14.0 CC AND M #

14.1 #

Our next aim is to go deeper into the analysis of CC. Such an analysis, however, is dependent upon a precise knowledge of the system of orders used in controlling the device, since the function of CC is to receive these orders, to interpret them, and then either to carry them out, or to stimulate properly those organs which will carry them out. It is therefore our immediate task to provide a list of the orders which control the device, i.e. to describe the code to be used in the device, and to define the mathematical and logical meaning and the operational significance of its code words.

Before we can formulate this code, we must go through some general considerations concerning the functions of CC and its relation to M.

The orders which are received by CC come from M, i.e. from the same place where the numerical material is stored. (Cf. 2.4 and 12.3 in particular (b).) The content of M consists of minor cycles (cf. 12.2 and 12.7), hence by the above each minor cycle must contain a distinguishing mark which indicates whether it is a standard number or an order.

The orders which CC receives fall naturally into these four classes: (a) orders for CC to instruct CA to carry out one of its ten specific operations (cf. 11.4); (b) orders for CC to cause the transfer of a standard number from one place to another; (c) orders for CC to transfer its own connection with M to a different point in M, with the purpose of getting its next order from there; (d) orders controlling the operation of the input and the output of the device (i.e. I of 2.7 and O of 2.8).

Let us now consider these classes (a)–(d) separately. We cannot at this time add anything to the statements of 11.4 concerning (a) (cf. however {}). The discussion of (d) is also better delayed (cf. {}). We propose, however, to discuss (b) and (c) now.

14.2 #

Ad (b): These transfers can occur within M, or within CA, or between M and CA. The first kind can always be replaced by two operations of the last kind, i.e. all transfers within M can be routed through CA. We propose to do this, since this is in accord with the general principle of 5.6 (cf. also the discussion of the second question in 11.1), and in this way we eliminate all transfers of the first kind. Transfers of the second kind are obviously handled by the operating controls of CA. Hence those of the last kind alone remain. They fall obviously into two classes: Transfers from M to CA and transfers from CA to M. We may break up accordingly (b) into (bj) and (bjj), corresponding to these two operations.

14.3 #

Ad (c): In principle CC should be instructed, after each order, where to find the next order that it is to carry out. We saw, however, that this is undesirable per se, and that it should be reserved for exceptional occasions, while as a normal routine CC should obey the orders in the temporal sequence in which they naturally appear at the output of the DLA organ to which CC is connected. (cf. the corresponding discussion for the iconoscope memory, (c) in 12.8.) There must, however, be orders available, which may be used at the exceptional occasions referred to, to instruct CC to transfer its connection to any other desired point in M. This is primarily a transfer of this connection to a different DLA organ (i.e. a organ in the sense of 12.7). Since, however, the connection actually wanted must be with a definite minor cycle, the order in question must consist of two instructions: First, the connection of CC is to be transferred to a definite DLA organ. Second, CC is to wait there until a definite τ -period, the one in which the desired minor cycle appears at the output of this DLA, and CC is to accept an order at this time only.

Apart from this, such a transfer order might provide that, after receiving and carrying out the order in the desired minor cycle, CC should return its connection to the DLA organ which contains the minor cycle that follows upon the one containing the transfer order, wait until this minor cycle appears at the output, and then continue to accept orders from there on in the natural temporal sequence. Alternatively, after receiving and carrying out the order in the desired minor cycle, CC

should continue with that connection, and accept orders from there on in the natural temporal sequence. It is convenient to call a transfer of the first type a transient one, and one of the second type a permanent one.

It is clear that permanent transfers are frequently needed, hence the second type is certainly necessary. Transient transfers are undoubtedly required in connection with transferring standard numbers (orders (cj) and (cjj), cf. the end of 14.2 and in more detail in 14.4 below). It seems very doubtful whether they are ever needed in true orders, particularly since such orders constitute only a small part of the contents of M (cf. (b) in 12.3), and a transient transfer order can always be expressed by two permanent transfer orders. We will therefore make all transfers permanent, except those connected with transferring standard numbers, as indicated above.

14.4 #

Ad (b) again: Such a transfer between CA and a definite minor cycle in M (in either direction, corresponding to (bj) or (bjj), cf. the end of 14.2) is similar to a transfer affecting CC in the sense of (c), since it requires establishing a connection with the desired DLA organ, and then waiting for the appearance of the desired minor cycle at the output. Indeed, since only one connection between M and CC (actually CC or CA, i.e. C) is possible at one time, such a number transfer requires abandoning the present connection of CC with M, and then establishing a new connection, exactly as if a transfer affecting CC in the sense of (c) were intended. Since, however, actually no such transfer of CC is desired, the connection of CC with its original DLA organ must be reestablished, after the number transfer has been carried out, and the waiting for the proper minor cycle (that one following in the natural temporal sequence upon the transfer order) is also necessary. I.e. this is a transient transfer, as indicated at the end of 14.3.

It should be noted that during a transient transfer the place of the minor cycle which contained the transfer order must be remembered, since CC will have to return to its successor. I.e. CC must be able to remember the number of the DLA organ which contains this minor cycle, and the number of τ periods after which the minor cycle will appear at the output. (cf. for details {}.)

14.5 #

Some further remarks:

First: Every permanent transfer involves waiting for the desired minor cycle, i.e. on the average for half a transit through a DLA organ, 512 periods τ . A transient transfer involves two such waiting periods, which add up exactly to one transit through a DLA organ, 1,024 periods τ . One might shorten certain transient transfers by appropriate timing tricks, but this seems inadvisable, at least at this stage of the discussion, since the switching operation itself (i.e. changing the connection of CC) may consume a nonnegligible fraction of a minor cycle and may therefore interfere with the timing.

Second: It is sometimes desirable to make a transfer from M to CA, or conversely, without any waiting time. In this case the minor cycle in M, which is involved in this transfer, should be the one immediately following (in time and in the same DLA organ) upon the one containing the transfer order. This obviously calls for an extra type of immediate transfer in addition to the two types introduced in 14.3. This type will be discussed more fully in {15.3}.

Third: The 256 DLA organs have numbers 0, 1,… , 255, i.e. all 8-digit binary numbers. It is desirable to give the 32 minor cycles in each DLA organ equally fixed numbers 0, 1,…, 31 i.e. all 5-digit binary numbers. Now the DLA organs are definite physical objects, hence their enumeration offers no difficulties. The minor cycles in a given DLA organ, on the other hand, are merely moving loci, at which certain combinations of 32 possible stimuli may be located. Alternatively, looking at the situation at the output end of the DLA organ, a minor cycle is a sequence of 32 periods τ , this sequence being considered to be periodically returning after every 1,024 periods τ . One might say that a minor cycle is a 32τ “hour” of a 1,024τ “day,” the “day” thus having 32 “hours.” It is now convenient to fix one of these “hours,” i.e. minor cycles, as zero or {“first”} and let it be at the same time at the outputs of all 256 DLA organs of M. We can then attribute each “hour”, i.e. minor cycle, its number 0, 1,…, 31, by counting from there. We assume accordingly that such a convention is established—noting that the minor cycles of any given number appear at the same time at the outputs of all 256 DLA organs of M.

Thus each DLA organ has now a number µ = 0, 1,…, 255 (or 8-digit binary), and each minor cycle in it has a number ρ = 0, 1,…, 31 (or 5-digit binary). A minor cycle is completely defined within M by specifying both numbers µ, ρ. Due to these relationships we propose to call a DLA organ a major cycle.

Fourth: As the contents of a minor cycle make their transit across a DLA organ, i.e. a major cycle, the minor cycles number ρ clearly remains the same. When it reaches the output and is then cycled back into the input of a major cycle the number ρ is still not changed (since it will reach the output again after 1,024 periods τ , and we have synchronism in all DLA organs, and a 1,024 τ periodicity, cf. above), but µ changes to the number of the new major cycle. For individual cycling, the arrangement of Figure 19 (a), this means that µ, too, remains unchanged. For serial cycling, the arrangement of Figure 19 (b), this means that µ usually increases by 1, except that at the end of such a series of, say, s major cycles it decreases by s − 1.

These observations about the fate of a minor cycle after it has appeared at the output of its major cycle apply as such when that major cycle is undisturbed, i.e. when it is off in the sense of 13.2. When it is on, in the same sense, but in the first case of 13.3, then our observations are obviously still valid—i.e. they hold as long as the minor cycle is not being cleared. When it is being cleared, i.e. in the second case of 13.3, then those observations apply to the minor cycle which replaces the one that has been cleared.