# Proposed Electronic Calculator/Chapter 11

​11. Details of Logical Control.
In this section we shall describe circuits for the logical control in terms of the circuit elements introduced in § 5. It is assumed that § 5, 6 are well understood.
The main components of LC are as follows:—
(1) A short storage (like a TS) called current data CD. This contains nothing but the appropriate instruction number IN, i.e. the position of the next instruction to be carried out.
(2) A short storage called current instructions CI. This contains the instruction being or about to be carried out.
(3) A tree for the selection of a particular delay line, with a view to finding a particular instruction.
(4) Timing system for the selection of a particular minor cycle from a delay line.
(5) Timing system for the selection of particular pulses from within a minor cycle.
(6) Arrangements for controlling CA, i.e. for passing instructions on to CA.
(7) Arrangements for the continual change of the contents of CD, CI.
(8) Timing arrangements for LC itself.
(9) Starting device.
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. This forms one of the monitoring devices. We are not showing many of them in the present circuits (Fig. 14).
The timing system for the selection of minor cycles is quite simple, consisting chiefly of a ‘slow counter’ SCA, which counts up to 255 in the scale of 2, keeping the total in a delay line of length 8. The pulses counted are restricted to appearing at intervals which are multiples of eight. As shown (Fig. 15) it is counting the pulses P 10. The suppression of the outputs at P 9 prevents undesirable carries, from the most significant digit to the least.
The information in CD and CI being in dynamic (time) form is not very convenient for control purposes. We therefore convert this information into static form, i.e. we transfer it on to trigger circuits (Fig. 16).
​It will be convenient to make use of a symbolic notation in connection with the valve circuits. We write A & B (or manuscript A & B) to mean ‘A and B’. If A and B are thought of as numbers 0 or 1 then A & B is just AB. We write A v B for ‘A or B’. With numbers AvB is 1-(1-A)(1-B). We also write ~A (manuscript ~A) for ‘not A’ or 1-A. Other logical symbols will not be used. Where a whole sequence of pulses is involved, it is to be understood that these operations are to be carried out separately pulse by pulse. We shall combine these symbols with the symbol + which refers to the operations of the adder. Thus for example (A + (P3 v P4))& -P5 means that we take the signal A and add to it a signal consisting of pulses in positions 3 and 4 and nowhere else (addition in the sense of the adder circuit), and that we then suppress any pulses in position 5, as in Fig. 17. We will also abbreviate such expressions as P5 v P6 v P7 v . . . P19 to P5-19, and expressions such as A & P14-18 to A 14-18.
In circuit diagrams we have the alternatives of showing the logical combinations by formulae or by circuits. There is little to choose but there may be something to be said for an arrangement by which purely logical combination is not shown in circuit form, in order that the circuits may bring out more clearly the time effects.
We have agreed that there shall be two kinds of instructions, A and B. These are distinguished by CI 3. The standard forms for the two types of instructions are:
Type A. Carry out the CA operations given by digits CI 5-32, and construct a new CD according to the equation CD = (CD’ + P19) & - P17.
Type B. Construct a new CD according to the equation CD = CI 17-32. Pass the old CD into TS 13.
CD’ here represents the old CD. The significance of the formula for CD in case A is this. Normally it is intended that after an operation of type A the next instruction to be followed will be that with the next number, and it might be supposed therefore that the formula CD = CD’ + P17 would apply. Actually we deviate from this simple arrangement in two ways. Firstly we find it convenient to have a facility by which an instruction may be taken from a TS, viz. TS 6: this has considerable time saving effects. The convention is that a digit 1 in column 17 indicates that the next instruction is to be taken from TS 6. This will involve our having only the digits CI 18-32 available to indicate normal positions for instructions and would suggest that the formula should be CD = CD’ + P18. However if we did this we should always be obliged to have orders of type B in TS 6, for if we had an order of type A we should find that we had to go on repeating that order. If however we have the formula CD = (CD’ + P18) & -P17 we can obey an instruction in TS 6 and then revert to the instruction given by CI 18-32; a much more convenient arrangement. It remains to explain why we have P19 rather than P18. This is due to the fact that we wish to avoid the necessity of waiting a long time for our instructions. If the equation were the one with P18 it would mean that the next instruction to be obeyed, after one of type A, is always adjacent to it in time. This would mean that even with the shortest CA operations the next instruction would have gone by before we were ready to apply it; we should always just miss the boat. By putting P19 instead of P18 we give ourselves an extra minor cycle of time which is normally just what we need. In order that the consecutive instructions may be consecutively numbered in spite of this it is best to adopt a slightly unconventional numbering system for the minor cycles (see Fig. 19).
​A number of trigger circuits are employed to keep track of the stages which the various processes have reached at any moment. The most important of these are listed below with a short description of the functions of each.
OKCI. This is stimulated when the new instruction has been found and is available at the input of CI, and the CA operations belonging to the last instruction have been carried out. Stimulation begins simultaneously with stimulation of P1, and ends on a P32. The end of OKCI has to wait for the gating of CD, indicating that the new CD is available at its input.
OKCA. Only applies in case A and indicates that the CA operations have been finished.
OKCK. Indicates that we may now begin to look for the next instruction with a view to putting it into CI. It is stimulated when OKCI is extinguished, and is itself extinguished when the new CI has been found.
We may now describe the time cycle of LC. Let us begin at the point where OKLK is stimulated indicating that the search for the new CI may now begin, because we have finished with the old one and information for finding the new one is now available in CD. The new CI is determined by digits 17-32 of CD. Of these digits 23-32 determine the delay line and 18-22 determine the minor cycle within the delay line. A digit 1 in column 17 indicates that the order is to be taken from TS 6 instead of from the longer delay lines. This digit is erased whenever we obey an instruction of type A. Digits 23-32 are set up on trigger circuits and operate via trees as described below. Digits 18-22 determine the time at which we must take the output of the delay line. We compare these digits with the output of the slow counter SCA (Fig. 15) and when they agree we know that the right moment has come. It is convenient to arrange that the slow counter is always one minor cycle ahead of time, so as to give us time to organise ourselves before taking the required output. As has been mentioned the order of the digits in CD is arranged rather unconventionally in order to put consecutively numbered minor cycles in alternate positions; this has time saving effects. The required minor cycle now passes into CI and the signal OKSS is given; OKLK is suppressed. When the CA operations belonging to the last instruction have been finished OKCA is stimulated and with it OKCI. We are now able to initiate any new CA operations (case A) and to set up the new CD. When this has been done we have finished with CI and suppress OKCI, which automatically stimulates OKLK beginning the cycle over again (Figs. 22, 22a).
The digits 23-32 determine the delay line required. This amounts to 10 digits and will certainly be adequate for our present programme. Treeing is done in two stages, going first through trees for three or four digits only. These are TRA 000 . . . TRA 111, TRB 000 . . . TRB 111, TRC 0000, . . ., TRC 1111. These number 32 valve elements. At the second stage there are 1024 valve elements TREECI 0000000000, . . . TREECI 1111111111. The connections are shown for TREECI 1011101101. The connection from CI 17 prevents any of the TREECI elements being stimulated when CI 17 is stimulated. This is required to deal with the case where the next order is taken from TS 6 and not from the delay lines (Fig. 20).
It is very probable that some other form of tree circuit, not capable of being drawn in terms of our valve elements, will be used, and the same will apply to many parts of the circuit. It is thought worth while however to draw these circuits, if only to clarify what it is intended the circuits should do.
​We have a similar tree system for the selection of temporary storages.