WO1984000431A1

WO1984000431A1 - Process and electronic apparatus for teaching and using number systems by means of letters and numbers

Info

Publication number: WO1984000431A1
Application number: PCT/HU1983/000036
Authority: WO
Inventors: Lajos Hajnal; Endre Simonyi
Original assignee: Konsumex Kuelkereskedelmi Vall
Priority date: 1982-07-13
Filing date: 1983-07-07
Publication date: 1984-02-02
Also published as: DE3390090T1; PT76971A; EP0112880A1; JPS59501248A; GB2135100A; NL8320202A; GB8405424D0

Abstract

A process for using and teaching mathematical basic operations in an optionally chosen number system, as well as to the electronic apparatus for the realization of said process which contains a memory, display with screens and keys. The essence according to the invention lies in that the person performing the operation is setting the task in form of letters, while during the time of solving the task always the same number is co-ordinated to one certain letter, the tasks figuring in form of letters is displayed on the screen. Thereafter the result of the given operation is also displayed in form of letters, thereafter, the numerical values considered as corresponding to the single letters by the person trying to solve the task are displayed on the place corresponding to the local value of the given letters by pressing the proper key. In case of an incorrect choice of letter and digit, i.e. if a mathematically impossible result is obtained, the error is indicated for the person performing the operation. A further essence of the invention lies in that the electronic apparatus contains a central microprocessor unit, one input channel each of which is connected to a fixed and random memory, to the letter input and displaying unit, the unit for setting the selected number system, for the input of signs of operation and equality, to the unit for correction of the data input, as well as to the cancelling unit. The output channels each of the microprocessor is connected to the fixed and random memory, the letter input and display unit, the unit for the input, and display of digits, as well as to the unit displaying the erroneous result and the unit for the display of the correct result.

Description

PROCESS AND ELECTRONIC APPARATUS FOR TEACHING AND USING NUMBER SYSTEMS BY MEAN3 OF LETTERS AND NUMBERS

The invention relates to a process and electronical means having been designed for the realization of said process, for teaching the number systems, practicing the operations preformed therein by the aid of letters and numbers; both the process and the apparatus can be successfully used as a toy developing power of thinking and logical skill.

Algebraic problems are known, at the solution of which one word is added to another and the third word, we are searching for is forming the result. The task lies in to determine the values of the numbers belonging to the letters figuring in the words. So e.g.

S E N D + M O R E M O N E Y However, up to now neither tasks, nor means for solving them are known, wherein the number system is changing. Neither are tasks known with which the re-suit is also representing a series of letters and in course of solution the whole legend is to be determined.

A plurality of computers is known, by the aid of which arithmetic basis operations can be performed and on the display element of which data, re- suits in the decimal system can be displayed numerically, in a given case alphanumerically. However, neither electronic means nor computers are known, by the aid of which mathematical operations could be performed by trains of letters in any optional number system.

The aim of the invention is to develop a process and an electronic device, by the aid of which mathematic basic operations can be performed by means of optional letters and in optional number systems so, that solution in a given number system is to be obtained by the way of logical thinking. The apparatus according to the invention controls the solution of the task, it displays the proper result and also the erroneous answer.

Accordingly, the invention relates to a process for using and teaching mathematical basic operations in any optional number system.

The essence of the process according to the invention lies in that the person performing the operation is giving the task in form of letters, while during the time of solving the task the same number is co-ordinated at random to one certain letter, the task figuring in form of letters is written on the display, thereafter the result of the given operation is also written in form of letters; thereafter, the numerical values considered as corresponding to the single letters by the person trying to solve the task are displayed on the place corresponding to the local value of the given letter by means of keys; in case of an improper choice of the pair of letter and digit, i.e. if a mathematically impossible result is obtained, the error is indicated for the person performing the operation. With a preferred embodiment of the invention two screens are used for solving and control of the task, one for the display of the letters, the other one for the numbers. The essence of the method lies in that the digits - when substituted for the given letters - are leading to a mathematically correct solution, are to be found by logical thinking, step by step. This method is really advantageous, because - either we intend to use the electronic apparatus for teaching, using or play - solving the task requires thinking at all means, as the apparatus is evaluating only and indicates the result of evaluation.

Accordingly, the invention relates to a process for using, teaching mathematical basic operations in an optionally chosen number system - or simply playing a game - and the essence of the process according to the invention lies in that the person performing the operation is giving the task in form of letters, while during the time of solving the task always the same number is co-ordinated at random to one certain letter, the task figuring in form of letters is written on the screen, thereafter the result of the given operation is also written in form of letters; thereafter the numerical values considered as corresponding to the single letters by the person trying to solve the task are displayed on the place corresponding to the local value of the given letter by means of pressing the proper key; in case of an incorrect choice of the pair of letter and digit, i.e. if a mathematically impossible result is obtained, the error is indicated for the person performing the operation.

In course of the process according to the invention the number system in which we intend to operate is given in the order of sequence, thereafter the first operandus of the operation is introduced in form of letters, followed by the sign of the operation; in the next step the second operandus of the operation is introduced also in form of letters, - in case of several lines, alternatively the next operandus - thereafter the sign of the operation, the sign of equality; after having performed all the steps, the apparatus according to the invention writes the solution of the task in form of letters. In course of a given task or a game the electronic apparatus co-ordinates always the same digit - chosen at random - to a letter having been already introduced. In the next step we introduce the digits considered as proper, one by one, to the place of the corresponding letters. The apparatus according to the invention is designed so, as in case of the input of a number, which would lead to a mathematically impossible result, the apparatus is giving immediately a signal, i.e. if the place value of a partial numerical structure is not in the correct compliance with the letter structure.

The invention also relates to the electronical apparatus for realizing the process according to the invention containing the units satisfying the aimed functions.

The essence of the electronical apparatus according to the invention lies in that it contains a central microprocessor unit, one input channel each of which is connected to a fixed and random memory, the letter-input and display unit, the unit for the adjustment of the selected number system, to the digit input and display unit, the unit for the input of the mathematical operator and equality, with the unit for correction the data-input, as well as with the canceling unit; the output channel each of said central microprocessor unit is connected to the fixed and random memory, with the letter input- and display unit, the digit input- and display unit, as well as the unit displaying the erroneous result and the unit for the display of the correct result.

An advantageous embodiment of the invention is characterized in that the unit for the input and display of the digits is provided with a row of keys having been designed for the input of the digits. With a further preferred embodiment of the invention the unit for the input of the letters and for the display thereof is provided with a row of keys being suitable for the input of the letters.

The process and the apparatus according to the invention will be described in details by means of preferred embodiments, by the aid of the drawings enclosed, wherein figure 1 illustrates the block scheme of the electronic apparatus according to the invention, figure 2 is showing the frontal plate of the preferred embodiment of the electronic apparatus according to the invention with, the manipulating elements serving as an example. The block scheme of the electronic apparatus having been developed for realizing the process according to the invention is to be seen in figure 1. The circuit arrangement contains the central microprocessor unit 3, connected to the fixed and random memory 1. The central microprocessor unit 3 is connected to the unit 2 for the input and display of the letters, by the aid of which the selected or predetermined letters can be written by pressing the proper keys 11. In addition, the central microprocessor unit 3 is connected to the unit 5 for the adjustment of the selected number system, formed in the present embodiment serving as an example as a push-switch 14, the push-switch 14 is to set to the base figure of the selected number system. Further input channels of the central microprocessor unit 3 are connected to the unit 6 for the input of the mathematical operator and equality, respectively, as well as with the unit 9 for the required correction of the dates having been already introduced, as well as with the canceling unit 10; the output channels are connected with the unit 7 displaying the correct result and with the unit 8 displaying the incorrect results, as well as with the units 2 and 4.

The frontal plate of a preferred embodiment of the circuit arrangement according to the invention and the manipulating organs thereon are to be seen in figure 2. The keys are arranged on the frontal plate in an ergonomically advantageous manner. The embodiment illustrated here and serving as an example can be used up to the decimal number system, however, it goes without saying, that the number of the number systems can be optionally larger or smaller.

In the centre of the frontal plate the two screens 13, 19 are arranged, screen 13 writes the letters, while screen 19 writes the digits. In a line five letters each can be written at most, with the exception of the third line, wherein in dependence of the result six letters may appear. Beside the screen 13 and 19 the keys 16, 17 for the input of the operational signs are to be found, underneath the lamp 20 indicating the correctness or incorrectness of the chosen number, as well as the lamp 22 indicating the correct choice. The lamp 22 is lighting with a discontinuous or continuous light depending on whether the solution found is representing one of the possible solutions, or perhaps a solution, the apparatushas also "thought" of. On the lower part of the frontal plate the keys 11 for the selectable letters and keys 12 for the selectable digits are arranged, mutual co-cordination and input becomes possible by means of the key 18 arranged inbetween. The further keys on the frontal plate is the key 21 for canceling the last introduced digit and the key 23 for canceling the whole - i.e. already solved - task or an interrupted operation, as well as the key 15 for switching-on the apparatus.

The embodiment described here represents but one possible version of realization, so e.g. different display means, instead of the keys other switching elements may be used, or the keys may be omitted at all.

The principle of operation of the process, and the electronic apparatus for realizing said process, is, as follows:

The apparatus is suitable for playing in number systems, by using the model serving as an example addition and subraction may be performed from the binary number system up to the decimal system. First of all, the digits are adjusted in form of letters, thereafter the values of the digits having been substituted by the letters are to be determined by reasoning and to introduce them into the apparatus. In the drawing illustrating the toy ten keys 11 for the letters and ten keys 12 for the digits are to be found. Whichever of the letter-keys is pressed down, the electronics of the toy select at random a one-figure number, it records to which of the letters it belongs and stores it in its memory. We never know the number the electronics are chosing, whenever a letter-key is actuated. The letters may be pressed in any optional order of sequence. Electronics may choose any number to any letter, accordingly, any letter may stand for any number.

Within one task, e.g. within addition, the same letter-key can be repeatedly pressed down, the value of which will be a memorized digit. Within one task the same digit cannot belong to different letters, this possibility is excluded from the principle of the toy. Whenever a new task is to be solved, different numbers will belong to the same letter. The choice is at random, random character is automatically assured.

The letters appear on the screen 13. A line consisting of 2 x 5 letters the most can be written onto the screen. Binary system

The push-switch 14 is to be set onto the graduation two /2/. In the two-position any letter can be pressed and in any optional order of sequence, but not more, than two. The numerical value in any order of sequence may be either 0, or 1, as in the binary system only these two digits exist.

It is the task of the push-switch 14 to restrict the number of piece of the digits to be used, in an increasing order of sequence and in any number system. If a third letter-key is pressed, the apparatus does not react at all, no letter appears on the screen 13, as no third digit can be given. The two letters already chosen - appearing also in the screen 13 - can be repeatedly actuated. The two selected letters can be varied on the screen 13, on 1 to 5 letter-places per line. Ternary system

In this case the push-switch 14 of the number system is to be set onto the graduation 3 of the scale. In the three-position any letter-key and in any optional order of sequence can be actuated, but three at most. The numerical value thereof can be 0, 1 and 2 in any optional order of sequence, as in the ternary system only these digits exist. /Restriction is assured by the push-switch 14./

If a fourth letter-key is pressed, the toy does not response, the letter does not appear on the screen either, because no fourth digit can be given. It goes without saying that the three letters having been already chosen and appearing on the screen can be repeatedly selected. The selected three letters can be varied on the screen 13, on 1 to 5 places per line. Number systems from the quaternary to the number system 9

The principle is identical with those of the binary and ternary systems. In the increasing order of sequence of the number systems always one more letter differing from the previous one can be used. Decimal system

In the decimal system the push-switch 14 is to be set on the graduation 10. All the ten letter symbols can be used in an optional order of sequence. In this case every one of the ten letter symbols has its digit-pair. It is possible to use less letters, if the lines consisting of 2 x 5 letter places are not completely occupied or a letter is repeatedly used. In this case some of the ten digits - not known for us - will not be memorized. The essence of the game lies in to determine by reasoning the digits which correspond to the letters appearing in the line consisting of 2 x 5 letter places and in the result-line comprising six letter places, from two to ten, in some pre-selected number system. The game can be played individually or in groups. So e.g. any order of sequence of the letters in any number system can be set as a task for a group, e.g. for the pupils of a class.

In course of the game the following aims can be set:

- let us search for at least one correct solution;

- let us search for the solution having been chosen by the apparatus;

- let us search for all the possible solutions, etc. Conversion of different number systems may form a task too. The toy is excellently suitable for the estimation of concluding ability of a group or the individuals therein, in form of a game, simultaneously comprehension and teaching of the number systems can be also promoted. How to play or use?

Let us switch-on the current source by using the key 15. Let us appoint the task.

1/ First of all, let us decide on the number system we want to play or use with and let us set the push-switch 14.

2/ We are allowed to play with as many letters, as it is enabled by the number system chosen. By pressing the letter-keys in an optionally Ghosen order of sequence, we are filling 1 to 5 letter places in the first line, among them similar letters may be also chosen. The letters appear on the screen. 3/ Depending on the operation we intend to perform, we press the key 16, either "+" or "-". Writing into the second line is permitted only after having pressed the proper sign-key. If. e.g. only two-three letters were taken up into the first line by,pressing down the sign-key, it will be assured, that the second line follows.

4/ By pressing the letter-keys, 1 to 5 letter places are occupied in the second line in an optional order of sequence, however, within the limits of the number system. The letters may be identical with those in the first line.

5/ We are pressing the key 17 for the sign of equality and the apparatus records the result of the operation performed in the result-line. Let us suppose, that the following task was set in the decimal system:

DLA

/+/KDF

CCDC The solution can be : 208 or 307 /+/ 923 /+/ 834

1131 1141

Or in the quaternary system: KCCL, corresponding to 3221 /+/ CHHK /+/ 2003

LLCKH 11230 corresponding to the numbers possible in the quaternary system. Both solutions are in compliance with the train of letters, that is, what we are searching for.

How, when substraction is performed, it may happen in any number system that the second line is showing a larger number having been chosen by the electronics. In this case the toy is putting a "-" sign into the 6th position of the result-line, while this result represents the absolute value of a difference.

E. g. in the decimal system: the task: DFX the chosen digits 532

BKC 814

/-/ XBX /-/ 282

E.g. in the number system "5" the task KAL 231

ACK 342

/-/ LLL /-/ 111

This can be immediately recognized by simple glance and the task can be solved. Searching for the solution 1/ Let us think over the train of letters to be seen on the screen 13!

- In which number system the game is taking place?

- Which numbers are possible?

- How many varieties of letters were taken? - How many figures are contained in the result? 2/ Considering the above mentioned, we may suppose that one of the letters, let us say, the letter C equals to 3, i.e. C = 3. Now let us press the key for the letter C, the key 18 of the sign of equality and the key 12 of the digit-sign 3. On the second searcher screen 19 the number 3 appears and on every place, where the letter C appeared on the first screen 13. The numbers are substituted into the places of the letters. 3/ All the possibilities are repeatedly taken into consideration. We are chossing a newer number to a newer letter, we are substituting and proceed till reaching the complete solution. 4/ In case if in any phase of performance one of the suppositions is unreal, i.e. the train of digits having been produced does not correspond to the train of letters, the red lamp 20 is lightening. In this case the last supposition may be cancelled by simply pressing down once the key 21 with the sign CC and a new digit can be chosen. If we intend to cancel the complete train of numbers having been taken up, because we want to start, with new suppositions, the key 21 is to be pressed twice. 5/ If the green lamp 22 is continuously lighting, the solution is in compliance with the train of letters and we succeeded in finding the memorized numbers. A full hit!

However, if the lamp 22 is lightening, the solution corresponds to the train of letters, but we could not find the variation chosen by the apparatus. In this case the result can be cancelled by pressing twice the key 21 with the sign CC and the player may begin to search for the variation having been chosen by the toy or any other still existing variation. 6/ The key 23 with the sign CE is cancelling everything, the letters, the numbers and the whole contents of the memory. The toy is empty, a new game may be begun.

In the binary system there are 4 variations for each place value, that means totally 4⁵ = 1024 variables, accordingly, it seems to be advantageous to begin the game in this number system. In this system two letters, i.e. two digits - 0 and 1 - may occur. In the ternary system 9 variations for each place value exist, that means totally 9⁵ = 59049 variations.

In the decimal system 100 variations are possible for each of the place values, accordingly, totally 10 milliards of variations are possible. It is proposed to begin the play with identical letters and not more, than two-three letters per line, and only after having gained the experience, four-five letters can be written in a line. The table of the number systems is enclosed to the toy. From the table the interpretation of the single number systems and their numerical values on the single value places can be read out.

The digits which may be chosen by the toy in the single number systems:

Number system 2: 0 1

Number system 3: 0 1 2

Number system 4: 0 1 2 3

Number system 5: 0 1 2 3 4

Number system 6: 0 1 2 3 4 5

Number system 7: 0 1 2 3 4 5 6

Number system 8: 0 1 2 3 4 5 6 7

Number system 9: 0 1 2 3 4 5 6 7 8

Number system 10: 0 1 2 3 4 5 6 7 8 9

Claims

WHAT WE CLAIM:

1. Process for using and teaching mathematical basic operations to be performed in an optionally chosen number system, c h a r a c t e r i z e d in that the person performing the operation is setting the task in form of letters, while during the time of solving the task always the same number is co-ordinated at random to one certain letter, the task figuring in form of letters is displayed on the screen, thereafter the result of the given operation is also displayed in form of letters, thereafter the numerical values considered as corresponding to the single letters by the person trying to solve the task are displayed on the place corresponding to the local value of the given letters by pressing the proper key, in case of an incorrect choice of the pair of letter and digit, i.e. if a mathematically impossible result is obtained, the error is indicated for the person performing the operation.

2. Electronic apparatus for realising the process according to claim 1, containing a memory, screens, as well as keys, c h a r a c t e r i z e d in that it contains a central microprocessor unit /3/, one input channel each of which is connected to a fixed and random memory /1/, the letter input and display unit /2/, the unit for the adjustment of the selected number system /5/, the unit for the input and display of the digits /4/, the unit /6/ for the input of the signs of operation and equality, with the unit /9/ for correction of the data input, as well as with the cancelling unit /10/; the output channel each of the microprocessor /3/ is connected to the fix and random memory /1/, the letter input and display unit /2/ the unit /4/ for the input and display of the digits, as well as to the unit /8/ displaying the erroneous result and the unit /7/ for the display of the correct result.

3. Electronic apparatus as claimed in claim 2, c h a r a c t e r i z e d in that the unit /4/ for the input and display of the digits contains keys being suitable for the introduction of the digits.

4. Electronic apparatus as claimed in claim 2 or 3, c h a r a c t e r i z e d in that the unit /2/ for the input and display of letters contains keys for the introduction of the letters.