DE967534C - High-speed decimal calculator - Google Patents

Description

The invention is concerned with decimal high-speed calculating machines for the four basic types of calculation as well as for the second and third degree rooting. The multiplication can optionally be carried out as a complete one 5 or as an abbreviated multiplication with automatic rounding up or down of the result, whereby by means of special inventive measures the possibility is gained, even then, exact, d. H. not Achieve rounded results when in a «digit Calculating machine a product of almost twice the number of digits is to be determined, so if the capacity of the machine is not sufficient to hold the complete product.

If z. B. in a calculating machine with only six digits, the product of two five digits each Factors is calculated, then the product is a nine- to ten-digit number. Provided the product formation - as in the present invention - is solved by continued addition, then become at These summations only ever add a maximum of six-digit numbers. So below is sufficient for the arithmetic unit all circumstances, d. H. even with exact calculation of all positions of a product, a capacity from only six digits. For holding the complete product with up to ten digits on the other hand, the capacity would have to be almost twice as large.

In a calculating machine of the present invention, however, the arithmetic unit in which the additions are carried out, at the same time also represents the results. In a ten-digit result and arithmetic unit So only six places would be involved in the actual calculation process, while the other places only exercise memory functions.

709 '782/57

The idea of the invention now consists in the capacity of the calculating machine not according to the higher Claims of the result work, but to be measured according to the lesser of the arithmetic unit in order to be able to use them Way to limit the size of the machine and its price to about half of what is rated according to the capacity required for the result.

Of course, this renunciation must be compensated for in some way. And that happens after of the invention in two ways: Either one collects those that can no longer be taken up by the result work Digits in a suitable memory, or some of the digits of the product are dropped, but taking into account the contribution of the lower digits to this abbreviated product by adding only the last digit is discarded, which after the transfer does not have a contribution can do more for higher positions.

So, unless the digits are simply discarded, it takes a memory that does not have any arithmetic functions needs to carry out those digits which the machine has already calculated correctly which, for mathematical reasons, no longer occurred in the further course of the calculation can be changed because there are no more contributions from lower positions up to the higher positions to be delivered. And the arithmetic unit creates itself before each job transfer by discarding the already correctly and invariably calculated digit the necessary space for the calculation of a new digit.

Another idea of the invention is to determine the complete product even without a memory. Included the entire digits of the unabridged product are determined in two stages by first one half, preferably the first digits of the product, and then in one iteration of the process the last digits of the product can be determined. These two stages of work only differ in that once the intermediate products are shifted to the right and the other time one Suffer places shift to the left, with the last digit on the right or left from the arithmetic unit deleted and the vacant position is replaced by the number zero.

In the following scheme of the written multiplication are indicated by the dotted line TrennungsHnie identifies the two sub-processes that the machine has to reproduce. In the the scheme of the sequence of these two sub-processes entered arrows indicate the direction of the required Set displacement on (to the right or left).

52108 1.2345

26I0540
2 0 8143 2

1563: 24
ι ο 4 2 i | 6

052108;
06432 7; 3 260

i. Digit group

260540 ->

^ 26054

208432

2. Group of digits

- <- 052108
52io8jzi
104216

234486 -> -
^ 23448
156324 - * - 625296
25296 ^
156324 179772 - »-
2Ί7977
I042I6 - <- 409284
09284 /
208432 I22I93 - + -
3Ί22Ι9
052108 - <- 301272
01272 ^
260540 064327 - »-
006432 - «- 273260
732600

The root calculation χ =] / y in the subject matter of the invention is reduced to a sequence of divisions, namely to the problem y: χ = χ. If χ were already known, then of course this identical equation would result. Instead, only a rough approximation X _{1 is} known, i.e. χ = X ₁ - \ - Ax ₁ .

If the division y: X ₁ = X _{1 is carried} out with this approximate value X ₁ , then one of the two numbers X ₁ or X _{1 must be} larger, but the other smaller than the true root value χ . It is therefore obvious to form a better approximation X ₂ = 0.5 · (X ₁ + X ₁ ) from both numbers.

With this approximation the division y : X ₂ = X _{2 is carried} out and in this way two narrower limits are obtained, between which the true root value must lie. This entry procedure can be repeated until the A th approximation _{Xj 1} no longer differs from x { due to the limited number of digits in the machine. The method converges surprisingly quickly. It is almost irrelevant how well the first approximation X _{1 was} chosen.

This has the following meaning for the structural design of a square root calculating machine: The Calculating a root of the second or third degree is a combination of the four basic types of calculation This program is in itself without any further technical means with the calculating machine feasible, with the necessary operating controls being carried out by hand. For one faster execution, however, an automatic device is desirable, which the program flow controls without any further action on the part of the computer. Creating such facilities is with the to Technical means known at the time are easily possible, since the operating handles are carried out by hand can also be transferred to a machine.

However, the method described above assumes that the computer already has a root approximation value disposes.

In a further improvement of the invention, the same approximation X ₁ is now used for all roots χ - | / y ~ of the range y = 1 to y = 100. This

Of course, X ₁ should be in the (geometric) center of the two outermost limits, that is

X ₁ = ] / i · io sä 10/3.
A numerical example may explain this:

] / 40 = 6.324555204 ...,
X ₁ = 10/3 = 3.333333 ···.
40: 10/3 = 40 x 3/10 = 12 == X ₁ .

(The first division process y: X ₁ can be reduced to the one-part multiplication y 0.3 because of the appropriate choice of X _{1 - 10/3 = 3.333 ...)}

= 0.5 * (X ₁ + X ₁ ') = 0.5

(3,333 1-12)

= 7.6665,

40: 7.6665 = 5.2i75 = * a ',
7.6665 + 5.2175 = 12.8840,

x ₃ = 0.5 x 12.8840 =

4jzf: 6.4420 =

= 0.5 · {x _s + X ₃ ') =

4 & : 6.3256 =

₅ = ° .5 * (Xi + Xi) =

6.4420,
6.2092 = X ₃ ,
6.3256,
6.3235108 =

6.3245554

After just three divisions and a very short (single-digit) multiplication process, the root was determined with an error of only 0.0000002, although the first approximation X ₁ = 3.333 ... was very far from the true value χ = 6.3245552.

After what has been said so far, it is easy to understand that instead of the first approximation X ₁ == 10/3 = 3.333 .... which the division y : 10/3 to the (technically easier and faster solvable) multiplication y · 0 , 3 allowed to be traced back, also by other approximate values, e.g. B. X ₁ - 10/2, can be replaced so that the machine has to perform the multiplication y 0.2 in the first step of the root calculation method. The same applies to y · 0.1; y - 0.5 and the like. The approximate values X ₁ = 10 correspond to these tasks; X ₁ = 2 and the like.
The value X ₁ - 10 is recommended, for example, radicand y in the vicinity of the value y = 60 to 100. The computer has here therefore a simple procedure at hand, without account a value suitable for a multiplication process approximation X ₁ be selected according to the predetermined radicand .

Finally, the machine can also be automated in such a way that it automatically selects a suitable X ₁ for each y in a relatively simple manner. This has the advantage that the convergence of the root calculation method compared to the fixed approximate value X ₁ = 3.333 3 ... is occasionally shortened by one or two division processes.

The following scheme may serve as a guide for finding such an X ₁ :

Radikand y * i Multiplication to be performed
V · Φι ι to 2
2 to 10
10 to 40
40 to 100 I.
2
5
IO yI
yo, 5
y · 0.2
y 0.1

For the calculation of cubic roots, mutatis mutandis, the same applies in accordance with the approximation equation

] / T + ~ z = ι + z / 3,
which takes the place of the equation

] / r + ζ = ι + z / 2

occurs.

An exemplary embodiment is described below. As switching elements are preferred Electro-magnetic relay chosen as a single relay as opposed to a single electron tube can perform several switching functions according to the number of contacts. That is enough Working speed perfectly for many purposes.

The drawing shows the circuit diagram of a counter ring for the decade D ₀ . In the following, all variables identified with the index 0 identify their affiliation to the decade D ₀ . The same applies to the decades D _-1 , D ₊₁ ... The gaps left open in the circuits represent switches (not shown). Each number entered in a gap denotes a relay which has the same number and which is all in the working state closes those switches that have this number. However, attention must be paid to the different indices, as the same numbers recur in every decade. Quiescent switches, which are closed when the relay is not energized (quiescent state), but open when the relay is energized (working state), have been identified by a point added to the number. Such switches are therefore opened when their relay is energized.

The five-ring of every decade Dn (h - - 1; 0; +1 ...) consists of the five relays 0%, Ij ₁ , 2 / j, 3ä, 4 &. The double ring consists of a single relay b%. It is used to store five. The relay labeled Ju is used for the transmission of tens, if necessary, in the following addition process. The seven relays of the decade D ₀ were grouped together in the drawing by a thicker frame to form the result set R ₀ . The two relays 6 and 7 (if errors appear excluded, the specification of distinguishing indices should be omitted for the sake of simplicity) are connected to voltage via branch line 36, whereas the group of five relays 0, 1, 2, 3 and 4 are connected to voltage via branch 35 . With the help of these two relay groups z. B. the problem 8 + 6 = 14 is solved in two simultaneous parallel processes, namely in the process of adding up the full fives (5 + 5 = 10) and in the process of adding up the amount of five

Excess amounts (3 + 1 = 4) via branch 35. One of the six is used for entering numbers Relay 20 to 25 existing (but not shown) relay group provided. The ones operated by these relays However, switches can also be replaced by hand-operated or punched card-operated switches. Another relay group, not shown, is used to count in the course of a multiplication or Division performed addition processes. Your re

If necessary, the relay switches a (not shown) A control magnet that supplies the working voltage for the relays 0 to 7 to one of the supply lines 28 to 34 and in this way controls the flow of the entire process.

The machine works as follows: Before starting the first calculation, the machine is made ready to start. Voltage is applied to line 31. So far none of the relays has been energized. So all work switches are open. On the other hand, the rest switch ο j releases a current path each decade Dj ₁ via the relay Oj ₁ . These therefore respond and prepare with their switches _{Oj 1} , which are attached to the branch line 35, a current path through the relays 0 to 4, but only one of them will be set up later

is selected illustratively. The voltage is now applied from the starting line 31 to the self-holding line 30, so that all energized relays Oj ₁ keep themselves energized.
Let us add the number 3 in the decade D _{0, for example. Then the four switches 23 0 are} closed by means of a manual switch or a relay switch. In this way, one of the five lines 35 is selected. Switch 7I ₁ is closed as a closed switch of the non-excited relay 7_ _x of the decade D _-1 preceding the decade D ₀ . As soon as the voltage from line 30 is briefly applied to pulse line 29, a current path is free via switch 7 ^ ₁ , 23, line 35, switch 0, relay 3, return line 44. Relay 3 responds, relay 0 drops out. Immediately the

Voltage is applied to the self-holding line 30, so that relay 3 is kept under voltage until the next change. The addition "+3" is now carried out.
The multiplication is through continued addition

solved. The position shifts in the multiplication and in the division, which are achieved in mechanical machines by the slide movement, are carried out according to the present invention in a very simple manner via the lines 33 and 34 with the aid of the o_ _x ... 7 ^ and O _{+ 1} ... 7 ₊₁ . The advantage of this solution is that the setting of switches 20 to 25 does not have to be changed in a decade. These switches remain unchanged in their position during the entire multiplication or division process.

Claims (3)

PATENT CLAIMS: 1. Decimal high-speed calculating machine, characterized in that each relay with each decade a switch of the relay of the same name lying on a first connecting line (34) in each case next higher decade and with one lying on a second connecting line (33) Switch of the relay of the same name of the next lower decade is connected, so that a Current surge through the first connecting line (34) and the switches connected to it Relay energized every decade according to the operating status of the next higher decade, during a current surge through the second connecting line (33) and through those connected to it Switch the relays every decade according to the operating status of the next decade energized, so that these measures can be used to shift the digits in the arithmetic unit to the right or left, with the digit furthest to the right or left at The position shift is deleted from the arithmetic unit and the number zero in the decade that has become free is introduced by energizing relay (0) of that decade. 2. Decimal high-speed calculating machine according to claim i, characterized in that at each Moving the digit to be erased in the arithmetic unit is given in a storage unit, which keeps them available for registration of the complete, non-rounded product. 3. Decimal high-speed calculating machine according to claims 1 and 2 for calculating roots, characterized in that instead of a storage device for an approximate value X ₁ that can be selected by the computer for all roots χ = fy each of a certain interval α rg y <| b each a fixed approximate value is stored in the machine in such a way that the machine carries out a multiplication which can be carried out considerably more quickly with a single-digit factor, if possible, instead of the first formation of the quotient. Publications considered: i °° German patent specifications No. 546 534, 731706, 806; British Patent No. 484,150; U.S. Patent No. 2402988; The Annals of the Computation Laboratory of Harvard University, Vol. XVI, 1948, p. 4off. For this purpose i sheet of drawings 709 782/57 11:57