Page:Alan Turing - Proposed Electronic Calculator (1945).pdf/27

 before adding, in which case we must stimulate CANCEL for a period of two minor cycles. The quantity to be added or subtracted is expressible as the product of a quantity known as the ‘multiplicand’ and an integer which may be taken to lie in the range -7 to 15, positive values being the more normal. The multiplicand may be taken from TS 3 or from the partial sums register itself. This latter case is convenient for the purpose of multiplying the partial sum by a small integer without a complicated series of previous transfers; if the multiplicand is taken from the partial sums register then SELF is stimulated. The multiplier may also be taken from a variety of sources. It may be taken from TS 2 or from CI or from TS 11, and we accordingly stimulate NOR, GIV or ERR. The multiplier consists of four consecutive digits from whichever source is chosen. The choice of the digits is made by means of a choice of one of the pulses P1 to P32 to enter on a certain line (DIGIT). At present it is suggested that in case NOR this should be P1, resulting in the use of digits 1,2,3,4, in case IV it should be P 23 resulting in the use of digits 23,24,25,26, in case ERR1 it should be P 10, and in case ERR2 it should be P 14. In case DIFF these arrangements are to be overridden and the pulse will be stored in TS 12 and taken from there.

In case AUTO the above fundamental process is repeated eight times. In each repetition the multiplicand is taken from TS 3, but it is modified each time by multiplication by 24, this effect being obtained by allowing it to circulate in a DL34 during AUTO. We also wish to take different digits of the multiplier at each repetition of the process; this is done by taking our pulse from TS 12 but allowing it to circulate in a DL 34 also. Facilities are also provided for multiplying the partial sum by a power of 2. Although the circuits are arranged so that this could be combined with other operations, it is not intended that this should be done. The facility consists in enabling the partial sums to be delayed by any time up to 63 and passed through for a period of 2 or 3 minor cycles as desired. The amount of delay is taken from digits 1-5 of TS 7. We stimulate ROTATE 2 or ROTATE 3 according as we wish the rotation to last for 2 or 3 minor cycles.

It may be as well to describe how some rather definite operations are done.

Addition. We do not have a facility for addition of two given numbers so much as for the addition of a given number into the partial sum. To add the content of TS 3 into the partial sum we must stimulate S, POS, GIV, and must also set up the number 1 in columns 24-27. The multiplicand is then TS 3 and the multiplier is 1.

Subtraction. As addition but we do not stimulate POS.

Short multiplication (A). To multiply TS 3 by 6 (say) proceed as for addition with 0110 in columns 24-27 instead of 1000. We shall very likely also want to cancel the original content of the partial sums register and therefore stimulate CANCEL.

Short multiplication (B). To multiply the partial sum by 6 we must stimulate S, POS, CANCEL, SELF, GIV, and set up 0110 in CI 24-27.

Short multiplication (C). As B but do not cancel and put 1010 in CI 24-27.

Short multiplication with addition. We wish to multiply TS 3 by TS 2 and add into the partial sum. We stimulate POS, NOR, AUTO, DIFF. Long/