Alan Turing

“ We also wish to be able to arrange for the splitting up of operations into subsidiary operations. This should be done in such a way that once we have written down how an operation is to be done we can use it as a subsidiary to any other operation.
These requirements can largely be met by having the instructions on a form of erasible memory, such as the delay lines. This gives the machine the possibility of constructing its own orders; i.e. there is always the possibility of taking a particular minor cycle out of storage and treating it as an order to be carried out. This can be very powerful. ”

“ UNBURY (General Description) . The minor cycle whose position is given in TS 31 is taken to be position of the next instruction.
MULTIP (General Description) . The number in TS 18, 19 is multiplied by the number in TS 20, 21: the result is brought to standard form by shift of decimal point. An error is obtained for the product by using the errors in the given numbers and allowing for rounding off. The result is stored in TS 22, 23.
ADD is analogous to MULTIP.
As an example of a more complicated process, I have chosen the calculation of the value of a polynomial. ”

“ For the majority of purposes we like a form of storage to be erasible, although there are a number of purposes, such as function tables and the greater part of the instruction tables, for which this is not necessary. For the majority of purposes we also like to have a short accessibility time, defining the accessibility time to be the average time which one has to wait in order to find out the value of a stored digit. ”

“ At megacycle frequencies however various difficulties tend to arise. The input capacities of valves prevent us from ignoring the nature of the circuit into which we are working; limiting circuits do not work very satisfactorily: capacities and transit times are bound to cause delays between input and output. These difficulties may be best resolved by bending before the storm. The delays may be tolerated by accepting them and working out a time table which takes them into account. Indefiniteness in output may be tolerated by thinking in terms of ‘classes of outputs’. ”

“ It must be recognized however that other forms of storage are possible, and have important advantages over the delay line type. We should be wise to occupy time which falls free due to any kind of hold-up by researching into these possibilities. As soon as any really hopeful scheme emerges some more systematic arrangement must be made.
We must be ready to make a change over from one kind of storage to another, or to use two kinds at once. The possibility of developing a new and better type of storage is a very real one, but is too uncertain, especially as regards time, for us to wait for it ”

“ Electromagnetic conversion efficiency. The delay line may best be considered as forming an electrical network of the kind usually (rather misleadingly) described as ‘four-pole’, i.e. a network which has one input current and one input voltage which together determine an output voltage and current. Such a network is described by three complex numbers at each frequency. In the case where there is little coupling between the output and input, which will apply to our problem, we may take these quantities to be the input and output admittances and the ‘transfer admittance’. ”

“ Each time a subsidiary operation is required we have to repeat B, BURY, and each time we make a transfer we have to do it in two stages, each of which uses a whole minor cycle of which most is wasted. It is possible to avoid this waste of space by keeping the instruction tables in some abbreviated form, and expanding each table whenever we want it. ”

“ The delay due to transit time may be calculated, in the case of a plane structure, to be 3d (m/2eV) 1⁄2 where m, e are respectively the mass and charge of the electron, V is the voltage of the grid referred to cut-off and d is the grid-cathode spacing. In other words the transit time may be calculated on the assumption that the average velocity of the electrons between cathode and grid is one-third of the velocity when passing the grid. ”

“ This work will go on whilst the machine is being built, in order to avoid some of the delay between the delivery of the machine and the production of results. Delay there must be, due to the virtually inevitable snags, for up to a point it is better to let the snags be there than to spend such time in design that there are none (how many decades would this course take?) . This process of constructing instruction tables should be very fascinating. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself. ”

“ When the multiplicand is taken from TS 3 we have to make some slight modifications to it before it is in suitable condition for adding into the partial sum. We have to convert the periodic signal with period 32 or 34 into a sequence of 64 digits of which 32 form the original content of TS 3, and the rest is a sort of padding. We may call the 32 digits the genuine digits. Those digits of padding which are less significant than the genuine digits are to be all zero, those which are more significant are to be the same as the most significant genuine digit. ”

“ It seems probable that a suitable storage system can be developed without involving any new types of tube, using in fact an ordinary cathode ray tube with tin-foil over the screen to act as a signal plate. It will be necessary to furbish up the charge pattern from time to time, as it will tend to become dissipated. The pattern is said to last for days when there is no electron beam, but if we have a beam scanning one part of the target it will send out secondary electrons which will tend to destroy the remainder of the pattern. ”

“ A trigger circuit, which is shown as an ellipse, differs from a limiting amplifier circuit in that once the inputs have reached the threshold so that it emits one pulse, it will continue to emit pulses until it receives an inhibitory stimulus. ”

“ The notation of the decimal form is such that the content of DL 10 can be passed out onto a card in the usual way and if the card is then listed the digits of the numbers α,m will then appear on the listing paper in the usual way. Or in other words only the first 10 minor cycles of DL 10 are used, and a decimal digit is represented by the minor cycle in which a pulse occurs, and its significance by the position of it within the minor cycle. ”

“ I list below a number of questions which must be answered in our design of delay lines. In order to fix ideas I have added the most probable answers in brackets after each question.
(1) What liquid should be used in the line? (Either mercury or a water-alcohol mixture.)
(2) Should we use a carrier? If so, of what frequency? (Yes, certainly use a carrier. Frequency should be about 10 Mc/s with water-alcohol mixture, but may be higher if desired when mercury is used) .
(3) What should be the clock-pulse frequency? (1 Mc/s) . ”

“ When the pulse recurrence frequency is as high as a megacycle we shall have to be more careful about the design, but we need not fear any real difficulties of principle about working at these frequencies, and with such band widths. The successful working of television equipment gives us every encouragement in this respect. ”

“ In this problem we are likely to be limited by the storage capacity of the machine. If the coefficients in the equations are essentially random we shall need to be able to store the whole matrix of coefficients and probably also at least one subsidiary matrix. If we have a storage capacity of 6400 numbers we cannot expect to be able to solve equations in more than about 50 unknowns. In practice, however, the majority of problems have very degenerate matrices and we do not need to store anything like as much. ”

“ At high frequencies we cannot get a very effective limiting effect at cathode voltage, owing to the fact that the grid must be supplied from a comparatively low impedance source to avoid a large delay arising from input capacity, but on the other hand, in order to get a limiting effect we need a high impedance, high compared with the grid conduction impedance (about 2000 ohms probably) . At high frequencies it is probably better to use a ‘Kipp relay’ circuit. ”

“ Let us first describe the starting device. This merely emits pulses synchronously with the clock from a certain point onwards, on the closing of a switch manually. The switch causes a voltage to rise and this eventually operates a trigger limiter. This starting mechanism sets a pulse running round a ring of valve elements providing the timing within a minor cycle. (Fig. 12, 13) .
In order to check that this circuit is behaving we compare P32 with a signal which should coincide with it and which is obtained in another way, stimulating an SOS signal when there is failure. ”

“ We may also occasionally wish to make connection to a trigger circuit in such a way that stimulus always changes the condition of the trigger circuit, either from stimulation to non-stimulation or vice-versa. ”

“ In cases M, N, R, T, it is only permitted to last for one minor cycle. In case Q it is also only allowed to last for half a minor cycle. In cases O, P the extinguishing signal is CARDEX, which is given by the card reproducer or reader on the final exit of the card, via a trigger-limiter. In case S the signal comes from FINARITH.
The facilities provided under type S are not easily enumerated, because they do not consist of a number of different operations stimulated by different tree valve elements, as for instance applies in the case of the logical processes. ”

“ In the case of the output arrangements we have the full power of the calculator behind us, i.e. we can do the conversion of the information into the required form as an ITO. In the case of the input organ we must go more warily. If we are putting the instruction tables into delay lines, then when the power has been turned off all memory will have been effaced, including the instruction tables. We cannot use instruction tables to get the information back, because the instruction tables are not there. ”

“ When applied to a mixed electrical and mechanical system this states that the velocity produced at the mechanical end by unit voltage at the electrical end is equal to the current produced at the electrical end by unit force at the mechanical end. ”

“ With a square crystal whose side is 1 cm and a frequency of 15 Mc/s this would mean that we get the first zero in the response for a tilt of about 26', The setting is probably not really as critical as this, owing to curvature of the wave fronts. If the crystals are operating in a free medium without the tube this effect is easily estimable and we find that, for crystals sufficiently far apart the allowable angles of tilt are of the order of the angle subtended at one crystal by the other. ”

“ Rather it means that normally the amount of mathematical argument required to get a reliable prophecy of the behaviour of a circuit is out of proportion to the small trouble required to try it out, at any rate if one is in an electrical laboratory. In practice one compromises with a rough mathematical argument and then follows up with experiment. ”

“ It can be used to supply all the trigger limiters. The trigger circuit Q should be tripped by the combination of pulse from P and continuous input, and will itself trip R. The arrangement of two trigger circuits prevents any danger of half-pulse outputs, which we are most anxious to avoid. In order that there might be a half-pulse output the trigger circuit Q would have to remain near its unstable state of equilibrium for a period of time of 1 μs. In order that this may happen the magnitude of the continuous input voltage has to be exceedingly finely adjusted ”

“ The electron beam brings the charge density back to a standard value and the charge lost by the mosaic registers itself through its capacity to a ‘signal plate’ behind the mosaic. The information stored in this way on an iconoscope, using a 500 line system, corresponds to a quarter of a million digits. ”

“ If we like to consider LC as the analogue of a computer then CA must be considered a desk calculating machine. It carries out the four fundamental arithmetical processes (with possible exception of division, see p. 27) , and various others of the nature of copying, substituting, and the like. To a large extent these processes can be reduced to one another by various roundabout means; judgment is therefore required in choosing an appropriate set of fundamental processes. ”