PROCEEDINGS OF THE I.R.E.

Machine Aid for Switching Circuit Design *CLAUDE E. SHANNONt, FELLOW, IRE AND EDWARD F. MOOREt, ASSOCIATE, IRE

Summary-The design of circuits composed of logical elementsmay be facilitated by auxiliary machines. This paper describes onesuch machine, made of relays, selector switches, gas diodes, andgermanium diodes. This machine (called the relay circuit analyzer)has as inputs both a relay contact circuit and the specifications thecircuit is expected to satisfy. The analyzer (1) verifies whether thecircuit satisfies the specifications, (2) makes systematic attempts tosimplify the circuit by removing redundant contacts, and also (3) ob-tains mathematically rigorous lower bounds for the numbers andtypes of contacts needed to satisfy the specifications. A specialfeature of the analyzer is its ability to take advantage of circuitspecifications which are incompletely stated. The auxiliary machinemethod of doing these and similar operations is compared with themethod of coding them on a general-purpose digital computer.

INTRODUCTION

(CSOME OPERATIONS which assist in the design ofrelay circuits or other types of switching circuitscan be described in very simple form, and machines

can be constructed which perform them more quicklyand more accurately than a human being can. It seemspossible that machines of this type will be useful tothose whose work involves the design of such circuits.The present machine, called the relay circuit analyzer,

is intended for use in connection with the design of twoterminal circuits made up of contacts on at most fourrelays. The principles upon which this machine is basedare not limited to two terminal networks or to fourrelays, although an enlarged machine would requiremore time to operate. Each addition of one relay tothe circuits considered would approximately doublethe size of the machine and quadruple the length oftime required for its operation. This type of machine isnot applicable to sequential circuits, however, so it willbe of use only in connection with parts of the relay cir-cuits which contain contacts, but no relay coils.

OPERATION OF THE MACHINE

The machine, as can be seen from Fig. 1, containssixteen 3-position switches, which are used to specifythe requirements of the circuit. One switch correspondsto each of the 24= 16 states in which the four relays canbe put. Switch number two in the upper right handcorner, for instance, is labeled W+X+ Y'+Z, whichcorresponds to the state of the circuit in which the re-lays labeled W, X, and Z are operated, and the relaylabeled Y is released.The three positions of this switch correspond to the

requirements which can be imposed on the condition ofthe circuit when the relays are in the corresponding

* Decimal classification: 621.375.2XR257. Original manuscriptreceived by the Institute, May 28, 1953; revised manuscript receivedJune 29, 1953.

t Bell Telephone Laboratories, Inc., Murray Hill, N. J.

state. Since any single relay contact circuit assumesonly one of two values (open or closed) the inclusion ofa third value (doesn't matter, don't care, or vacuous,as it has been called by various persons) merits someexplanation. If the machine, of which the relay circuitbeing designed is to be a part, only permits these relaysto take on a fraction of the 2" combinations of which nrelays are capable, then it will not matter what thecircuit does in the excluded states. The user indicatesthe optional nature of these requirements by placingthe corresponding switches in the "don't care" positions.With these options, there is a wider range of circuitssatisfying the requirements, and hence more likelihoodthat a circuit with fewer contacts will suffice. The six-teen 3-position switches thus permit the user not onlyto require the circuit under consideration to have ex-actly some particular hindrance function, but alsoallow the machine more freedom in the cases where thecircuit need not be specified completely.

In order to make a machine of this type to deal withn relays (this particular machine was made for the 'casen = 4), 2n such switches would be required, correspond-ing to the 2" states n relays can assume. In each of thesestates the circuit can be either open or closed, so thereare 22" functionally distinct circuits. But since eachswitch has 3 positions, there are 32" distinct circuit re-quirements specifiable on the switches, which in thecase n=4 amounts to 43,046,721. Thus, the number ofproblems which the analyzer must deal with is quitelarge, even in the case of only four relays.The left half of the front panel of the machine (see

Fig. 1) is a plugboard on which the circuit being ana-lyzed can be represented. There are three transfers fromeach of the four relays, W, X, Y, and Z brought out tojacks on this panel, and jacks representing the terminalsof the network are at the top and bottom. Using patchcords, it is possible to plug up any circuit using atmost three transfers on each of the four relays. Thisnumber of contacts is sufficient to give a circuit repre-senting any switching function of four variables.

If the specifications for the circuit have been puton the sixteen switches, and if the circuit has been puton the plugboard, the relay circuit analyzer is thenready to operate.With the main control switch and the evaluate-com-

pare switch both in the "evaluate" position, pressing thestart button will cause the analyzer to evaluate the cir-cuit plugged in, i.e. to indicate in which of the states thecircuit is closed by lighting up the corresponding indi-cator lamps.Turning the evaluate-compare switch to the "com-

pare" position, the analyzer then checks whether the

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Shannon and Moore: Machine Aid for Switching Circuit Design

Fig. 1-View of front panel of the relay circuit analyzer.

circuit disagrees with the requirements given on theswitches. A disagreement is indicated by lighting thelamp corresponding to the state in question. If a switchis set for closed and the actual circuit is open in thatstate, or vice versa, a disagreement is indicated, but nodisagreement is ever registered when the switch is setin the "don't care" position, regardless of the circuitcondition. The compare position, while it gives informa-tion equivalent to that given in the evaluate position,gives it in a form more convenient for noticing errors.

After a circuit has been found which agrees entirelywith the requirements, the main control switch is thenturned to the "short test" position and the start buttonis pressed again. The machine then determines whetherany of the contacts in this circuit could have beenshorted out, with the circuit still satisfying the require-

ments. The machine indicates on the lamps beside thecontacts which ones have this property.

It may be surprising to the reader that anyone wouldever need the assistance of a machine to find a contactwhich could be shorted out without affecting its circuit.While this is certainly true of simple examples, in morecomplicated circuits such redundant elements are oftenfar from obvious (particularly if there are some statesfor which the switches are in the "don't care" position,since the simplified circuit may be functionally dif-ferent from the original one, as long as it differs pnly inthe "don't care" state). It is often quite difficult to seethe simplification in these cases.The analyzer is also helpful in case the circuit being

analyzed is a bridge, because of the complications in-volved in tracing out all paths in the bridge. The circuit

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PROCEEDINGS OF THE I.R.E.

shown in Fig. 2 is an example of a circuit which was notknown to be inefficiently designed until put on theanalyzer. It determined in` less than two mi-nutes (in-cluding the :time required to plug the circuit into theplugboard) that one of the contacts shown can beshorted out. How likely would a human being be to solvethis same problem in the same length of time?

After the short test has been performed, putting themain control switch in the "open test" position permitsthe analyzer to perform another analogous test, thistime opening the contacts one at a time.

w

Fig. 2-The relay circuit analyzer was able to simplify this circuit,removing one contact, in less than two minutes total time. Canyou do as well?

These two particular types of circuit changes were

chosen because they are easy to carry out, and wheneversuccessful, either one reduces the number of contacts re-

quired. There are other types of circuit simplificationwhich it might be desirable to have a machine perform,including various rearrangements of the circuit. Thesewould have required more time as well as more equip-ment to perform, but would probably have caused themachine to be more frequently successful in simplifyingthe circuit. Using such techniques, it might be possibleto build a machine which could design circuits efficientlystarting from basic principles, perhaps by starting with a

complete Boolean expansion for the desired functionand simplifying it step by step. Such a machine wouldbe rather slow (unless it were built to operate at elec-tronic speeds, and perhaps even in this case), and notenough planning has been done to know whether such a

machine is practically feasible. However, the fact thatsuch a machine is theoretically possible is certainly ofinterest, whether anyone builds one or not.

Another question of theoretical interest is whether a

logical machine could be built which could design an

improved version of itself, or perhaps build some ma-

chine whose over-all purpose was more complicatedthan its own. There seems to be no logical contradictioninvolved in such a machine, although it will requiregreat advances in the general theory of automata beforeany such project could be confidently undertaken.To return to the relay circuit analyzer, a final opera-

tion which it performs is done with the main controlswitch in the prove position. Pressing the start buttonand moving the other 4-position switch successivelythrough the W, X, Y and Z positions, then certain of theeight lamps W, W', X, X', Y, Y', Z, Z' will light up.

The analyzer has carried out a proof as to which kinds

of contacts are required to synthesize the function usingthe method of reduction to functions of one variable,which will be explained in a forthcoming paper. Theanalyzer here ignores whatever circuit has been pluggedin the plugboard, and considers only the function speci-fied by the sixteen 3-position switches. If every circuitwhich satisfied these specifications requires a back con-tact on the W relay, the W' light will go on, etc.

If, for instance, seven of the eight lights are on, anycircuit for the function requires at least seven contacts,and if there is, in fact, a circuit which uses just seven,the machine has in effect, given a complete proof thatthis circuit is minimal. Circuits for which the machinecan give such a complete proof are fairly common, al-though there are also circuits (which can be shown tobe minimal by more subtle methods of proof) which thismachine could not prove minimal. An example is thecircuit of Fig. 2. This can be simplified by the analyzerto a circuit of nine contacts, but in the prove positionthe analyzer merely indicates that at least eight contactsare necessary. It can be shown by other methods thatthe 9-contact circuit is minimal. But at any rate, theanalyzer always gives a mathematically rigorous lowerbound for the number of contacts.The small size and portability of this machine depends

on the fact that a mixture of relay and electronic circuitelements were used. The gas diodes are particularlysuited for use where a small memory element having anassociated visual display is required, and the relays andselector switches are particularly suited for use wherethe ability to sequence and interconnect, using only asmall weight and space, is required. In all, the relay cir-cuit analyzer uses only 24 relays, 2 selector switches,48 miniature gas diodes, and 14 germanium diodes asits logical elements.

It may be of interest to those familiar with generalpurpose digital computers to compare this method ofsolution of this problem on such a small, special-purposemachine with the more conventional method of codingit for solution on a high-speed general-purpose com-puter. One basic way in which the two methods differis in the directness with which the circuits beinganalyzed are represented. On a general-purpose com-puter it would be necessary to have a symbolic descrip-tion of the circuit, probably in the form of a numericalcode describing the interconnections of the circuit dia-gram, and representing the types of contacts that occurin the various parts of the circuit by means of a list ofnumbers in successive memory locations of the com-puter. On the other hand, the relay circuit analyzer rep-resents the circuit in a more direct and natural manner,by actually having a copy of it plugged up on the frontpanel.

This difference in the directness of representation hastwo effects. First, it would be somewhat harder to usethe general-purpose computer, because the steps oftranslating the circuit diagram into the coded descrip-tion and of typing it onto the input medium of the

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Shannon and Moore: Machine Aid for Switching Circuit Design

computer would be more complicated and lengthy thanthe step of plugging up a circuit directly. The secondeffect is in the relative number of logical operations(and hence, indirectly, the time) required by the twokinds of machines. To carry out the fundamental stepin this procedure of determining whether the given cir-cuit (or some modification of it obtained by opening orshorting a contact) is open or closed for some particularstate of the relays, requires only a single relay operatetime for the relay circuit analyzer. However, the carry-ing out of this fundamental step on a general-purposedigital computer would require going through severalkinds of subroutines many times. There would be severalways of coding the problem, but in a typical one ofthem the computer would first go through a subroutineto determine whether a given contact were open orclosed, repeating this one for each contact in the circuit,and then would go through another subroutine once foreach node of the network. Altogether this would prob-ably involve the execution of several hundred orders onthe computer, although by sufficiently ingenious codingthis might be cut down to perhaps 100. Since each orderof a computer takes perhaps 100 times the duration of asingle logical operation (i.e., a pulse time, if the com-puter is clock-driven), actually what takes 1 operationtime on one machine takes perhaps 10,000 on another.

Since 10,000 is approximately the ratio between thespeed of a relay and of a vacuum tube in performinglogical operations, this gain of about 10,000 from thedirectness of the representation permits this relaymachine to be as fast at this kind of problem as ageneral-pupose electronic computer.

This great disparity between the speeds of a gen-eral-purpose and of a special-purpose computer is nottypical of all kinds of problems, since a typical problemin numerical analysis might only permit of a speed-upby a factor of 10 on a special-purpose machine (since

multiplications and divisions required in the problemuse up perhaps a tenth of the time of the problem).However, it seems to be typical of combinatorial prob-lems that a tremendous gain in speed is possible by theuse of special rather than general-purpose digital com-puters. This means that the general-purpose machinesare not really general in purpose, but are specialized insuch a direction as to favor problems in analysis. It iscertainly true that the so-called general purpose ma-chines are logically capable of solving such combina-torial problems, but their efficiency in such use is defi-nitely very low. The problems involved in the design ofa general-purpose machine suitable for a wide varietyof combinatorial problems seem to be quite difficult,although certainly of great theoretical interest.

CONCLUSIONSAn interesting feature of the relay circuit analyzer

is its ability to deal directly with logical circuits interms of 3-valued logic. There would be considerableinterest in techniques permitting easy manipulation onpaper with such a logic, because of its direct applicationto the design of economical switching circuits. Eventhough such techniques have not yet been developed,machines such as this can be of value in connectionwith 3-valued problems.Whether or not this particular kind of machine ever

proves to be useful in the design of practical relay cir-cuits, the possibility of making machines which canassist in logical design procedure promises to be of valueto everyone associated with the design of switching cir-cuits. Just as the slide rule and present-day types ofdigital computers can help perform part of the routinework associated with the design of linear electricalnetworks, machines such as this may someday lightenmuch of the routine work associated with the design oflogical circuits.

C..A.3D

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