their change overs, two windings of relay 'IF. Since the carry over represented by the combined operation of relays H (units digit 6) and F (units digit 4) cannot exceed 1, TH is used as the carry over relay and is operated either over its own upper winding or by front contacts TF1 or front contacts THAI.

Relay D represents 256 and relay B 1024. The contacts of relays D and B are therefore arranged similarly to those of H and F respectively, (since they have 6 and 4, respectively, in the units column), with carry-over relays TB, TD and TDA. Operation of relay TD thus represents a carry over of 1 to the tens denomination in respect to the sum of the units digits represented by relays D and B.

Each of the relays A (2048), E (128) and I (8) represents 8 in the units column. The contacts of these relays are so arranged that they add 8, v 6 or 4 according as one, two or all three of therelays are operated. Contacts Al, El and II nor-- mal extend ground to the moving contacts Bl to add 0. Contacts Al operated, E2 normal and I3 normal or contacts AI normal, El operated and I3 normal or contacts Al and El normal and II operated extend ground to contacts B4 to add 8.. Contacts Al and E2 operated and I2 normal extend ground over winding of TE to B3; contacts AI operated, E2 normal and I3 operated extend ground over winding of TI to B3; contacts Al normal, El operated and I3 operated extend. ground over a second winding of TI to contacts B3 add 6 in the units denomination whilst registering by the operation of TE or TI a carry over' of 1 to the tens denomination. Contacts A1,. E2 and I2 all operated extend ground over the: Winding of TE and the upper winding of TI tocontacts B2 to add 4 and register a carry over of 2 to the tens denomination.

It will be seen that, by arranging the con-- tacts of those relays that represent a units figure of 8 at the end of the chain remote from the lamps, a considerable saving in carry over windings is effected. If these relays were at the otherend of the chain five contact sets and four carry 16 over windings for each relay would have been needed.

When a number expressed in radix two is entered on the relays AL, Fig. 4, the units column is added up immediately by the units chain shown in Fig. 6 and the resultant units digit appears on one of the lamps shown at the bottom of Fig. 6 Whilst one or more carry over relays in series may be operated. For example, upon the radix two number 101010101011 being entered, relays A, C, E, G, I, K and L will be operated and a circuit will be closed from ground, Al front, E2 front, winding of TE, I2 front, winding of TI, B2 back, D3 back, F3 back, H3 back, C3 front, G4 front, J5 back, K5 front, lower winding of TK, Ll front, lamp for value 1, battery. Relays TE, TI, and TK operate to register a carry over of 3 to the tens denomination and lamp l lights.

The contacts of the relays TI, TD, TH, TK and TE form a contact chain, as shown in Fig. 4 for relays ZT, YT and KT. Any one of the carry over relays operated, causes the operation of ZT, any two together the operation of YT, any three together the operation of both YT and ZT on their second windings in series, any four operate XT and all five together operate XT and Z'I. in series.

The relay chain for the tens digit, Fig. 5 is arranged somewhat difierently from that for the units digit. Relays I, J, K and L do not repre sent any tens digit. This is because the number 9 in radix ten is the highest number with a single digit and is equivalent to 1001 in radix two. Therefore, the four relays I, J, K and L must be used for the number 9 and in consequence contacts of these relays do not appear in the chain. Several of the relays A-H represent numbers having an odd tens digit and the carry over total from the units may be odd. These odd digits are therefore considered as consisting of an even digit plus 1, e. g. H represents 0+1 and D represents 4+1 whilst in an odd carry over total the 1 is represented already by ZT. An auxiliary tens contact chain is formed for relays ST, RT and QT. (Fig. 4) to add up the figures 1 so obtained, and consists of contacts of D representing (4+1), of G representing 2+1, of C representing 0+1, H representing 0+1 and ZT representing 1 in the carry over figure. This chain operates relays ST, RT and QT in such a way that ST represents 1, RT represents 2 and QT represents 4.

Thus in Fig. 5 all odd digits in the tens addition are replaced by one odd digit stored on ST, and even digits stored on YT, XT, RT and QT. The remainder of the chain of Fig. 5 is formed on the same plan as the units chain. Contacts of ST act like those of L in the units chain. Contacts of RT and YT are connected so as each to add 2, those of QT and KT to add 4, contacts of A (representing 2048) to add 4, contacts of D (256) to add 4 (=51), contacts of F (64) to add 6, contacts of G (32) to add 2 (=3-1), of E (128) and B (1024) also to add 2.

Carry over relays HR, HQ, HX, HA, HD and HF are inserted in the chain to register the carry over to the hundredths denomination. A third winding on relay HF and carry over relay for contacts of B, E, G and F are avoided by locating these contacts at the commencement of the chain. The maximum carry over figure from tens to hundreds is 2, but as not many contacts are required it is not worth while to combine the carry over relays as was done for the units chain.

Taking as an example the same number entered as was referred to above, a circuit is closed over 1 order.

17 contacts of the three carry over relays TE, TI and TK as follows (Fig. 4): Ground, TI! front, T202 back, TH! back, TK2 front, TE3 front, lower winding of YT, upper winding of ZT to battery. Relays YT and ZT operate. A circuit is closed from ground, DH back, G9 front, C9 front, H8 back, ZT3. front, windings of RT and ST to battery. Relays RT and ST operate. A

circuit is then closed from ground, (top of Fig.

135 back, E3 front, G1 front, F8 back, D8 back, A4 front, XT5 back, QT5 back, Y'ISfront, upper winding HR, RT] front, ST2 front, lamp 3 to battery. The lamp for tens digit 3 lights and relay HR operates to register a carry over of l to the hundreds denomination.

A contact chain is formed from contacts of the carry over relays HF, HD, HA, HX, HQ, and HR. for relays ZH and YH (Fig. 4) by means of which ZH may be operated to store a carry over of 1 and YB a carry over of 2. I

An auxiliary hundreds chain is formed to sum the figures 1 obtained from the odd hundreds digits and from a tens carry over figure of 1. Contacts of relays C, E and ZH appear in this chain and operate relay SH for 1, RH for 2 or RH and SH in series for 3 (Fig. 4). The main hundreds chain (Fig. 4) is now formed on the same plan as for the tens and units chains. Contacts of SH represent an addition of 1, contacts of RH and YH each an addition of 2, contacts of C an addition of 4 (51) and of D an addition of 2. Only one carry over relay MR is required since the .chain is so short.

Taking again the same radix number as before 101010101011, the tens carry over relay HR completes a circuit from ground, HFI back, HDI back, HA1 back, HXI back, I-IQI back, I-IRI front for relay ZH which operates. A circuit is then closed from ground, Cll front, E6 front, ZH3 front for relays RH and SH in series, which relays operate. A circuit is then .closed from ground, Dl2 back, C5 front, YH3 back, R113 front, 8H4 front for lamp No. 7 which lights.

Finally the thousands chain is formed from contacts of relays A and B and of the hundreds carry over relay MR. Contacts of MR operated add 1, contacts of A operated add 2 and contacts of B operated add 1. Taking the same example as before a circuit is closed from ground, B6 back, A'I front, MR3 back for lamp No. 2. The complete number displayed is thus 2731. The total time needed to display this complete number is inappreciable to the eye and is estimated to be one fifth of a second maximum.

It will be clear that it does not matter for the final result whether the relays A-L are operated simultaneously or in any particular Thus the radix two number could be entered digit by digit, either commencing with the digit of highest denomination or with the digit of lowest denomination or in any order. The circuits readjust themselves to indicate the radix ten number corresponding to the radix two number set up at the time.

What is claimed is:

1. Calculating equipment comprising means for entering therein by individual digits a number expressed in radix two, electrically operated means for automatically separating said number into numbers of predetermined magnitudes the sum of which is equal to or less than the entered number, registering means for registering said magnitudes, and circuits closed by said registering means for rendering available the number in radix ten which is equivalent to the sum of said series of numbers of predetermined magnitudes.

2. Calculating equipment as claimed in claim 1 in which the means for automatically separating said number into a series of predetermined magnitudes comprises means for performing an attempted series of subtractions of numbers expressing said magnitudes in decreasing order of magnitude, commencing with a subtraction from said first mentioned number and continuing with subtractions from either the said first mentioned number or from the remainder resulting from a previous subtraction according as the previous subtrahend was greater or less than the minuend.

3. Calculating equipment as claimed in claim 1 in which a set of storage elements is provided one for each of said magnitudes, each of said elements. being placed in one condition or another to register the presence or absence of its corresponding magnitude in the said series of magnitudes.

4. Calculating equipment as claimed in claim 1 in which said registering means comprises a plurality of storage elements and each of said storage elements serves to register by its condition the value zero or one for the digits of each number of said series of numbers of predetermined magnitudes and said storage elements close contacts in chain circuits which indicate the sum of the said series of numbers of predetermined magnitudes expressed in radix ten.

5. Calculating equipment as claimed in claim 1 in which said registering means comprises a plurality of storage elements and each of said storage elements comprises a relay for each denomination of the digits of the number to be entered and serves to register by its condition the value 0 or 1 for a digit of said first mentioned radix two number, the said relays being operated for digital values of 1, and in which said registering means comprises a relay for each of the series of numbers of predetermined magnitudes and contacts of said relays are arranged in chain circuits to render available the digits of the equivalent number in radix ten by applying ground to appropriate wires to represent the different digits.

6. A calculating apparatus comprising means for entering thereinto a number expressed in radix two by individual digits, means for performing an attempted series of subtractions of a series of predetermined numbers expressing magnitudes in decreasing order of magnitude and for carrying out said subtractions where possible comprising a first group of relays including one relay for each digit of the number entered, a second group of relays including one relay for each digit of the number entered, a second group of relays including one relay for each digit except the units digit for the numbers to be subtracted and a plurality of diiference relays operated by circuits including the contacts of said first and second group of relays, means to register whether or not the subtraction of each successive predetermined number is possible, and means controlled by said registering means and said difference relays to express the said radix two number as the sums of the numbers successfully subtracted and the remainder, respectively.

'7. A calculating apparatus comprising means to enter thereinto a number expressed in radix two, electrical means for automatically attempting a succession of subtractions of a series of predetermined numbers expressing diminishing magnitudes from said entered number and for carrying but said subtractions'where possible,

means to'register whether or not a subtraction is possible each time a subtraction is attempted, means controlled by said registering means to cause succeeding subtractions to be made either from said first mentioned number or from the remainder resulting from a previous subtraction according as the previous subtrahend was greater or less than the minuend, means to store the remainder after the last subtraction and means controlled by said registering means and said remainder storing means to add the number successfully subtracted and the remainder after the last subtraction and to represent the sum in to be subtracted are io A, 10 B, 10 0,

10 D, Io A, 10 B, lo C, iIWD, IO' A. 10 3, 10"- C,' 10"- D, and a series of successive terms with decreasing powers of 10 until a. remainder expressed "in the terms 10A, 10B, 10C, 10D is obtained; where n equals the number of digits in the first subtracted number and A, B, C, D are integers arranged indescending order of magnitude, which integers, either alone or in selected combinations, have the values 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

GEORGE CLIFFORD HARTLEY.

JOHN RIDD GOULD.

LESLIE BAINES HAIGH.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS 0 Number Name Date 2,191,567 Hofgaard Feb. 27, 1940 2,318,591 Couffignal May 11, 1943 2,364,540 Luhn Dec. 5, 1944 1.25 FOREIGN PATENTS Number Country Date 410,129 Great Britain May 9, 1934

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