Page:Alan Turing - Proposed Electronic Calculator (1945).pdf/22

 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/