US3643347A

US3643347A - Numeral base conversion instructional device

Info

Publication number: US3643347A
Application number: US4484A
Authority: US
Inventors: Sigi Ziering
Original assignee: Individual
Current assignee: Individual
Priority date: 1970-01-21
Filing date: 1970-01-21
Publication date: 1972-02-22
Anticipated expiration: 1989-02-22

Abstract

The instant invention involves a conversion device which enables the ready conversion of numerals in a first numeral base, such as the base 10, or decimal system, to another and different, numeral base system, such as the base 2, or binary system. The conversion device generally comprises a container divided into an upper section, a midsection and a lower section. The upper section serves as a reservoir for discrete measuring units, such as balls. The midsection serves as an area of transfer for the balls between the reservoir and the lower section. The lower section consists of a plurality of parallel channels, each adapted to receive a preselected number of balls. A selector bar, moveable along the lower section, has means for defining the number of balls which can be contained in each column. The device is operated by a gravity feed. If a predetermined number of balls is released from the reservoir into the midsection, and selectively directed to the lower section, the balls will fill up varying numbers of the columns, depending upon the location of the selector bar. By observing this number of columns filled up by the balls, one can readily determine the corresponding numeral in a particular base system. The corresponding numeral in a different base system for the same amount of balls can readily be determined by moving the balls from the columns back into the midsection, relocating the selector bar again allowing the columns to fill up with balls, and then noting the number of filled columns.

Description

United States Patent [151 3,643,347 Ziering 51 Feb. 22, 1972 54] NUMERAL BASE CONVERSION INSTRUCTIONAL DEVICE [72] Inventor: Sigi Ziering, 720 North Walden Drive,

Beverly Hills, Calif. 90210 [22] Filed: Jan. 21, 1970 [211 App]. No.: 4,484

Primary Examiner-Wm. H. Grieb Attorney-John .l. Posta, Jr.

[57] ABSTRACT The instant invention involves a conversion device which enables the ready conversion of numerals in a first numeral base,

such as the base 10, or decimal system, to another and different, numeral base system, such as the base 2, or binary system. The conversion device generally comprises a container divided into an upper section, a midsection and a lower section. The upper section serves as a reservoir for discrete measuring units, such as balls. The midsection serves as an area of transfer for the balls between the reservoir and the lower section. The lower section consists of a plurality of parallel channels, each adapted to receive a preselected number of balls. A selector bar, moveable along the lower section, has means for defining the number of balls which can be contained in each column. The device is operated by a gravity feed. If a predetermined number of balls is released from the reservoir into the midsection, and selectively directed to the lower section, the balls will fill up varying numbers of the columns, depending upon the location of the selector bar. By observing this number of columns filled up by the balls, one can readily determine the corresponding numeral in a particular base system. The corresponding numeral in a different base system for the same amount of balls can readily be determined by moving the balls from the columns back into the midsection, relocating the selector bar again allowing the columns to fill up with balls, and then noting the number of filled columns.

3 Claims, 5 Drawing Figures MOUNTS l6 Q N?" 1 Lime H U U Air -40 I UUUULJUUJUUUW NUMERAL BASE CONVERSION INSTRUCTIONAL DEVICE BACKGROUND OF THE INVENTION 1. Field of the Invention The invention is directed to the field of numerical conversion devices and more particularly to the field of instruction instruments for enabling a comprehension of the methodology for converting numerals in a first base system to numerals in a second base system.

2. Description of Prior Art The prior art relating to the invention is generally set forth in US. Pat. No. 3,055,121, issued to W. A. Neal on Sept. 25, I962, entitled Numeral Base Conversion Device" and US. Pat. No. 3,332,156, issued to Thomas E. Reeves on July 25, 1967, entitled Numerical Base Conversion Device. Both these devices purport to provide a base conversion device for converting numerals from one base system to a second base system. The Neal patent does provide a mechanism for aiding one to convert from one base system to another, but the device does not do the conversion in and by itself, and is cumbersome to operate, quite time-consuming and in any event, significantly different both in construction and operation from applicants invention. The Reevespatent discloses a device for converting a numeral from a decimal system to a binary system by used a device having a plurality of congruently stacked sheets of material. Here again, applicants device is significantly different in construction and operation from the Reevesdevice; and furthermore, applicant can easily and simply convert numerals from a fist base system to any or all of a plurality of second base systems in a continuous manner.

SUMMARY OF THE INVENTION An object of the invention is to provide a numeral base conversion device.

Another object of the invention is to provide a numeral base conversion device for converting a numeral in a first base system to its corresponding numeral in a second base system.

A further object of the invention is to provide a numeral base conversion device which iscapable of converting a numeral of a first base system to its corresponding numeral in anyone of a plurality of different second base systems, and if desired, subsequently and directly into anyone of a plurality of third base systems.

Still another object of the invention is to provide a numeral base conversion device which is useful in instructing individuals to gain an understanding of the difference between various base systems and a comprehension of the mathematical processes involved in converting a numeral from one base system to its corresponding numeral in a second base system.

Yet another object of the invention is to provide a numeral base conversion device which is simple and inexpensive in construction and easy to use.

The invention generally comprises a container having a backing member, side closure members and a transparent cover member opposite the backing member. The interior of the container is divided into three sections; an upper section, a midsection and a lower section, by moveable section separator means. The assembly is adapted to contain a plurality of measuring units, such as balls, with the thickness of the container slightly larger than the diameter of the balls. A first passage sufficiently large enough to enable a single ball to pass therethrough is incorporated at one end of the separator means located between the upper and midsections. A second channel means defining an opening sufficiently large enough to enable a plurality of balls to simultaneously pass therethrough is provided at the other end of the separator means located between the upper and midsections.

The lower section contains a plurality of longitudinally extending dividers defining a plurality of channels having a width equal to the approximate diameter of the balls. Openings are provided in the transparent cover over each channel formed in the lower section. Such openings extend longitudinally along the entire length of each channel but are not sufficiently wide to permit the passage of balls therethrough.

A base selector bar is provided having a series of aligned pegs, equal in number to the channels provided, extending perpendicular from the selector bar. A plurality of holes are drilled in each side member of the container, which are adapted to receive locating pins carried by and extending from each side of the selector bar.

When in operation, the selector bar is positioned by its locating pins on the container in such a manner that the pegs extend into each channel of the lower section, thereby foreshortening each column an equal amount.

The upper channel acts as a resevoir for the balls. If one desires to convert a numeral such as 47 in base 10 to its equivalent numeral in a second base system, such as the base 7 one first proceeds to place the selector bar in a position whereby only seven balls can be held in each foreshortened column of the lower section. The separator means between the resevoir and the midsection is moved to enable only 47 balls to fall, by gravity, into the midsection, after which the separator means is moved to a closed position. The separator means between the midsection and lower section is then moved to uncover one channel at a time to thereby allow successive columns to be filled with the 47 balls. With the selector bar set for conversion to the base 7, a total of six columns will be completely filled, with the seventh column having five balls in it. The numeral in the base 7 corresponding to 47 in the base 10 is derived by using the number of balls in the unfilled column, i.e., 5, as the first digit (from right to left) of the corresponding numeral, and using the number of filled columns i.e., 6 as the second digit of the corresponding numeral. Accordingly, 47 base 10 is equivalent to 65 base 7.

If one now desires to convert to other base systems, it can readily be accomplished by an appropriate relocation of the selector bar and a repetition of the steps outlined above.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a front elevation of the conversion device embodying the principals of the present invention.

FIG. 2 is a transverse section taken along line 22 in FIG. 5.

FIG. 3 is a cross-sectional view taken along line 3-3 of FIG. 5.

FIg. 4 is a front elevation view of the conversion device showing placement of the selector bar for a determination of a base 4 numeral.

FIG. 5 is a front elevation view of a conversion device showing placement of the selector bar for a determination of a base 7 numeral.

DESCRIPTION OF THE PREFERRED EMBODIMENT The invention is directed to a novel numeral base conversion device for enabling one to convert a numeral in a first base system to its corresponding numeral in a different base system.

Preliminary to a detailed description of the structure of the subject device, it is believed helpful to provide antecedent basis for certain terminology used in such description. Thus, when reference is made hereafter to conversion of a fist numeral having a first base system to a second numeral having a second base system, each numeral will be considered to be composed of one or more digits, with each digit being referred to as the first digit, second digit, etc., as read from right to left. In the decimal, or base 10 system, the first digit would correspond to the unit" position, the second digit would correspond to the ten position, the third unit would correspond to the hundred" position, etc.

Turning now more particularly to the drawings, FIGS. 1 and 2 show a container generally referred to as 2 having a rectangular backing member 3 and

end closure members

4, 5, 6 and 7. The backing and end closure members can be fabricated from any suitable, rigid materials such as wood or plastic. A cover sheet 8 of transparent plastic overlies the face of container 2.

Openings

9 and 10 are provided in

end closures members

4 and 5, respectively, and are adapted to slideably receive and retain separator bar 11. This distance of opening 10 from end closure member 7 is greater than the distance of opening 9 from end closure member 7, and accordingly, separator bar 11 does not extend perpendicularly from either

end closure member

4 or 5, for reasons hereafter set forth. Guide members l2, l3 and 14 are provided to guide balls 15 to a predetermined location as hereinafter set forth. Guide member 13 also acts as a support for separator bar 11. The distance between

guide members

12 and 14 and end closure member 4 is approximately the diameter of ball 15. The passage 21 between guide member 12 and separator bar 11 is also approximately the diameter of ball 15.

Openings l6 and 17 are also provided in

end closure membets

4 and 5, respectively, and are adapted to slideably receive and retain separator bar 18. The distance between opening 16 and end closure member 6 is shorter than the distance between openings 17 and end closure member 6. Accordingly, separator bar 18 does not extend perpendicularly from either

end closure member

4 or 5, for reasons hereinafter more fully explained. Y

The separator bars 11 and l8 effectively set off a series of

compartments

20, 30 and 40 in container 2. Compartment 20 can be considered a compartment for storing balls or a resevoir. Compartment 30 can be considered a ball transfer area and compartment 40 is the area for retaining balls in a columnar relationship.

Asis more clearly shown in FIG. 3, compartment 40 includes a plurality of longitudinally extending, parallel channel dividers 19 which serve to define and form a plurality of channels or columns extending therebetween. Each channel has a width approximating the width of the balls 15. The distance between the tops of channel dividers l9 and cover sheet 8 is less than the diameter of balls 15 to prevent the balls 15 from jumping the channel dividers l9. I

A series of longitudinally extending openings 22 are provided in cover sheet 8 over and above each channel, with the width of such openings 22 being less than the diameter of balls 15 and the length being the entire length of compartment 40.

A base selector bar is adapted to be placed on top of cover sheet 8 at different positions along the length of compartment 40. Suitable positioning means, such as pins 23, extend downward from selector bar 25 and are adapted to be inserted in any pair of locating holes 24 which are bored in end closure members 4 and 5-along the edge of compartment 40. Holes 24 are located such that when the selector bar 25 is placed in an operating position, it will be parallel to separator member 18. Selector bar 25 also has a plurality of pegs 27, equal in number to the amount of separate channels, extending through'openings 22 in cover sheet 6 and into each channel, as shown in FIG. 3. It is rather obvious that movement of selector bar 25 along the length of compartment 40 will serve to automatically either increase or decrease the length of the channels.

A phantom showing of a counter 28 is included in FIG. 1. No specific type of counter must be employed in applicants invention, and in fact, no counter'at all is absolutely required, so details of same have not been included in the drawings. A counter, such as any well known trip counter or photoelectric or other counter, can be employed in applicants invention in the operation thereof.

OPERATION The invention operates by utilization of the force of gravity and accordingly, end closure member 6 must be higher than end closure member 7 to operate thedevice by enabling the balls 15 to fall along separator member 11 from compartment 20 to compartment and thence to compartment 40. To cause the balls 50 to roll from

compartments

40 and 30 to

compartments

30 and 20 respectively, the container 2 is tilted so that end closure member 7 is higher than end closure member 8.

A reservoir of balls 15 are located in compartment 20, as shown in FIG. 1. If one desired to determine the numeral in for example, the base system 7, for the numeral 39 in the base system 10 (decimal system) one proceeds'to move separator member 11 to the right to uncover passage 29. The presence of guide member 12 allows only a single ball to pass through

passages

21 and 29. The number of balls crossing passage 29 can be counted mentally or by a suitable counter as hereinabove noted. When 39 balls have passed from compartment 20 to compartment 30, separator member 11 is moved to the left through opening 10 to prevent any more balls from entering compartment 30. Next the selector bar 25 is positioned along the upper surface of container 2 to a point whereby pins 23 will be inserted in those holes 24 which would cause pegs 19 to be inserted in the channels of compartment 40 at a point whereby said channels are foreshortened to a length of approximately seven times the diameter of the balls 15. The container 2 is then tilted by raising end closure member 5 above end closure member4, causing the 39 balls to roll towards opening 16. Separator member 18 is then moved to the right to uncover the channel in compartment 40 closest end closure member 4, and allowing'the column to be filled with seven balls. Adjacent columnsare likewise successi'vely uncovered, and allowed to fillwith' balls until no'further balls remain in compartment 30. The filled columns with the selector bar in a base'system 7 position is shown in FIG. 5.

The numeral in the base system 7 corresponding to 39 in the base system 10 can then be determined in the following manner. One first counts the number of filled columns. The number is then divided by the desired base system number, i.e., 7, to determine how many sets of seven columns exist. The number of sets of seven columns is thethird digit of the corresponding numeral. In our example of 39 balls as shown in FIG. 5, there are less than seven, total columns, so the third digit of our corresponding numeral is zero. One then counts the number of full columns left after subtracting the complete sets of seven columns, to determine the number acting as the second digit of our corresponding numeral. In our example shown in FIG. 5, we have five such columns, so the second digit of our corresponding numeral is 5.

We then next count the number of balls in the last column. If the column is completely filled, the first digit of our corresponding numeral is zero. If the columnis not completely filled, one counts the number of balls therein, and this number becomesthe first digit of our corresponding numeral. In our example shown in FIG. 5, we have four balls left over so the first digit of our corresponding numeral is 4. Combining the above information, we .find that the numeral in the base system 7 corresponding to the numeral 39 in the base system 10 is 054.

The above procedure can be followed to determine any corresponding numeral in any base system selected by movement of the selector bar 25 to the appropriate position and proceeding to fill the columns in compartment 40.

Applicants invention also enables one to convert from a first base system directly to a second base system and again directly to third, fourth, etc. base system. Taking the example shown in FIG. 5, wherein the device is set up to determine a base system 7 numeral, we can directly determine the corresponding numeral in another base system, e.g., the base system 4, in the following manner.

' The separator member 18 is moved to uncover all columns containing balls 15, and the container 2 is tilted to cause the 39 balls to roll into compartment 30, after which separator member 18 is moved into a position covering all columns. The selector bar 25 is then located along the surface of a container 2 to a position wherein the pegs 19 extend into the channels to foreshorten same to a length whereby they can each contain only four balls. The procedure of filling the columns with balls, successively from left to right, is again followed, by

gradually moving the separator bar from left to right and tilting the container to cause all 39 of the balls 15 to roll from compartment 30 to the columns in compartment 40, as shown in FlG. 4.

Using the procedure and analysis outlined above, we find there are columns with balls in them. Ten columns have two sets of four columns, so the third digit of our corresponding numeral is 2. There is one remaining full column of balls, after subtracting the two full sets of columns, so the second digit of our corresponding number is l. The last column is partially filled with three balls, so the first digit of our corresponding numeral is 3. Combining the foregoing data, we find that the numeral 213 in the base 4 corresponds to the numeral 054 in the base 7, and 039 in the base 10.

if one desires to increase the number of discrete units or balls being employed, one can allow further balls to pass through

passages

21 and 29 into compartment 30. On the other hand, should one decide to employ fewer units or balls, the separator member 11 can be moved to the left out of opening 9 to uncover the passage formed between the end of guide member 13 and end closure member 5, and thereby enable balls 15 to pass from compartment 30 to compartment by appropriately tilting container 2.

it is apparent that most of the components can be manufactured from wood, plastic, metal or any other suitable structural materials, provided however that the cover sheet 8 be made in a manner and of a material to allow the operator to view the balls 15 within the container 2.

it can readily be appreciated that the type of means shown in the drawings for removably securing the selector bar to the edges of container 2, as well as the selector means itself, is illustrative in nature. Other equivalent means can be employed, with full effect, such as for example, a pair of magnets imbedded in a selector bar adapted to coact with a magnetic strip extending along the top side of

edge closure members

4 and 5, or perhaps, a simple mechanical indexing means attached to one end of the container 2 and adapted to coact with one end of a selector bar. The number of parallel channels included in compartment 40 as well as the length thereof can readily be varied to suit any particular design, as can both the size of

compartments

20 and 30, and the number of balls 15 employed.

To aid in readily determining the particular base system defined by a specific placement of the selector bar 25, appropriate legends or indica such as are shown in 31 can be placed on the cover sheet 8. Further legends or indicia, such as shown at 32, can be placed on the cover sheet 8 to indicate the corresponding numerals, or parts therefore, for different locations of selector bar 25, as viewed in conjunction with the columns of balls 15.

It is also obvious, by natural extension of the analysis presented above, that numerals in a first base system can be converted to corresponding numerals in a second base system which have digits in excess of 3, if one keeps in mind the fact that the selected base system number taken to the first power is the second digit, the selected base number taken to the second power is the third digit, the selected base number taken to the third power is the fourth digit, etc., with the remainder column of less than the selected base number being the first digit.

The embodiment of the invention shown in the drawings and described above can be varied in many respects without departing from the scope and spirit of applicant's invention. For instance, applicant shows herein, by way of example only, the use of balls as a measuring unit. If desired, the container 2 could readily be modified to employ a set of blocks rather than balls. Other measuring units also come to mind, as for example, a quantity of particulate material, such as sand, which can be segregated into discrete unit volumes, with a predetermined finite volume being broken out into volume units and converted, using the concept set forth above, into discrete groupings, of multiunit bits, to convert from one base system to another. Likewise discrete volumes of a colored liquid can be used in lieu of particulate matter, with the container being modified in a manner obvious to one skilled in the art, without departing from the scope of the invention. In the latter embodiment, the columns in compartment 40 might take the form of cylinders having plungers slideable therein to increase or decrease the length and, ergo, retentive capacity of each cylinder, with each cylinders plunger being interconnected to the other cylinders plungers to provide concurrent movement thereof. Specific details of construction are merely a matter of design.

Obviously, the type of counter employed in a specific embodiment of the invention would, in no small way, be dependent upon the type of variable measuring unit employed. In some instances, a dispenser might be employed in lieu of or in combination with a counter.

The device can be used by one who desires to convert from one base to another base, and can also be used to instruct other individuals, especially students, of the methodology behind converting from one base to another base.

The embodiments shown are meant to illustrate only a few of the embodiments obtainable by use of the invention. The invention may be embodied in other specific forms without departing from the spirit and essential characteristics thereof. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore extended to be embraced therein.

What is claimed and desired to be secured by United States Letters Patent is:

l. A conversion device comprising means for converting a first numeral having a first base to its corresponding numeral in a second base, said means including a plurality of measuring units,

a first area for storing a plurality of units,

a second area used for the intermediate storage of units,

a third area used for collecting said units,

said third area including a plurality of parallel channel members,

each of said channel members being of a different size,

selector means to vary the lengths of said channel members,

separator means disposed between the second and third areas,

said selector means and separator means running parallel to one another and extending in a nonperpendicular manner with respect to said channel members,

whereby said selector means and separator means jointly coact with said channel members to form equal sized compartments for holding a preselected number of such units.

2. A conversion device as set forth in claim 1 wherein said measuring units are balls.

3. A conversion device as set forth in claim 1 including a separator bar disposed between said first and second areas,

said separator bar extending in a nonparallel manner with respect to said selector means.

Claims

1. A conversion device comprising means for converting a first numeral having a first base to its corresponding numeral in a second base, said means including a plurality of measuring units, a first area for storing a plurality of units, a second area used for the intermediate storage of units, a third area used for collecting said units, said third area including a plurality of parallel channel members, each of said channel members being of a different size, selector means to vary the lengths of said channel members, separator means disposed between the second and third areas, said selector means and separator means running parallel to one another and extending in a nonperpendicular manner with respect to said channel members, whereby said selector means and separator means jointly coact with said channel members to form equal sized compartments for holding a preselected number of such units.

3. A conversion device as set forth in claim 1 including a separator bar disposed between said first and second areas, said separator bar extending in a nonparallel manner with respect to said selector means.