GB1560679A - Production of a series of random numbers - Google Patents

Description

(54) IMPROVEMENTS IN OR RELATING TO THE PRODUCTION OF A SERIES OF RANDOM NUMBERS (71) I, HIS MAJESTY'S POST MASTER GENERAL of the General Post Office, London, E.C.1. do hereby declare the nature of this invention and in what manner the same is to be performed, to be particularly described and ascertained in and by the following statement: This invention relates to the production of a series of random numbers and more particularly to apparatus for producing such a series.

Series of random numbers are employed for example in solving statistical problems and problems based upon the mathematical theory of probability and it is an object of the invention to provide apparatus which will provide a record of events which are caused by a source of random events in such form as will obey a law which is, or is sufficiently closely, random.

According to the invention. apparatus for producing the numbers of a series of random numbers comprises a counting device adapted to be actuated by electrical impulses initiated by a source of events known to be random to perform a series of counting operations and to repeat said series of operations after completing any one of such series, means for effecting actuation of the device upon the occurrence of events produced by a source of events known to be random and means for indicating at time intervals spaced from one another in a predetermined manner, the serial number corresponding to the last counting operation performed by the device between said intervals.

The theory on which the invention is based may be stated broadly as follows.

Suppose a series of numbers 0 to n arranged in a closed ring, that events from a random source are counted on the ring, starting each count from the same or any number and carrying on the count by moving from one number to the next succeeding number of the series in order as the count occurs, that the count is stopped after a period of time in no way related to the number of events which have occurred during the said period of time and that the last number to be reached before the count is stopped is recorded for each count. In such case the series of numbers recorded more nearly approach a random series as the average count increases but a sufficiently close approach to a random count is obtainable with moderate average counts, for example an average count of ten when making a series of the numbers 0 and 1.

The invention will be described by way of example with reference to the accompanying drawings in which Figure 1 shows diagrammatically the arrangement of an electrical apparatus arranged for use with known telegraphic reperforator mechanism for recording electrical signals.

Figure 2 is a diagrammatic front elevation of a distributor for use with the known reperforator mechanism and Figure 3 is an end view of the distributor of Figure 2.

The telegraphic reperforator mechanism is of known form known as the United States Teletype Model 14 described in Bell Laboratories Record, April, 1942 at page 209. The reperforator employs single magnet operation and comprises motor-driven selector mechanism for determing the particular unit of a five-unit code which is to be recorded by punching or otherwise marking a paper or like tape. The known mechanism is modified by providing it with a distributor as shown in Figures 2 and 3 which is adapted to emit an electrical impulse of negative potential at the commencement of the period of selection of each of the five units which correspond to any one character and the known apparatus is operated to carry out the invention with the motor drive locked to the selecting mechanism.

Of the known reperforator mechanism the operating winding of the selecting magnet only is shown in Figure 1.

Referring to the drawings, negative going impulses, each having a duration of about 0.2 milliseconds are emitted by the distributor of the reperforator apparatus and are applied to the line 1 and voltages produced by the source of random events are applied to the line 2. Resistance or valve noise which appears as a continuous but variable voltage in the output circuit of a high-gain amplifier may be the source of random events but other sources may provide the voltages applied to line 2, for example the voltages may be provided by a counter used to observed particles of radio-active material.

The voltages on the line 2 are applied to the control grid of a valve 30 the anode of which is connected via condenser 015 to the suppressor grid of which is connected via condenser 015 to the suppressor grid of a pentode valve 010. The valve 010 with a similar valve 020 are included in a selfresetting or flip-flop circuit. Each valve has its cathode held at earth potential, its screen grid connected to a potential +V1 positive with respect to earch potential and its anode connected via resistor 011 and 021 respectively to positive potential + V1. The control grid of valve 020 is connected via condenser 012 to the anode of valve 020 and via resistor 013 to earth.The control grid of valve 010 is connected via the parallel connected resistor 022 and condenser 023 to the anode of valve 010 and via resistor 024 to a source of potential - V1 negative with respect to earch potential. The suppressor grid of valve 010 is connected via resistor 014 to earch and also via condenser 015 to the anode of valve 30. The suppressor grid of valve 020 is connected to earth. In the quiescent condition current flows in the anode circuit of valve 010. A valve having current flowing in its anode circuit is. in this specification, said to be conducting. The resistors 022 and 024 are so chosen that when valve 010 is conducting the valve 020 is cut off, that is, no anode current flows in valve 020, and when valve 010 is cut off as hereafter described, valve 020 is conducting.

Voltage negative with respect of earth potential exceeding a critical value, and applied to the suppressor grid of valve 010 causes the valve 010 to be cut off and valve 020 to conduct, the change taking place with a trigger action in well-known manner and being maintained until, after a time determined chiefly by the condenser 012 the resistor 013. and the values of the positive potential + V1. the resistor 021 and the valve 020, the action is reversed with a trigger action and valve 010 becomes conducting and valve 020 cut-off. A substantially square voltage pulse is thus produced in the anode circuit of each of the valves 010 and 020. The impulse produced in the anode circuit of valve 010 is positive going and that in the anode circuit of valve 020 negative going, the duration of both impulses being about 0.1 millisecond.Condenser 023 improves the squareness of the impulses produced. The time constant of the condenser 015 and resistor 014 is arranged so that the suppressor grid of valve 010 has returned substantially to earth potential at the end of the impulse time when the valve 010 is required once more to become conducting.

Connections similar to those of the pair of valves 010 and 020 are arranged for the pairs of valves 110 and 120 and 210 and 220, corresponding elements being identified by references having similar second and third digits. The duration of the impulses produced in the anode circuits of valves 210 and 220 are each arranged to be about one half of that of each of the impulses produced in the anode circuit of the valves 110 and 120, such impulse duration being about one millisecond. The pairs of valves 110 and 120 and 210 and 220 are also arranged in self-restoring trigger or flip-flop circuits.

The trigger valves 110, 120. 210 and 220 are all caused to emit their impulses by the negative going impulses emitted by the reperforator distributor, these latter impulses being received over lead 1 and connected to the suppressor grids of valves 110 and 210 via condesners 115 and 215 respectively. The trigger circuit comprising valves 010 and 020 is triggered by the source of random events. This source, which is not shown, may as stated above, be for example, resistance or valve noise in an amplifier output circuit. This circuit is connected over lead 2 to the grid of valve 30 as described above and via grid leak 31 to earth.The cathode of valve 30 is connected to the moving contact of potentiometer 32 connected between earth and the positive potential + V1 and also connected via a condenser 33 to earth to prevent the potentiometer resistance from reducing the amplification of the-valve except at the lowest frequencies. The screen grid of valve 30 is connected to the positive potential + V1, the anode via a resistor 33 to the positive potential + V1 and to the condenser 015 as already described, while the suppressor grid is connected via the high resistance 34 to the cathode and via condenser 35 to the anode of valve 120. Condenser 35 and resistor 34 have a time constant which is long compared with the one millisecond duration of the impulse emitted by the valve 120. When the suppressor grid of valve 30 is at cathode potential and the control grid at earth potential, the cathode potential is biassed positively by the potentiometer 32 to a point well past the cut-off of the valve which will then conduct only when the posiive peaks of voltage received over lead 2 approach or exceed the bias voltage. For each peak a negative going voltage impulse is produced in the anode circuit of valve 30. Each impulse is communicated to the suppressor grid of valve 010 and those impulses of sufficient amplitude cause the trigger circuit including valves 010 and 020 to emit via the lead to condenser 41 one positive going impulse as described above.

The anode of valve 010 is connected to a capacity resistance circuit comprising condenser 41 and resistors 42 and 43, the timeconstant of the condenser and the parallel resistance of the two resistors being short compared with the duration of the impulses emitted by valve 010. For each impulse therefore there is produced at the junction point of the condenser and resistors first a positive going impulse having a steep leading edge and an exponential trailing edge, then a negative going impulse also having a steep leading edge and exponential trailing edge. These impulses are applied to the grid of valve 40, the anode of which is connected to the positive voltage + V1 and the cathode via resistor 44 to earth.The resistors 42 and 43 form a potentiometer connected between earth and the negative potential - V1 and are so chosen that valve 40 is biased beyond the cut-off point. Only the positive going pulses which result from the full operation of the trigger or flip-flop circuit comprising valves 010 and 020 are therefore effective in producing impulses at the cathode of value 40, and these are particularly suitable for operating the scale-of-two counting circuits which includes valves 50 and 60 and which will now be described.

The cathodes of valves 50 and 60 are both earthed, their screen grids are connected to the positive potential + V1, their anodes connected via resistors 51 and 61 respectively to the positive potential + V1 and their suppressor grids connected via resistors 56 and 66 respectively to earth. The anode of valve 50 is connected via resistor 62 and grid stopper resistor 64 to the grid of valve 60.

The junction of resistors 62 and 64 is connected to one side of resistor 63. the other side of which is connected to a potentiometer 69 connected between earth and the negative potential - V1. The resistors 52, 53 and 54 are similarly connected, the anode of valve 60 being connected to the grid of valve 50 via resistor 52. The connections associated with valves 50 and 60 so far described are those of a trigger circuit having two equilibrium conditions, one condition being that valve 50 is conducting and valve 60 is cut-off, the second condition being valve 50 cut-off and valve 60 conducting. The trigger is made to change from one equilibrium condition to the other for each impulse appearing at the cathode of valve 40 and communicated to the control grid circuits of valves 50 and 60 by the condensers 55 and 65 respectively.The change is brought about by the connections between the anode of valve 50 and the suppressor grid of valve 60 via condenser 68 and resistor 67 in series and the similar connections between the anode of valve 50 via condenser 58 and resistor 57.

The potentials of the control grids of the valves 70 and 80 are made the same as those of valves 50 and 60 respectively by connecting them via stopper resistances 71 and 81 to the common points of resistors 52, 53, 54 and 62, 63, 64 respectively. The cathodes of valves 70 and 80 are connected to earth and their suppressor grids have a common connection to earth via resistor 73, and to the anode of valve 90, the cathode and suppressor grid of which are directly joined, and the control grid joined via resistors 91 and 92, to the negative potential - V1. The screen-grid is at earth potential. The valve 90 is normally conducting on its anode, thus applying a negative bias to the suppressor grids of valves 70 and 80 sufficient to cut-off the anode current flow in these valves.The one valve of the pair of valves 70 and 80 which is conducting at any one time conducts for most of that time only on its screen-grid circuit. The screen grids of the valves are therefore joined via protective resistors 72 and 82 to the positive potential + V1. The control grid of valve 90 is connected via resistor 92 and condenser 93 to the anode of valve 210. The time constant of the condenser 93 and the resistors 91 and 92 in parallel is made small compared with the duration of the impulse emitted by the valve 210. These impulses are positive going. The leading edge has no effect on valve 90 which is already fully conducting in the normal state.

The trailing edge however, puts a negative going impulse on the grid of valve 90, thus momentarily cutting off valve 90 and raising the potential of the suppressor grids of valves 70 and 80 to their cathode potentials.

At this instant, as explained hereafter, the trigger circuit including valves 50 and 60 is in one of its two stable states of equilibrium.

Valve 70 or 80 thus momentarily conducts on its anode circuit depending upon whether valve 50 or 60 respectively is conducting.

This momentary conductor has the effect of setting the storage trigger circuit including valves 200 and 300 into one of its two states of equilibrium, with valves 300 ar 200 conducting depending on whether valve 50 or 60 respectively is conducting. The trigger valves 200 and 300 each have their cathodes and suppressor grids at earth potential, their screen grids at the positive potential + V1 and their anodes connected via resistors 201 and 301 respectively to the positive potential + V1, and via resistors 302 and 202 respectively to the control grids of valves 300 and 200 respectively. The control grids of the two valves 200 and 300 are joined via resistors 203 and 303 respectively to the negative potential - V1.The two valve and their associated resistors and power supplies are so chosen as to form a trigger circuit having two states of stable equilibrium, each state comprising one of the valves conducting and other cut-off. The anodes of valves 200 and 300 are connected to the anodes of valves 80 and 70 respectively so that when valve 70 becomes momentarily conducting on its anode circuit as already described, the trigger is set with valve 300 conducting and when valve 80 becomes momentarily conducting the trigger is set with valve 200 conducting. The grid of valve 300 is connected to the grid of valve 400 shown as a triode, the cathode of valve 400 being earthed and its anode connected via the selecting magnets 401 of the reperforator to the positive potential + V1. Valve 400 is thus conducting or cut-off accordingly as valve 300 is conducting or cut-off.

The distributor which is illustrated in Figures 2 and 3 comprises a rotor a, having five arms al ...a5 of soft iron, which is driven by the main timing shaft b of the known reperforator, through a permanently locked clutch c. The free ends of the rotor arms al are moved in succession through the field of a fixed magnet d which is provided with windings e and which has pole-piecesf, so that the desired impulses are generated in the windings e and transmitted to line 1 of Figure 1. The magnetic axis of the magnet d is indicated by the broken line X - Y of Figure 2.

The apparatus is adjusted and operates in the following manner. The reperforator is set running and thus emits an impulse from its distributor at the commencement of the period of selection of each unit in each 5-unit character. The time between impulses is 20 milliseconds at the normal speed of working. Each impulse causes the valve 120 to emit a negative going impulse one millisecond long which renders valve 30 nonconducting on its anode circuit and therefore ineffective as an amplifier for the duration of the impulse.Between impulses the valve 30 is effective as an amplifier, and in this condition the mean amplitude of the random voltage applied to its control grid over lead 2 and the positive bias applied to its cathode by potentiometer 32 are adjusted so that in the time between two distributor impulses, the mean number of times the pair of valves 010 and 020 emit an impulse closely approximates to the desired number.

The impulses emitted by valves 010 are counted continuously by the trigger circuit including valves 50 and 60, but the trigger circuit including valves 110 and 120 by its in hibiting action on valves 30 ensures that no count will be initiated for about one millisecond when each reperforator distributor impulse occurs. The distributor impulse also triggers the flip-flop circuit including valves 210 and 220, causing valves 210 to emit a positive going impulse, the leading edge of which is ineffective, but the trailing edge momentarily cuts off valve 90 and permits one of the valves 70 or 80 to conduct as already described. This momentary conduction takes place roughly during the second half of the impulse emitted by the flip-flop circuit including valves 110 and 120 because the length of this impulse is roughly twice that emitted by the flip-flop circuit including valves 210 and 220.The counting trigger including valves 50 and 60 is thus given time to reach a stable condition if it is changing over at the instant the reperforator distributor impulse starts before that condition is transferred to that of the storage trigger including valves 200 and 300. The last mentioned trigger circuit remains in the condition in which it is set during one distributor impulse at least until the next distributor impulse and thus controls the reperforator selecting magnet 401 in the well-known manner to produce punched paper tape having 5-unit characters each of which may be a hole or a blank according to a law which is very closely random.

While in Figure 1, there is shown a counting ring of two to produce a random series of numbers 0 and 1 it will be appreciated that a counting ring of any other number of valves may be used, for example ten valves such as are employed in decade electronic counters, may be used to produce a random series of the numbers 0 to 9.

Having now particularly described and ascertained the nature of our said invention and in what manner the same is to be performed, we declare that: WHAT WE CLAIM IS 1. Apparatus for producing the numbers of a series of random numbers which comprise a counting device adapted to be actuated by electrical impulses initiated by a source of events known to be random to perform a series of counting operations and to repeat said series of operations after completing any one of such series, means for effecting actuation of the device upon the occurrence of events produced by a source of events known to be random and means for indicating at time intervals spaced from one another in a predetermined man ner, the serial number corresponding to the last counting operation performed by the device between said intervals.

2. Apparatus as claimed in Claim 1

**WARNING** end of DESC field may overlap start of CLMS **.

Claims (22)

**WARNING** start of CLMS field may overlap end of DESC **. and their anodes connected via resistors 201 and 301 respectively to the positive potential + V1, and via resistors 302 and 202 respectively to the control grids of valves 300 and 200 respectively. The control grids of the two valves 200 and 300 are joined via resistors 203 and 303 respectively to the negative potential - V1. The two valve and their associated resistors and power supplies are so chosen as to form a trigger circuit having two states of stable equilibrium, each state comprising one of the valves conducting and other cut-off.The anodes of valves 200 and 300 are connected to the anodes of valves 80 and 70 respectively so that when valve 70 becomes momentarily conducting on its anode circuit as already described, the trigger is set with valve 300 conducting and when valve 80 becomes momentarily conducting the trigger is set with valve 200 conducting. The grid of valve 300 is connected to the grid of valve 400 shown as a triode, the cathode of valve 400 being earthed and its anode connected via the selecting magnets 401 of the reperforator to the positive potential + V1. Valve 400 is thus conducting or cut-off accordingly as valve 300 is conducting or cut-off. The distributor which is illustrated in Figures 2 and 3 comprises a rotor a, having five arms al ...a5 of soft iron, which is driven by the main timing shaft b of the known reperforator, through a permanently locked clutch c. The free ends of the rotor arms al are moved in succession through the field of a fixed magnet d which is provided with windings e and which has pole-piecesf, so that the desired impulses are generated in the windings e and transmitted to line 1 of Figure 1. The magnetic axis of the magnet d is indicated by the broken line X - Y of Figure 2. The apparatus is adjusted and operates in the following manner. The reperforator is set running and thus emits an impulse from its distributor at the commencement of the period of selection of each unit in each 5-unit character. The time between impulses is 20 milliseconds at the normal speed of working. Each impulse causes the valve 120 to emit a negative going impulse one millisecond long which renders valve 30 nonconducting on its anode circuit and therefore ineffective as an amplifier for the duration of the impulse.Between impulses the valve 30 is effective as an amplifier, and in this condition the mean amplitude of the random voltage applied to its control grid over lead 2 and the positive bias applied to its cathode by potentiometer 32 are adjusted so that in the time between two distributor impulses, the mean number of times the pair of valves 010 and 020 emit an impulse closely approximates to the desired number. The impulses emitted by valves 010 are counted continuously by the trigger circuit including valves 50 and 60, but the trigger circuit including valves 110 and 120 by its in hibiting action on valves 30 ensures that no count will be initiated for about one millisecond when each reperforator distributor impulse occurs. The distributor impulse also triggers the flip-flop circuit including valves 210 and 220, causing valves 210 to emit a positive going impulse, the leading edge of which is ineffective, but the trailing edge momentarily cuts off valve 90 and permits one of the valves 70 or 80 to conduct as already described. This momentary conduction takes place roughly during the second half of the impulse emitted by the flip-flop circuit including valves 110 and 120 because the length of this impulse is roughly twice that emitted by the flip-flop circuit including valves 210 and 220.The counting trigger including valves 50 and 60 is thus given time to reach a stable condition if it is changing over at the instant the reperforator distributor impulse starts before that condition is transferred to that of the storage trigger including valves 200 and 300. The last mentioned trigger circuit remains in the condition in which it is set during one distributor impulse at least until the next distributor impulse and thus controls the reperforator selecting magnet 401 in the well-known manner to produce punched paper tape having 5-unit characters each of which may be a hole or a blank according to a law which is very closely random. While in Figure 1, there is shown a counting ring of two to produce a random series of numbers 0 and 1 it will be appreciated that a counting ring of any other number of valves may be used, for example ten valves such as are employed in decade electronic counters, may be used to produce a random series of the numbers 0 to 9. Having now particularly described and ascertained the nature of our said invention and in what manner the same is to be performed, we declare that: WHAT WE CLAIM IS

1. Apparatus for producing the numbers of a series of random numbers which comprise a counting device adapted to be actuated by electrical impulses initiated by a source of events known to be random to perform a series of counting operations and to repeat said series of operations after completing any one of such series, means for effecting actuation of the device upon the occurrence of events produced by a source of events known to be random and means for indicating at time intervals spaced from one another in a predetermined man ner, the serial number corresponding to the last counting operation performed by the device between said intervals.

2. Apparatus as claimed in Claim 1

which comprises means arranged to be operated at time intervals spaced in a predetermined manner to receive the counted number of operations from the counting device.

3. Apparatus as claimed in Claims 1 or 2 wherein the counting device is adapted to be stopped at any one in the series of counting operations and when restarted to perform the next succeeding operation in the series.

4. Apparatus as claimed in Claim 1, 2 or 3 which comprises a storage circuit arranged to be conditioned at the spaced time intervals to receive the counted number from the counting device.

5. Apparatus as claimed in any of the preceding Claims wherein the random events are arranged to produce electrical voltages and such voltages are applied to an electronic detector.

6. Apparatus as claimed in Claim 5 which comprises an electronic valve circuit arranged to count electrical impulses and an electronic valve circuit arranged to be controlled by voltages produced by the random events and to produce electrical impulses for application to the counting circuit.

7. Apparatus as claimed in Claim 6 wherein the counting circuit is arranged to be temporarily coupled to an electronic valve storage circuit which controls the operation of an indicating and/or recording device.

8. Apparatus as claimed in Claim 7 wherein both the counting and storage circuits are electronic valve ring circuits which are arranged to be coupled to effect operation of the storage circuit.

9. Apparatus as claimed in Claim 8 wherein the counting and storage circuits are arranged to be coupled to effect operation of the storage circuit by one of a number of normally non-conducting valves said valve being selected and rendered conducting at the spaced time intervals.

10. Apparatus as claimed in any of Claims 1 to 9 which comprise means for applying electrical impulses to the counting device only between the spaced time intervals.

11. Apparatus as claimed in any of Claims 6 to 10 which comprises means for preventing the voltages produced by the random events from exciting the circuit which is arranged to produce impulses for application to the counting circuit.

12. Apparatus as claimed in claim 5 which comprises means arranged to provide electrical impulses at spaced time intervals and means responsive to said spaced impulses and arranged to prevent the voltages produced by the random events from exciting the circuit which is arranged to produce impulses for application to the counting circuit during the existence of a said spaced impulse.

13. Apparatus as claimed in claim 12 which comprises two timing circuits one of which is arranged to control the means for preventing the said voltages from exciting the circuit which produces impulses for application to the counting circuit, the second of the timing circuits being arranged to control a device for indicating the numbers counted by the counting circuit.

14. Apparatus as claimed in claim 13 wherein the timing circuits are arranged to generate electrical impulses for controlling the said means and device respectively, the duration of the impulse generated by the second mentioned circuit being shorter than the duration of the impulse generated by the first-mentioned timing circuit.

15. Apparatus as claimed in Claim 14 wherein the impulse generated by the second-mentioned timing circuit is arranged to condition the indicating device to indicate a number during the latter part of the duration of the impulse generated by the other timing circuit.

16. Apparatus as claimed in claim 14 wherein the impulse generated by the second-mentioned timing circuit is arranged to couple the counting circuit with an electronic valve storage circuit which controls the operation of an indicating and/or recording device.

17. Apparatus as claimed in any of Claims 13 to 16 wherein the counting and storage circuits are arranged to be coupled during the latter part of the impulse generated by the first-mentioned timing circuit.

18. Apparatus as claimed in Claim 5 and any of Claims 14 to 17 wherein the timing circuit which produces the electrical impulse of longer duration is arranged to apply said impulse to the electronic detector so that said detector is rendered inoperative to apply voltages to a self-resetting electronic valve trigger circuit.

19. Apparatus as claimed in any of Claims 13 to 18 wherein the timing circuits are self-resetting electronic valve trigger circuits.

20. Apparatus as claimed in any of Claims 6 to 19 which comprises means arranged to prevent impulses below a predetermined magnitude from being applied to the counting device.

21. Apparatus as claimed in any of Claims 7 to 20 which comprises a telegraphic reperforator apparatus which is arranged to emit electrical impulses so as to determine the time intervals while at substantially the same time energising a selector mechanism of a recording device, the operation of the recording device being controlled by the storage circuit.

22. Apparatus for producing the numbers of a series of random numbers, con structed and arranged to operate substantially as described herein and illustrated in the accompanying drawings.