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### 5 Relay Computers: A D Booth

Mr. M.V.Wilkes introduced Miss K. Britten who presented the paper.

### Summary.

A brief description is given of Relay Computers under construction or in operation and this is followed by a short discussion on the place of relay machines in large scale computing.

### Scale of Notation.

It is interesting to consider first the various scales of notation which have been used in relay machines.

The decimal scale as such is obviously inefficient since 10 storage elements would be needed for each digit. Moreover, addition in the decimal scale is a complicated process and built-in addition tables must be provided.

A more economical use of the storage elements can be attained by representing decimal digits by their equivalent
in the binary scale. This is known as the *Binary Decimal* scale and is used by Aiken in his Mark II
relay computer. It has the disadvantage that addition is still a complicated process and although it is possible to
add *directly* in Binary Decimal scale, 7 relays are needed for each digit.

This complication can be avoided by representing numbers in the true *Binary Scale* since addition
in them consists of the three operations

0 + 0 = 0 0 + 1 = 1 1 + 1 = 10

These can be performed directly using only two relays per digit. The conversion of numbers from decimal to binary scale and back again presents no difficulties as it can be performed by logical operations, involving no addition to the arithmetic unit of the machine. The Automatic Relay Computer designed by Dr. Booth, uses Binary Scale.

A third modification is the *Bi-quinary Scale* used by Bell Telephones in their computer.
In this system each decimal digit is represented by two digits.
The quinary digit has one of the values from 0 to 4 and the binary digit has the value 0 or 5.
The sum of the Binary and Quinary digits is equal to the decimal digit,
and 5 relays are used to represent the Quinary and 2 the Binary digits.
The sketch indicates which relays are operated in representing the number 93.

Quinary Digit Binary Digit 0 1 2 3 4 0 5 9 x x 3 x x

This system is, of course, wasteful by comparison with either the Binary Decimal or the Binary Scale. The following table gives the number of relays required to store a 6 figure decimal number in the various scales:-

Decimal 60 Binary Decimal 24 Binary 20 Bi-quinary 42

The Bi-quinary scale has the advantage, however, that a certain amount of checking is possible by making sure that one and only one relay is operated in each number.

Another scheme for representing numbers was suggested by Stibitz and is known as the *excess three* scale.
A decimal digit d is represented by the binary equivalent of d + 3.
This is claimed to simplify the design of the machine but the system has never been used for a relay computer.

### Relay Computers.

Relay Computers in America fall into two main groups - those built by the Bell Telephone Company of New York and the machines built by Professor Aiken at the Harvard Computation Laboratory. The Bell machines will be described first as they were the earliest in operation.

### The Bell Telephone Complex Number Calculator.

The first general purpose relay computer in operation was the Complex number Calculator built for the Bell Telephone Company by Stibitz a few years before the war. This machine will add, subtract, multiply and divide complex numbers and will present results in printed form. It is not a fully automatic computer as the term is now understood, since it is limited in operation to the four arithmetic processes mentioned and data has to be inserted by hand. The machine is interesting for two reasons, however, it has operated for 10 years and apparently gives little trouble from dirty or worn contacts; and it has a system of multiple input and output stations. At 3 different points in the Bell Labs, there are teletype stations from which it is possible to transmit data to the machine and at which the answers will be printed. There is also an ingenious control circuit which prevents two people from trying to use the machine at the same time.

### The Bell Telephone Computing Machine.

The first completely automatic relay computer to be put into operation was the Bell Telephone Computing Machine. This computer was built in duplicate, both units being intended for U.S. Government research establishments.

As mentioned above, it works in bi-guinary scale to an accuracy of 7 decimal digits and has a floating decimal
point between the limits 10^{-19} - 10^{19}. Addition is performed by means of a built in addition
table and subtraction is effected by adding the complement of the number. The machine has automatic multiplication,
division and square-rooting.

Input and output is via teletype tape and printer. The machine has 12 input tapes of which 5 are routine tapes and are used for inserting orders, 6 are table tapes which can be used for inserting the values of any mathematical function needed in the calculation. The remaining one is known as the problem tape and is used for the insertion of initial data such as boundary values etc.

The code of orders which the machine can carry out consists of orders governing the arithmetic operations, the transfer of numbers and a discrimination order which makes it possible to distinguish whether a number is positive or negative.

The memory or storage capacity consists of 44 relay registers. Only 30 of these are available for general storage, however; the remaining 14 are associated with the arithmetic unit. This restriction in memory capacity is one defect of the Bell Computer and those who have had experience of preparing problems for the machine mention it as a serious limitation.

With regard to speed of operation, this is the slowest machine which has been built with the possible exception of Aiken's A.S.C.C. The time required to decode an order is 2 seconds, addition takes ⅓ second, multiplication 1 second, division and square-rooting 5 seconds and printing 3 seconds. This lack of speed is the price which must be paid for the checking system which is the most elaborate to have been built into any machine. Numbers are checked at each stage to make sure that one and only one relay is operated in both the Binary and Quinary digits. This scheme is not completely foolproof but it fails only when two relays mal-operate simultaneously and cancel each other.

A note on the size of the machine may be of interest. It contains 9,000 relays and 50 pieces of teletype, occupies a floor space of 1000 sq.feet and weighs 10 tons.

It has been used for a variety of problems including the solution of sets of linear equations, the solution of partial differential equations, the calculation of a table of the binomial function and the summation of Fourier and power series.

### The Harvard Machines.

The first machine built by Professor Aiken at the Harvard Computation Laboratory was the Automatic Sequence Controlled Calculator (A.S.C.C.).

This machine will not be described in detail for two reasons. Very complete descriptions have already appeared in print and, in any case, it is not a true relay machine. Relays are used only for the control circuits and for switching operations. One point might be noted, however. As originally designed this machine had no faculty for discrimination but this was found to be such a handicap when programming iterative sequences that a special unit was added for this purpose.

### The Mark II Relay Computer.

Aiken's second machine - the Mark II Computer is a true relay machine in that the arithmetic unit is built of relays and they are also used for the storage of numbers.

This machine works in Binary-Decimal scale to an accuracy of 10 decimal digits and has a floating decimal point. Two built-in addition tables are provided and form automatic multipliers. There is, however, no provision for automatic division.

Input and output is via punched tape and teleprinter and the machine has 4 input tapes.
The time required to insert a number or order into the machine is ⅓ second.
Addition takes ½ second, and multiplication 1 second.
The routines for calculating 1/x, 1/√x , 1og(x), e^{x}, cos(x), tan^{-1}(x)
are permanently inserted in the machine and do not have to be specified in full in the programme.
These operations take between 5 and 12 seconds per number.

No checking is provided except such as can be included in the programme. The coding of problems for this machine is rather complicated as, in order to use the machine to best capacity, all four multipliers must be working simultaneously. Moreover, the high speed storage capacity is small.

An interesting feature is that the printed results of the machine can be reproduced directly, thereby eliminating the necessity for type setting and proof reading when tables are to be published.

The Mark II calculator must be the largest relay computer in existence; it contains 13,000 relays, most of which were specially made at a cost of $15 each.

### English Relay Computers.

There are only two projects in England engaged in building relay computers. The first of these is at the Royal Aircraft Establishment, Farnborough, but as this machine will be described by Dr. Hollingdale, nothing more will be said about it here.

### The Automatic Relay Computer.

The second relay project in England is that under the direction of Dr. A.D.Booth of Birkbeck College. This project is concerned with the construction of the Automatic Relay Computer (A.R.C.) at the laboratories of the British Rubber Producers' Research Association, Welwyn Garden City.

This machine is a general purpose computer operating on numbers expressed in the binary scale to accuracy of 20 binary (6 decimal) digits and working with a fixed binary point.

Input and output is on binary-decimal scale via punched tape and teleprinter and the machine is programmed to perform the conversions to and from binary scale. Data can be fed in at the rate of 5 numbers or orders per second.

Addition is done directly and takes 1/50th second. Negative numbers are represented by their complements. Multiplication and division are automatic and take 4 and 2 seconds respectively. The time taken by the control to decode an order is 1/20th second.

A.R.C. differs from the relay machines described so far as it is the only one to possess a suitable high speed memory. This consists of 256 20 digit numbers (together with a sign indication) stored magnetically on a rotating nickel-plated drum. The average time of accession of any number is 1/50th second. This is considerably less than the time required to refer to punched-tape and it is therefore hoped that the overall speed of A.R.C. will be rather higher than that of the Bell Machine or the Mark II calculator.

The code of orders on which A.R.C. operates is very similar to that of the Princeton Electronic Computer. It contains orders governing the arithmetic operations and enabling numbers to be transferred from one part of the machine to another and a discrimination order. One point in which the code differs from that of any other machine is that the transfer and the control transfer orders are all made relative to the memory position containing the order. This means that sub-routines can be inserted into any memory position without modification. Experience has shown that the coding of problems is quite a simple operation. Care must be taken though prevent numbers growing (or shrinking) out of the range of the machine. No checking is provided except such as can be programmed.

The arithmetic unit of this machine has been in working order for 18 months but the memory is not completed and storage space for 8 numbers only is at present available. The machine has been in automatic action computing a table of squares.

As well as the magnetic memory an electro-mechanical memory is to be developed. This will probably eventually be used with the relay arithmetic unit and a faster electronic arithmetic unit built to operate with the magnetic memory.

Dr. Wijngaarden of the Mathematical Centre, Amsterdam, is building a computer rather similar to A.R.C.

### The Place of Relay Computers in High Speed Calculation.

Relays were probably originally used for computing circuits because they form ideal binary elements and are well adapted to multiple gating operations. They are also largely free from the oscillation and feed back troubles associated with valve circuits. It is theoretically possible to design relay circuits which will work immediately on correct assembly. Thus the control circuit of A.R.C., and this is generally thought to be the most complicated part of the machine, was designed, built, and put into operation in only three days.

Most computing machines have standard teletype apparatus for input and output and relays are well co-ordinated in speed with this equipment. This is not true of valves and most designers of electronic machines interpose a faster input and output on magnetic wire between the teletype and the machine.

Generally speaking it is desirable to make a computer as small and simple as possible since it should then be less liable to error. It is possible to build an all purpose relay computer with as few as 400 - 500 relays. A.R.C. is somewhat larger because very few multi-contact relays have been used.

An important consideration with general purpose computers is the provision of an adequate high-speed memory and this has been the chief limitation of relay machines, in the past. Unfortunately no economical electromechanical storage exists. Zuze, working in Bavaria, claims to have produced a form of mechanical storage with a capacity for 1,000 digits in 1 cu.ft., but no authoritative account has been given of this device. It is hoped that the electromechanical memory being developed for A.R.C. will have a capacity of this order.

The use of electronic storage, in conjunction with relays is not ideal, and in any case, if one is content with the speed of relays it is possible to build an electronic machine with only about 50 additional valves to the memory. This machine would have a multiplication time of about ¼ sec. Dr. Booth is developing a machine of this type which he hopes will contain less than 200 valves and have a memory capacity for 200, 32 digit binary numbers.

Probably the most important consideration when considering components for a computer is their reliability, and here relays have distinct disadvantages. Dust in the contacts can cause transient faults which are impossible to detect. It is of course possible to cover the machines and filter the air having access to them but this is costly and inconvenient. Valves do not of course suffer this disadvantage. It is important, however, that the use of thyratrons should be avoided as they are liable to spontaneous, transient breakdown. This has been our experience at Welwyn and the engineers at Princeton have encountered the same difficulty.

An important practical consideration in circuits is the ease with which elements can be replaced. Unfortunately there is no suitable plug-in relay on the market and the replacement of any number of relays is thus tantamount to re-building the machine.

Another disadvantage of relays is that, even when drawing only a small current, their contacts show signs of wear after a time. Spark quenches cannot always entirely prevent this effect.

Despite these defects relay machines can do much useful work in the field of large scale computers and valuable experience on the design of computer circuits can be obtained through working with relays.

The code of A.R.C. was formulated with the idea in mind that it could be transferred directly to an electronic machine and Dr. Booth intends to use it unchanged for the electronic machine he is designing for Birkbeck College, This machine will be used chiefly for crystallographic computations and has been provisionally christened A.P.E.X.C. (All Purpose Electronic X-ray Computer).