GB2130782A - Arithmetic teaching device - Google Patents

Abstract

The device is microcomputer controlled and has input and output means including a display section (2) capable of displaying an arithmetic problem in the vertical form normally used in hand-written calculations so as to enable the user to more easily learn the manner of problem solution. In addition and subtraction, a carry-up or carry-down digit is displayed (8) as necessary so as to facilitate the teaching of basic arithmetic. A "teach" key (3a) may be provided to allow the user to see the next step in solving the problem. Displays and a voice composer may be used to indicate correct or incorrect entries or answers, and to show the number of problems to be solved or the time remaining for problem solution. <IMAGE>

Description

Arithmetic teaching device This invention relates to a device for teaching mathematical calculations, which is driven by a built-in microcumputer.

A conventional teaching device of this type is shown in FIGS. 1 through 3.

FIG. 2 is a block diagram showing the arrangement of a conventional calculation teaching device. As shown in FIG. 2, key input means 2 for inputting answers, etc. is connected to a one-chip microcomputer 5, the output of which is connected to a liquid crystal driver IC 6.

The driver 6 is connected to a liquid crystal display device. The display device has digit segments 9, 10 and 1 3 arranged in a line. The display section employs the same display method as a conventional electronic desk calculator, so that about ten digits are arranged horizontally to display problems and answers. In the case of a teaching device having a display device such as a liquid crystal display, a problem is displayed as shown in FIG. 1 , the user calcuiates the problem mentally and inputs the answer, and it is determined whether the answer thus inputted is correct or not; however, the process of arriving at the solution of the problem is not expressed or displayed. That is, the technical concept of the calculation teaching device is merely similar to that of an electronic desk calculator.Thus, the conventional device operates merely as a device providing problems and determining whether or not the answer is correct.

If one example of a conventional learning device having a display device comprising liquid crystal elements or fluorescent display tubes, a problem is displayed, the user inputs an answer, and it is determined whether or not the answer is correct. The device displays the problem and the answer on the display section; however, the number of problems provided and the period of time remaining for solving the problem or problems is not displayed. Thus, the device is disadvantageous in that the user does not know the number of problems which have been solved or which remain to be solved and the period of time remaining for solution of the problems. With a microcomputer, a number of segments are necessary for separately displaying the abovedescribed date (the number of problems and the remaining period of time); that is, it is difficult in the sense of hardware to do so.

An object of this invention is to provide a new or improved teaching device.

According to one aspect of this invention there is provided a microcomputer controlled arithmetic teaching device comprising output means and input means, said output means including display means comprising digit segment elements arranged in a form permitting calculation display in vertical form.

According to another aspect of this invention there is provided a teaching device comprising input means having a plurality of keys for inputting answers, and display means for displaying a problem of characters or digits, said display means including a first picture display pattern segment which is driven when an answer is correct, and a second picture display pattern segment which is driven when an answer is not correct, said first and second picture display pattern segments being operated in synchronisation with voices produced by said voice composing means.

This invention will now be described in more detail, by way of example, with reference to the accompanying drawings, in which: Figure 1 is a perspective view showing a conventional arithmetic teaching device; Figure 2 is a block diagram showing the arrangement of the device of Figure 1; Figure 3 is an enlarged view showing the display section of the device of Figure 1; Figure 4 is a perspective view showing an arithmetic teaching device according to this invention; FIG. 5 is a block diagram showing the arrangement of the device of FIG. 4; FIG. 6 is a block diagram showing the device of FIG. 4 in more detail; FIG. 7 is an enlarged view showing the display section of the device of FIG. 4; FIG. 8 is an enlarged view showing the position of a cursor on the display section of FIG. 7;; FIG. 9 is an enlarged view showing the designs of a timer segment and a number-of-problems segment; FIG. 10, 14 and 1 5 are explanatory diagrams showing examples of a solution process involving bridging (carry up); FIG. 12, 1 6 and 17 are explanatory diagrams showing examples of a solution process involving bridging (carry down); FIG. 11 is a flow chart prepared taking into account the bridging step (carry up) which occurs in addition; FIG. 13 is a flow chart prepared taking into account the bridging step (carry down) which occurs in subtraction; FIGS. 18, 20 and 21 are explanatory diagrams showing other examples of the solution process including bridging (carry down); FIG. 19 is a flow chart showing the control operation of the microcomputer which is effected when bridging occurs in subtraction;; FIG. 22 is a block diagram for a description of the solution process including bridging (carry down); FIG. 23 is an explanatory diagram showing another example of the carry-down display in FIG.

22; FIG. 24 is a block diagram of the display section of FIG. 7; FIG. 25 is an explanatory diagram showing one example of division, which is carried out with a cursor; FIG. 26 is an explanatory diagram showing one example of addition, performed with a cursor; FIG. 27 is a flow chart for a description of the calculation of FIGS. 25 and 26; FIG. 28 is a block diagram showing an electronic circuit for voice composition; FIG. 28A is a diagram showing a concrete example of the electronic circuit shown in FIG. 28; FIG. 29 is an explanatory diagram showing displays which are made when the answer is correct; FIG. 30 is an explanatory diagram showing displays which are made when the answer is not correct; FIG. 31 is an explanatory diagram showing the fact that the inputted data are improper; FIG. 32 is a block diagram of the display section in FIG. 9;; FIG. 33 is a flow diagram illustrating a "Please teach" function; FIG. 34 is a flow diagram showing the use of a manual carry-up or carry-down function; and FIG. 35 illustrates an alternate display method for more effective teaching of long division.

The invention will be described in detail, with particular reference to a first embodiment shown in FIGS. 4 through 9.

In these figures, reference numeral 1 designates the body of an arithmetic teaching device according to the invention, which has a display device 2 comprising a liquid crystal display (LCD) means or fluorescent display tubes, and key input means 3, and which has a handle 4 so that the body 1 can be readily carried.

Reference numeral 5 designates a one-chip microcomputer in which the problems and answers necessary for the arithmetic teaching device are stored, the microcomputer 5 being connected to the key input means 3; and 6 is an LCD driver for receiving the contents of a problem provided by the one-chip microcomputer 5, the LCD driver 6 being connected to the display device 2. The LCD driver 6 is designed so that the user inputs answers by operating the keys, or inputs commands or the like to request a display of the solutions. Reference numeral 7 designates a digit display section of the above-described display device 2.The digit display section 7 has a digit display unit 8 (FIG. 7) for displaying carry-up and carry-down digits in the upper area thereof, digit display means 9 and 10 are arranged in two lines for providing problems below the digit display unit 8, and a display section 11 for displaying the four arithmetic operation signs, which is located on the left-hand side of the lower problem providing digit display unit 10. Reference numeral 1 2 designates a solution line, which is located below the problem providing digit display units 9 and 10 and the arithmetic operation sign 11. Reference numeral 1 3 designates an answering digit display unit which can display four digits at maximum.

Reference numerals 14, 15, 1 6 and 17 (FIG. 8) designate cursor lines which form the lower segments of 7-segment electrodes. Reference numeral 18 (FIG. 9) designates a graph indicating the number of problems or the remaining period of time, which comprises, for instance, ten segments 19 through 28. A "timer" displaying segment 29 and a "number of problems" displaying segment 30 are provided beside the graph 18, and are selectively turned on depending on the content of the graph.

A voice composing arrangement for the arithmetic learning device will now be described with reference to FIGS. 28, 28A, 29 and 30.

FIG. 28 is a diagram showing an electronic circuit of the invention, FIG. 28A is a diagram showing a concrete example of the electronic circuit shown in FIG. 28, FIG. 29 is a diagram showing the display made by the liquid crystal display unit when the answer is correct, and FIG.

30 is a diagram showing the display made by the LCD unit when the answer is not correct.

In FIGS. 28 and 28A, the key input means 3 having a problem specifying key, operator specifying keys and other keys for inputting answer digits is connected, as a key input to the one-chip microcomputer 5, the output of which is coupled to a voice composing one-chip LSI 31 in which voice data composed through compression are stored in a nonvolatile memory, and to a liquid crystal driver IC 6.

The output of the voice composing one-chip LSI 31 is subjected to digital-to-analog conversion and is then applied through an impedance changing transformer 32 to a loud-speaker 33.

The outputs of the liquid crystal driver 6 are connected to the large liquid crystal display means 2. More specifically, the outputs of the liquid crystal driver 6 are connected to the "problem" digit segments 9 and 10, the "answer" digit segments 13, picture display pattern segments 34 which are operated when the answer is correct, and picture display pattern segments 35 which are operated when the answer is not correct, in FIGS. 29 and 30.

As indicated blocks of FIG. 28A, SMC1 102 (Manufactured by Suwa Seikosha Co., Ltd.) or M58496 (Mitsubishi Denki K.K.) is used as a microcomputer 5; TMS5 111 (T.l. Ltd.) or M58817AP (Mitsubishi Denki K.K.) is used as a speech synthesizer and TMS6125 (TI. Ltd.) or M5881 8P (Mitsubishi Denki K.K.) is used as a memory (ROM). The speech synthesizer and ROM constitute the voice composing unit.

FIG. 32 is a block diagram showing the embodiment of FIG. 9. In FIG. 32, the microcomputer 5 receives key data from the input section 3 comprising the key switches, and the output of the microcomputer 5 controls the output driver 6 to operate the above-described display section 2.

The operations of various embodiments of the invention will now be described.

A program for generating random numbers and a program for generating addition problems, subtraction problems, etc. are stored in the ROM in the one-chip microcomputer. A problem is displayed on the liquid crystal device 2 as shown in FIG. 6, and the answer is inputted by the use of key input means 3, so that the "answer" digit segments 1 3 are lighted. The display is made in accordance with calculations as performed by writing. Accordingly, the display is made such that the user of the arithmetic teaching device such as a pupil, performs the calculation in the same manner as hue or she would if solving the problem in writing.For instance, in the case of addition, the calculation is performed by operating the keys beginning with the unit digits and then the tens digits, with any carry taken into account, until the correct answer is obtained.

One example of the display is shown in FIG. 10.

In this example, (58 + 6) is calculated with bridging (carry up). This calculation will be described with reference to a flow chart in FIG. 11.

Another example of the display is as shown in FIG.

1 2. In this example, (32 - 7) is calculated with bridging (carry down). This calculation will be described with reference to a flow chart in FIG. 1 3.

In the calculation of (58 + 6), first the microcomputer 5 selects Step 36 (addition). In Step 37, the addition of the unit digits is carried out. In Step 38, it is detected whether or not a carry-up flag is up (set). In this case (the example of FIG. 10), the answer is "yes", and Steps 39 and 40 are effected so that a "1" is displayed by the carry-up display unit 8 and "4" is displayed at the units position as shown in FIG. 14. In the next Step 41, the "1" displayed by the carry-up display unit 8 is added to the tens digit, and in Step 42 the result of addition is displayed as shown in FIG.

15. Thus, the calculation has been accomplished.

In this case, bridging (carry up) is performed, which occurs only in the addition of the units position. When no bridging is caused in Step 38, then in Step 43 addition of the digits is carried out and the result of addition is displayed. In FIGS.10, 14 and 15, the digits surrounded by the broken lines are those which are most currently displayed.

In the calculation of (32 - 7), similarly the microcomputer 5 selects Step 44 (subtraction) (Fig. 13). In Step 45, subtraction of the unit digits is carried out. In Step 46, it is detected whether or not the borrow flag is up (set). In this case, the result of detection is "yes", and therefore Steps 47 and 48 are effected. Thus, "1" is displayed by the "carry-down" display unit 8, while "1" is subtracted from the tens digit and the result of subtraction is then displayed as shown in FIG. 1 6.

Then, in Steps 49 and 50, the unit digit, which is the result of the subtraction, is displayed at the units position, and subtraction at the tens position is carried out and the result is displayed as shown in FIG. 1 7. Thus, the calculation has been accomplished. In this case, bridging (carry down) is performed, which occurs only in the subtraction at the units position. In FIGS. 12, 16 and 17, the digits surrounded by the broken lines are those which are most recently displayed.

The function of a "PLEASE TEACH" key 3a provided to the key input means 3 will now be briefly described.

As described above, an arithmetic operation is composed of a plurality of steps, and thus it is desired to reproduce the solution of a problem step by step, so that the user can understand the solution easily. According to the present invention, once the user depresses the "PLEASE TEACH" key 3a, one calculation step is advanced and displayed. This operation is accomplished according to the flow chart shown in FIG. 33.

Further, carry-up and carry down input keys are provided to the key input means 3 in order to input and display the carry-up or carry-down digits manually. An embodiment of a calculation using the manual carry function is shown in FIG. 34.

In the above-described embodiment, an LCD display board is employed as the display means; however, it may be replaced by other display means comprising, for instance, fluorescent display tubes. The carry-up and carry-down display unit is made up of seven-segment electrodes; however, the carry-up and carry-down function may be displayed by other symbols or the like.

Another example of the display is as shown in FIG. 18. In this example, the calculation (23 - 5) requires bridging (carry down). The calculation will be described with reference to a flow chart in FIG.

19.

First, the microcomputer 5 selects Step 44 (subtraction). In Step 45, subtraction at the units position is carried out. In Step 46, it is detected whether or not the borrow flag is up (set). In this case, the result of detection is "yes", and therefore Steps 51, 52, 53 and 54 are effected. In order to indicate the occurrence of bridging (carry down), an oblique line 55 is drawn across the digit "2" at the tens position, so that it is displayed on the display means 2 that "1" is carried down and the digit "2" at the tens position is changed to "1". In Steps 56, 57 and 58, the unit digit of the result of subtraction is displayed at the position of solution, and the result of subtraction of the tens position is displayed. Thus, the calculation has been achieved.In this case, bridging (carry down) is effected in the subtraction of two figures, which is caused only in the subtraction at the units position.

In the above-described embodiment, the oblique line 55 is used to indicate bridging (carry down): however, the same effect can be obtained by using an arrow 59 as shown in FIG. 23.

Furthermore, in the above-described embodiment, an LCD display board is employed as the display means; however, it may be replaced by other display means comprising fluorescent display tubes.

The solution of a problem (58 + 6) including bridging (carry up) will now be described with reference to FIGS. 7, 10, 14, 15 and 24. In the calculation of (58 + 6), the digits "5", "8" and "6" are displayed by the digit display units 91, 9 and 10, respectively; that is, the problem is provided as one which has been stored in advance. First, the user obtains the sum of the unit digits "8" and "6": 8 + 6 = 14. Therefore, the user inputs the unit digit "4". The digit "4" thus inputted is displayed by the digit display unit 1 3 by means of the microcomputer. Then, the user inputs the tens digit "1", which is the bridging number. The digit "1" thus inputted is displayed by the digit display unit 81 with the aid of the microcomputer. Then, the user obtains the sum of the tens digits "5" and "1": 5 + 1 = 6.Therefore, the user inputs the digit "6", which is displayed on the digit display unit 131. Thus, the answer "64" is obtained. A problem including bridging (carry down) can be solved and displayed similarly to the abovedescribed solution, and therefore a detailed solution will be omitted.

The solution of the problem (69/3) in which calculation is made beginning with the most significant digit as shown in FIG. 25, and the solution of a problem (17 + 14) in which calculation is made beginning with the least significant digit as shown in FIG. 26, will now be described with reference to a flow chart in FIG. 27.

(i)69-:3 This is a division problem. The problem is provided as shown in the flow chart of FIG. 27, with a cursor 14 displayed as shown in part (a) of FIG. 25. The user performs the calculation at the tens position (6/3 = 2), and inputs the result of calculation, which is "2" in this case. As the digit is inputted, the cursor 14 is erased; that is, it is shifted to the right, thus appearing as a cursor 1 5 as shown in part (b) of FIG. 25, and "2" is displayed at the position where the cursor 14 was.

Similarly, the user performs the calculation of the units position (9/3 = 3), and inputs the answer "3" so that it is displayed at the position of the cursor 1 5 (part (c) of FIG. 25). Thus, the solution (69/3 = 23) has been obtained. It can be detected by operating an enter key whether or not the solution is correct.

FIG. 35 illustrates an example of another display arrangement for a division problem.

This example more resembles in form the manner used in longhand division. A divisor 124 is separated from the dividend 126 by a bar 122 indicating division. Bars 121 and 123 separate the given numbers from the space for the answer, indicated by pointer 128. Because of the use of the bars 121 and 122, an operation indicator 125 is not necessarily needed in this case. Also, answer marker 127 does not appear in the case of division.

The user first enters the first answer digit for division in the tens column, and this digit appears beside indicator 1 28. Any remainder of residual 129 appears to the left of indicator 1 30. This digit may be either manually or automatically displayed. Taking the remainder into account, division is now performed with the remaining digit of the dividend. The answer is indicated to the left of marker 128, and any remainder is now displayed immediately to the left of marker 130.

In this example, effective display of the division process is enabled by merely adding a few additional display elements, and by changing the location of the display of the problem with respect to the answer, as compared with the other arithmetic functions.

(ii) 15 + 24 This is an addition problem. The problem is provided as shown in the flow chart of FIG. 27 with the cursor 1 7 displayed as shown in part (a) of FIG 26. The user performs the calculation at the units position (5 + 4 = 9) and inputs the digit "9".

The digit "9" is displayed at the position of a cursor 1 7. The cursor 1 7 is shifted left, thus appearing as a cursor 16. Similarly, the user performs the calculation at the tens position (1 + 1 = 2) and inputs the answer "2" so that it is displayed at the position of the cursor 16. Thus, the solution (15 + 14 = 29) has been obtained. In this case also, it can be detected by operating the enter key whether or not the solution is correct.

The operation of the device will ba described with reference to FIGS. 28, 29, 30 and 31.

Of the programmed instructions stored in the nonvolatile memory in the one-chip microcomputer, for instance a problem providing instruction is used so that data are transferred to the liquid crystal buffer IC 6 to allow the display of "2 + 5". When the answer is inputted by operating the key input section, it is compared with the correct answer in the microcomputer 5.

When both values coincide, a picture pattern segment 34 in FIG. 29, which is driven when the answer is correct, is driven. At the same time, a voice data address, which is provided when the answer is correct, and a voice production timing signal are applied to the voice composing LSI 31.

As a result, the pictures of a train and smoke from the train are displayed as shown in FIG. 29, while a voice "THE ANSWER IS CORRECT" is produced through the loudspeaker 33 of the body 1 of the arithmetic learning device.

When the answer is not correct, a liquid crystal picture display segment 35 in FIG. 30, which is driven when the answer is not correct, is driven. At the same time, a voice data address, which is provided when the answer is incorrect, is supplied so that a voice "THE ANSWER IS NOT CORRECT.

CALCULATE AGAIN" is produced through the loudspeaker. Thus, the user can clearly learn whether or not the answer is correct.

The arithmetic learning device according to the invention is constructed as described above.

Whether the answer is correct or not can be detected from the operations of the picture display segments of the liquid crystal as well as the voices produced. Therefore, the device is considerably effective as auxiliary means for assisting a child in the learning of calculations.

FIG. 31 shows one example of the display in which the answer is not correct. In this case, a segment 60 indicating the fact that inputted data 13 is wrong is lighted, so as to cause the user to input correct data. In this case, the method described with reference to FIG. 31 may be employed for firstly determining whether the answer is correct or not, and the method described with reference to FIG. 30 may be employed for secondly determining whether the answer is correct or not. In this connection, the voice "CALCULATE AGAIN" is produced for the first determination, and the voice "THE ANSWER IS WRONG. NEXT PROBLEM" is produced for the second determination. The arithmetic device of the invention thus becomes more effective in teaching calculations to school children.

The operation of the embodiment shown in FIGS. 9 and 31 will now be described. The microcomputer 5 forms a problem with the aid of the built-in program, and drives the output driver so that the problem is provided on the problem display section. The user inputs the answer by operating the input section 3, thus solving the problem. In a mode where problems are provided with a time limit of ten minutes for instance, the timer 29 is lighted and the segments 1 9 through 28 are turned off one after another beginning with the segment 19 in such a manner that one segment is turned off whenever one minute passes per problem. Thus, all the segments 19 through 28 are turned off in ten minutes.

Therefore, the user can detect how many minutes are left for solving the problems, by observing the graph indication.

In a mode that the number of problems is predetermined to be, for instance, "10", the number-of-problems segment 30 is lighted, and the segments 19 through 28 are turned off one after another in the stated order in such a manner that one segment is turned off whenever one problem is solved. Thus, when all the segments 1 9 through 28 are turned off, they indicate the tact that all ten problems have been solved.

Thus, the number of problems not yet solved or the number of problems which have been solved can be readily detected by observing the graphic indication. In addition, if the two modes are inputted by operating the input section 3, then the segments 1 9 through 28 can be selectively used as a means for indicating the remaining time or the remaining number of problems.

The segments 1 9 through 28 may be arranged in the form of a circular graph.

The arithmetic learning device of the invention is constructed as described above, and has the following merits: (1) In the device, data are inputted according to the traditional calculation-by-writing system. With the device, the user needs no notebook and pencil.

Thus, the device is convenient for a school child.

(2) The device has display means for indicating the solution process, including bridging (carry up and carry down), which is controlled by the microcomputer. Thus, the device of the invention is considerably effective in allowing a school child to understand the solution.

(3)A school child can effectively study the solution as the operation of bridging (carry up and carry down) is included in the display means. If the carry-up digit display unit 5A and the carry-down digit display unit 6A are colored differently or surrounded with frames of different color, then the carrying up and carrying down operation can be clearly distinguished from each other. This will contribute to an understanding of the concept of bridging.

(4) The calculation-by-writing system is employed, the answer is displayed beginning with the most significant digit or the least significant digit as the case requires, and a cursor is provided to indicate a position where the answering digit should be displayed. Therefore, the user can readily understand the solution process. Thus, the device of the invention is significant in learning how to solve problems.

(5) A graph means comprising a plurality of segments is used to selectively indicate the remaining time and the number of problems. Thus, the number of segments can be reduced by as much. The graph means allows the user to visually detect how many minutes are left or how many problems have been solved.

(6) According to whether the answer is correct or not, different display units are operated in synchronization with different sounds. This makes the device more effective in learning calculations.

Claims (21)

Claims

1. A microcomputer controlled arithmetic teaching device, comprising: output means and input means, said output means including display means comprising digit segment elements arranged in a form permitting calculation display in vertical form.

2. A device as claimed in claim 1, wherein said vertical form of calculation display is provided with a segment element summing line.

3. A device as claimed in claim 1, said display means being capable of displaying a provided calculation problem and the answer thereto, and, in the case of subtraction, a carry-down digit for illustrating the solution process of said problem, said carry-down digit being indicated by one or more display elements.

4. A display as claimed in claim 1, said display being capable of displaying a provided calculation problem and the answer thereto, and including a display element for displaying a carry-up or carrydown digit to illustrate the solution process of said problem.

5. A device as claimed in claim 4, wherein said input means comprises an input keyboard for inputting a carry-up or carry-down digit manually.

6. A device as claimed in claim 1, said display means being capable of displaying a calculation problem and the answer thereto, and a carry-up and carry-down digit for illustrating a solution process of said problem, said carry-up and carrydown digit being displayed in a color different from other digits, and said carry-up digit and said carry-down digit being displayed with frames different in color from each other.

7. A device as claimed in claim 1, said display means including a cursor for allowing the inputting of answer digits beginning with one of the most significant digit and the least significant digit.

8. A device as claimed in claim 7, wherein said cursor for allowing the inputting of answer digits is a part of a digit segment.

9. A teaching device, comprising; voice composing means; input means having a plurality of keys for inputting answers; and display means for displaying a problem of characters or digits, said display means including a first picture display pattern segment which is driven when an answer is correct, and a second picture display pattern segment which is driven when an answer is not correct, said first and second picture display pattern segments being operated in synchronization with voices produced by said voice composing means.

10. A device as claimed in claim 9, wherein said display means displays said problem in a vertical form of calculation.

11. A device as claimed in claim 1, wherein said display means further includes means for selectively displaying the number of problems provided and a period of time remaining for solving a problem or problems.

12. A device as claimed in claim 1, wherein said display means comprises at least one of liquid crystal elements, fluorescent display tubes, and light emitting diodes.

13. A device as claimed in claim 1, wherein said input means comprises a keyboard.

14. A device as claimed in claim 1, wherein said display means includes at least two columns for the display of problem and answer digits.

15. A device as claimed in claim 14, wherein said display means further includes means for displaying one of a carry-up and a carry down digit in the case of addition and subtraction, respectively, and for displaying a remainder, in the case of division.

16. A device as claimed in claim 14, wherein said display means further includes time indication means, problem number indication means, and correct and incorrect answer indicating means.

1 7. A device as claimed in claim 1, further including voice composing means for vocally indicating correct and incorrect answers.

1 8. A device as claimed in claim 13, said keyboard including keys for indicating problem answers and for manually entering carry-up and carry-down digits.

19. A device as claimed in claim 18, further including a teaching key for enabling display of the next step in the solution of said problem.

20. A device as claimed in claim 14, said display means further including arithmetic operation indicating means.

21. A device as claimed in claim 20, said indicating means including picture element means for indicating long division.