Page:Alan Turing - Proposed Electronic Calculator (1945).pdf/8

 $$| \xi - 2^m \beta | < \gamma$$

$$\beta = \sum_{s=1}^{31} s^{s-1} i_s - 2^{31} i_{32}$$

$$m = \sum_{t=1}^9 2^{t-1} j_t - 512$$

$$\gamma = \sum_{u=10}^{17} 2^{u+m-n} j_u$$

$$n = \sum_{v=18}^{23} 2^{v-18} j_v$$

This code allows us to specify numbers from ones which are smaller than 10−70 to ones which are larger than 1086, mentioning a value with sufficient figures that a difference of 1 in the last place corresponds to from 2.5 to 5 parts in 1010. An error can be described smaller than a unit in the last place or as large as 30,000 times the quantity itself (or by more if this quantity has its first few ‘significant’ digits zero).

(v) The operations of GA. The division of the storage into minor cycles is only of value so long as we can conveniently divide the operations to be done into unit operations to be performed on whole minor cycles. When we wish to do more elaborate types of process in which the digits get individual treatment we may find this form of division rather awkward, but we shall still be able to carry these processes out in some roundabout way provided the CA operations are sufficiently inclusive. A list is given below of the operations which will be included. Actually this account is distinctly simplified, and an accurate picture can only be obtained by reading § 12. The account is however quite adequate for an understanding of the main problems involved. The list is certainly theoretically adequate, i.e. given time and instruction tables any required operation can be carried out. The operations are:

(1) Transfers of material between different temporary storages, and between temporary storages and dynamic storage.

(2) Transfers of material from the DS to cards and from cards to DS. (3)/