US3604620A

US3604620A - Calculator for different numerical bases

Info

Publication number: US3604620A
Application number: US818744A
Authority: US
Inventors: Rodney S Rakes
Original assignee: Individual
Current assignee: Individual
Priority date: 1969-04-23
Filing date: 1969-04-23
Publication date: 1971-09-14
Anticipated expiration: 1988-09-14

Abstract

A calculating device for adding and subtracting quantities in at least two different base numerical systems of a type which has a plurality of sliding members for registering quantities which can be manually moved back and forth in grooves in the calculator housing. Digits inscribed on the sliding members register through sight openings in the face plate of the housing. Movement of the slide members is accomplished by inserting a pointed member through slots in the faceplate into selected notches provided in both sides of each sliding member. By moving the pointed member laterally in the groove, the sliding members likewise are moved. The carrying operation is accomplished through widened ends in each slot which limit the addition or subtraction in the next order of digits on the adjacent sliding member to one unit at a time. The numerical base system of the device is changed either by providing, in effect, different length slots, or by modifying the length of each slot-downwardly in both cases of the highest base number. Restrictive means are also provided to limit the movement of the sliding members so that only numbers of the base system involved can be displayed through the sight openings.

Description

United States Patent [72] Inventor RodneySJhkes 6918 Westhampton Drive, Alexandria, Va. 22307 [21] AppLNo. 818,744 [22] Filed Apr. 23,1969 [4S] Patented Sept. 14, 197] [54] CALCULATOR FOR DIFFERENT NUMERICAL BASES 9 Claims, 5 Drawing Figs. [52] 235/69 [51] lnt.Cl ........G06el7/00, G06c 27/00 [50] 235/69 [5 6 References Cited UNlTED STATES PATENTS l,422,944 7/1922 Edmondson 235/69 i,66l,277 3/1928 Thomas..... 235/69 1,955,672 4/1934 Duran 235/69 2,223,612 l2/l940 Grundlehner 235/69 Primary ExaminerStephen J. Tomsky Assistant ExaminerLawrence R. Franklin AttorneyMason, Mason 8|. Albright ABSTRACT: A calculating device for adding and subtracting quantities in at least two different base numerical systems of a type which has a plurality of sliding members for registering quantities which can be manually moved back and forth in grooves in the calculator housing. Digits inscribed on the sliding members register through sight openings in the face plate of the housing. Movement of the slide members is accomplished by inserting a pointed member through slots in the faceplate into selected notches provided in both sides of each sliding member. By moving the pointed member laterally in the groove, the sliding members likewise are moved. The carrying operation is accomplished through widened ends in each slot which limit the addition or subtraction in the next order of digits on the adjacent sliding member to one unit at a time. The numerical base system of the device is changed either by providing, in effect, different length slots, or by modifying the length of each slotdownwardly in both cases of the highest base number. Restrictive means are also provided to limit the movement of the sliding members so that only numbers of the base system involved can be displayed through the sight openings.

QQ-mwawaw mwncnan CALCULATOR FOR DIFFERENT NUMERICAL BASES BACKGROUND OF THE INVENTION Due largely to the advent of the digital computer, there has been an increasing use of base numeral systems other than one having l digits (including However, it has long been known that there are substantial advantages in other base systems for both the operative and applicative standpoints. For example, by utilizing a base number equivalent to 12, its is divisible by two, three, four and six. The

base

16, 10" is divisible by two, four, and eight and is also the cube, square and double of same, respectively.

In making calculations wherein the units are not divided into decimal parts, it is frequently advantageous to utilize a more natural base system. Thus, when working with inches which must be eventually converted to feet, a base system of 12 may be more convenient. In dealing with units of time, the base systems of four, six or 12 might provide more desirable. Certain computations necessary in the disciplines of physics and chemistry are frequently very amenable to a base eight or 16. Moreover, it is frequently advantageous to shift from one base to another. With respect to some digital computers wherein the base 16 is employed, the programmer must frequently change from base 16 to base 10 and vice versa. However, as one would expect, the programmer seldom has a familiarity with the arithmetic of base systems other than base ID. A simple problem in addition or subtraction can become very cumbersome in another base system. In view of the state of the art and the difficulties presently encountered in utilizing different base systems, it has occurred to the applicant that a simple calculator capable of computing more than one base system would alleviate many problems now encountered by those working in different base systems and, moreover, would make the utilization of different base systems as a computa tion technique more acceptable and widely used than now is the case.

SUMMARY OF THE INVENTION The invention involves the modification of an analog-type calculator adapted to add, subtract and multiply (by repeated additions) integers wherein a plurality of sliding members or other means adapted for registering a given quantity in integers are utilized in conjunction. Each such registration means is, in the invention, capable of registering the number of digits (including 0 in the highest numerical base system for which the computer is designed. Each registration means is adapted to indicate one digit of a rational number so that the registration means taken together is capable of representing any rational number which has no more digits than the number of registration means. The registration means for adjacent digits are coupled so that when an amount is summed into the registration means for the lower order of the digits which exceeds the base number, a unit is carried to the registration means for the next higher order of digits and the registration means for the lower digits registers a quantity corresponding to the sum which would have otherwise been obtained less the base number of the numerical system being utilized. Different numerical systems can be obtained by selection of the coupling location relative to the registration means and in the other embodiment through an adjustable coupling. Each registration means is associated with means to display the quantity actually registered on the registration means and for this purpose a number of limiting means are integrated into the calculator so that only digits which fall within the base numerical system involved will be displayed.

Such a calculator may, if desired, be relatively inexpensive to manufacture and of a compact nature adapted to be easily handled and carried about. Moreover, the device may be readily manipulated to obtain the results required in the given base system and to shift rapidly from one base system to another.

Other objects, adaptabilities and capabilities will appear as the description progresses, reference being had to the aceompanying drawings, in which:

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a plan view of a calculator in accordance with the invention with the faceplate partially broken to show the interior of the computer;

FIG. 2 is a cross-sectional view of the calculator of the invention taken on lines 11-11 of FIG. I;

FIG. 3 shows a fragmentary plan view of a modified faceplate with an adjustable coupler thereon;

FIG. 4 is an elevation of the adjustable coupler shown in FIG. 3; and

FIG. 5 is a broken side view of the modified calculator showing the limit means.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Referring now to FIG. 1, it will be noted that there is a plastic housing 10 which includes a faceplate ll affixed thereto. Plate 11 has a plurality of sight openings l2, l3, 14, I5, 16, 17, I8, and 19. The location of sight opening 12 is shown in dot-dash lines since this portion of plate 11 is broken away. Also the faceplate includes a plurality of slots 22, 23, 24, 25, 26, 27, and 28. Each sight opening 12-19 has a groove or track 30 disposed thereunder which extends longitudinally from one end of housing 10 to the other. Each track 30 slideably carries an integer registration means consisting of a slide member 31 marked with indicia 32 and including a plurality of notches designated 34 on the right side and 34a on the left. The slide members 31 are retained in the tracks 30 by crimped ends 35. Indicia 32 represents the digits of the highest base numerical base system to be used in the computer which, in FIG. 1, is a base l6. It will thus be appreciated that a, b, c, d, e, andf are single digit equivalents of 10, I], 12, I3, 14, and 15, respectively. Each digit in indicia 32 is spaced apart by a distance equal to the distance between adjacent notches 34 and 34a. Also each digit of indicia 32 is adapted to be displayed through the sight opening 12-19 which its slide member underlies. In opposite sides of the housing 10, grooves 36 slideably carry a reset bar 37 which includes a handle 40. When the reset bar 37 is within the housing 10 as shown in FIG. 1, it acts to limit the downward transverse movement of each slide member 31 to where the digit 1 is aligned in the appropriate sight opening 12-19. The upper end of the track 30 similarly limits the upward transverse movement of each slide member 31 in the other direction to a position wherein the digit 0 is displayed through the sight openings 12-19 for the corresponding slide member 31.

Except for their particular location on faceplate 11, slots 22-28 are identical. Each is widened at its

extreme ends

44 and 45 wherein the notches 34 of adjacent slide members 31 are exposed. Each slot has a narrow portion 46 under which only the notches 34a of the lower order slide member 31, which slides under the sight opening 12, are exposed. Each slot also has two further widened areas 50 (for base 12 compu tations) and 51 (for base It) computations). Further indicia 54 which consists of the digits for the base l6 spaced apart the same distance as notches 34 are disposed beside each slots 22-28, as shown. A pair of limit members comprising a first threaded bolt 55 and an identical second threaded bolt 56 are adapted to be screwed inwardly to extend into the housing 10 when the reset bar 37 is pulled upwardly a sufficient distance. Bolt 55 thereby limits the downward movement of the reset bar 37 to a position whereby only the digits 00-9 on each slide bar 31 can register under sight openings 12-19 and bolt 56 accomplishing the same thing relative to the indicia O-b for base Each of the widened

portions

44, 45, 50 and 51 are defined by a pair of

shoulders

60 and 61. These

shoulders

60 and 61 are spaced a sufficient amount apart so that movement of the adjacent slide member having the higher order of digits thereunder is limited to one unit in a single sliding operation from shoulder 60 to shoulder 61.

To operate, say it is desired to add the digits corresponding to 8 and 9 which under the base 10 system total 17 but under the base 16 system total 11. A pencil or other pointed instrument is placed in the notch 34a for the slide member having a first order of indicia which is displayed through sight opening 12 opposite the digit 9 in indicia 54. By means of the pencil moving downward in notch 340, the slide member 31 is thus moved as far as a pencil will go where it hits the widened end 45 and the digit 9 then registers under the sight opening 12. Next, the same procedure is repeated for the notch 34a now opposite the digit 8 of indicia 54. However, in this case the crimped end 35 contacts the reset bar 37 before the pencil in the notch involved reaches the end of the slot 22 and the operator then reverses the direction of the movement of the slide member 31 until the pencil is blocked within end 44 at which time the digit 1 is registered so as to be seen through the sight opening 12. The pencil is then moved by the operator laterally against the shoulder 60 of end 44, into the exposed notch 34 and downwardly to where it is blocked by shoulder 61 of such end, whereby the adjacent higher ordered slide member 31 has the digit 1 in register under the sight opening 13. The addition is thus then completed and the sum, 11, is appropriately displayed in the

sight opening

13 and 12. The same procedure may be utilized with any series of rational numbers in the base 16 and as long as the number of digits for the sum does not exceed the number of sight openings, the sum can be read in the sight openings 12-19 in the same manner. The base 16 sum thus arrived at may be inverted to a base 10 number through conversion formula and tables which, if desired, can be imprinted on the faceplate or on the back of the housing 10.

In the event that it is desired to utilize the same computer for a base 10 system, perhaps in conjunction with the base 16 sum thus obtained and converted, the same process is em ployed except that the reset bar 37 is first drawn above the bolt 55 which is adjusted inwardly whereby the reset bar is brought against the bolt 55, extending in the housing 10, by pressing down the handle 40. Taking then the same example, a pencil is placed in a notch 340 the right-hand slot 22 opposite the digit 9 and the slide member 31 is moved downward until the pencil can move no further because it contacts end 45. Also, in this example, the crimped end then contacts the top of the reset bar 37. Next the pencil is placed in the slot opposite the digit 8 of indicia 54 and, since it will not move downwardly it is moved upwardly to just opposite the shoulder 60 of the widened area 51. This brings the digit 7 of indicia 32 under the sight opening 12. The pencil is then moved to the left into the exposed notch 34 and then moved downwardly from shoulder 60 to shoulder 61 of the widened area 51 whereby the adjacent higher order slide member 31 has its digit 1 brought under the sight opening 13 thus displaying the sum 17 for the base 10.

If it is desired to use the base 12 then the base 10 bolt 55 is screwed outwardly and the base 12 bolt 56 is screwed inwardly so that the reset bar 37 is limited in its downward movement by bearing against the end of the bolt 56 which protrudes in the slot 36. The above described procedure is then again utilized except that the widened area 50 is utilized rather than the widened area 51 and the digits displayed under the

sight openings

13 and 12 are l and 5, respectively, or in other words, l5, which is the sum of 8 and 9 under the base 12 system.

For subtraction, basically a reverse procedure is used except that the operator must perceive the indicia 54 as reversed for each particular base numerical system. The number from which a deduction is to be taken is first set forth in the sight openings 12-19 by moving the slide members 31 as appropriate. Then the pencil is placed in the appropriate notches for the number to be deducted, keeping in mind that the indicia 54 must be considered reversed, and the pencil is moved first in the opposite direction to that utilized for adding to the appropriate shoulder 60 or, if it cannot be so moved because the upper crimped end 35 hits the end of the track 30 then it is moved oppositedly downwardly to the end 45. The pencil is then moved laterally and the adjacent slide member 31 is moved upwardly one unit.

it will be appreciated that if desired a plurality of similar plates 11 can be provided to be used alternatively with the apparatus for any base number system from three to 16 in the embodiment shown in which case there will be no widened areas such as 50 and 51; each slot 22-28 corresponding to the base numerical system desired. Also, in such event, appropriate limit means may extend downwardly from the plate 11 used and there is no need for bolts such as

bolts

55 and 56. However, such embodiment is not a preferred one since a relatively large number of plates would then necessarily have to be hinged or otherwise available, and the same function is more economically obtained through the modification shown in FIGS. 3-5.

Referring now to FIGS. 3-5, the housing 10 has a faceplate 64 which is identical to the faceplate 11 except that the slots 65 are wide throughout their length, a tab 66, however, defines an end 67 similar to the widened end 45 in plate 11. An adjustable coupler 70 includes slot parts 71 which serve the same purpose as the widened ends 44 and the widened areas 50 and 51 in the slots of plate 11. Slot part 71 includes upper and lower shoulders 72 and 73, respectively, which serve the same function of

shoulders

60 and 61 in the slots of plate 11. The adjustable coupler 70 is slideable up and down the housing 10 in such manner as to maintain itself at right angles with the slots 65. The adjustable coupler 70 includes an extension 74 which has imprinted thereon indicia 75 which is used for subtraction purposes in a manner which will be easily understood by those skilled in the art from the prior description of the operation of the calculator. In order to secure the adjustable coupler 70 relative to the housing 10, a pair of setscrews 76 are provided. lndicia 77 imprinted on the plate 64 indicates the base numerical system for which the calculator is set when the bottom of the adjustable coupler 70 is secured on the line leading from a selected one of such indicia. It will be noted that indicia 77 provides for numerical systems from a base three to a base 16. A base two numerical system can also be utilized by adjustment between 0 and l in the end portions 67, under tab 66 by those skilled in the art inasmuch as this requires in each instance merely a change between the digits 0 and l for each unit, carried to the left for addition, and the reverse operation for subtraction.

A series of limiting means comprising bolts 80 as seen in FIG. 5 perform the same function as

bolts

55 and 56 in the first embodiment for each numerical system. The bolts 80 are marked on their ends for the numerical system involved and as in the previous embodiment serve to limit the downward movement of the reset bar 37 and accordingly limit the similar movement of slide members 31.

It will be noted that in P16. 1, a further widened area is provided in slot 23 and a bolt 91, similar to

bolts

55 and 56, is threadably received through the bottom of housing 10 so as to be selectively receivable in the track 30 which underlies the slide member 31 having its notches 34a exposed by slot 23 and its indicia seen through sight opening 13. When bolt 91 is screwed so as to be received in track 30, it limits the downward movement of such slide member in track 30 and widened area 90 permits the use of

sight openings

12 and 13 to display minutes and the other sight openings for hours on a base 10 system. For example, if it is desired to add 30 and 45 minutes, the widened area 51 is used for slot 22 and widened area 90 for slot 23, with bolt 91 blocking downward movement of the underlying track 30, to provide a total in

sight openings

14, 13 and 12 of 115, representative of 1 hour and 15 minutes. Thus, a rapid addition or subtraction of minutes and hours is possible.

When it is stated in the claims that the calculator is adapted to add and subtract, this is intended to include other functions such as multiplication possible through repeated additions.

Having thus described my invention what I claim as new and desire to cover by Letters Patent of the United States is:

l. A calculator which comprises a housing having a face on one side and providing track means in said housing under said face, sight openings in the face of said housing, slide members carried by said housing and movable along said track means past said sight openings, said slide members bearing indicia for integer quantities arranged in numerical order, said housing including slots in its face, further indicia arranged in numerical order beside each slot, uniformly spaced notch means in both side edges of each of said slide members, the notch means on a first side of said slid member adapted to permit an operator of the calculator to move said slide member through a corresponding one of said slots along said track means, said notch means spaced to correspond to each said indicia thereon whereby when a said slide member is moved so that any one of said notch means is moved from beside one of said further indicia to beside another of said indicia adjacent to said one further indicia, the indicia on said slide member seen through its corresponding sight opening is changed by one numerical unit, each of said slots having widened ends with shoulder means, one of said widened ends having its outermost shoulder aligned with one element of said indicia denoting a number base, the notch means of two adjacent slide means being exposed within said widened ends of each of said slots to permit movement of said slide means having the notch means on the second side thereof exposed by a distance corresponding to one of said numerical units, at least one other widened area with further shoulder means in each of said slots between said widened ends exposing the notch means of two adjacent slide means and adapted to permit movement of said slide means by the notch means on the second side thereof by a distance corresponding to one of said numerical units, and the outermost shoulder of said other widened area being aligned with another element of said indicia denoting another number base.

2. A calculator in accordance with claim 1 including adjustable limit means whereby the movement of said slide means along said track means may be selectively limited.

3. A calculator in accordance with claim 2 including a reset bar for said slide means, said reset bar being included as a part of said limiting means.

4. A calculator in accordance with claim l wherein said one element corresponds to a base 16 numerical system and said widened area provides a calculation on a numerical system less than base I6.

5. In a calculator adapted to add, subtract, and multiply, a plurality of integer registration means for a first base numerical system, each of said registration means capable of registering a quantity for each integer of a single digit of said first base system, each said registration means adapted to represent any digit of a rational number in said first base system and being associated in an ordered sequence whereby said plurality of said registration means is capable of representing any rational number in said first base system having no more digits than the number of said registration means, a coupler guide means for adjacent registration means whereby if the quantity registered thereon is directly combined with a further quantity so that the combination thereof must be expressed in two digits, the adjacent registration means next higher in the ordered sequence is advanced to register a further digit and the adjacent registration means lower in the ordered sequence registers a quantity corresponding to said combination less the quantity of the base number of said numerical system, whereby quantities expressed in said first base system are combinable in the calculator, said coupler guide means being adjustable relative to said registration means to at least one further position for changing the calculator to a second base numerical system whereby each said registration means registers a quantity only in said second base system and quantities registered by said registration means in said second base system are combinable in the calculator. I

6. ln a calculator as defined in claim 5 including limit means associated with each of said registration means for limiting the quantity registrable thereon to a quantity one unit less than the selected base number.

7. In a calculator as defined in claim 6 wherein indicia means is associated with each of said registration means adapted to display the quantity registered thereon.

8. In a calculator adapted to add and subtract in a base l0 system, a plurality of successively higher order integer registration means, each of said registration means capable of registering a quantity for each integer from zero to nine, each of said registration means being adjacent at least one other of said registration means, a plurality of guide means, a pair of said guide means being arranged at opposite ends of each said registration means for coupling adjacent of said registration means whereby if quantities were summed in the lower order of said registration means to exceed nine said summed quantities are combined into the adjacent higher order registration means, the said higher order registration means having a further base six guide means positioned between said pair of guide means arranged at its opposite ends whereby said higher order registration means is adapted to combine with an adjacent still higher order registration means quantities from said higher order registration means on a base six system and a numerical system based on 60 divisions is selectively combined with the base l0 system of the calculator.

9. in a calculator in accordance with claim 8, limit means associated with said higher order registration means for limiting the quantity registrable thereon to a quantity of five.

Claims

1. A calculator which comprises a housing having a face on one side and providing track means in said housing under said face, sight openings in the face of said housing, slide members carried by said housing and movable along said track means past said sight openings, said slide members bearing indicia for integer quantities arranged in numerical order, said housing including slots in its face, further indicia arranged in numerical order beside each slot, uniformly spaced notch means in both side edges of each of said slide members, the notch means on a first side of said slid member adapted to permit an operator of the calculator to move said slide member through a corresponding one of said slots along said track means, said notch means spaced to correspond to each said indicia thereon whereby when a said slide member is moved so that any one of said notch means is moved from beside one of said further indicia to beside another of said indicia adjacent to said one further indicia, the indicia on said slide member seen through its corresponding sight opening is changed by one numerical unit, each of said slots having widened ends with shoulder means, one of said widened ends having its outermost shoulder aligned with one element of said indicia denoting a number base, the notch means of two adjacent slide means being exposed within said widened ends of each of said slots to permit movement of said slide means having the notch means on the second side thereof exposed by a distance corresponding to one of said numerical units, at least one other widened area with further shoulder means in each of said slots between said widened ends exposing the notch means of two adjacent slide means and adapted to permit movement of said slide means by the notch means on the second side thereof by a distance corresponding to one of said numerical units, and the outermost shoulder of said other widened area being aligned with another element of said indicia denoting another number base.

4. A calculator in accordance with claim 1 wherein said one element corresponds to a base 16 numerical system and said widened area provides a calculation on a numerical system less than base 16.

5. In a calculator adapted to add, subtract, and multiply, a plurality of integer registration means for a first base numerical system, each of said registration means capable of registering a quantity for each integer of a single digit of said first base system, each said registration means adapted to represent any digit of a rational number in said first base system and being associated in an ordered sequence whereby said plurality of said registration means is capable of representing any rational number in said first base system having no more digits than the number of said registration means, a coupler guide means for adjacent registration means whereby if the quantity registered thereon is directly combined with a further quantity so that the combination thereof must be expressed in two digits, the adjacent registration means next higher in the ordered sequence is advanced to register a further digit and the adjacent registration means lower in the ordered sequence registers a quantity corresponding to said combination less the quantity of the base number of said numerical system, whereby quantities expressed in said first base system are combinable in the calculator, said coupler guide means being adjustable relative to said registration means to at least one further position for changing the calculator to a second base numerical system whereby each said registration means registers a quantity only in said second base system and quantities registered by said registration means in said second base system are combinable in the calculator.

6. In a calculator as defined in claim 5 including limit means associated with each of said registration means for limiting the quantity registrable thereon to a quantity one unit less than the selected base number.

8. In a calculator adapted to add and subtract in a base 10 system, a plurality of successively higher order integer registration means, each of said registration means capable of registering a quantity for each integer from zero to nine, each of said registration means being adjacent at least one other of said registration means, a plurality of guide means, a pair of said guide means being arranged at opposite ends of each said registration means for coupling adjacent of said registration means whereby if quantities were summed in the lower order of said registration means to exceed nine said summed quantities are combined into the adjacent higher order registration means, the said higher order registration means having a further base Six guide means positioned between said pair of guide means arranged at its opposite ends whereby said higher order registration means is adapted to combine with an adjacent still higher order registration means quantities from said higher order registration means on a base six system and a numerical system based on 60 divisions is selectively combined with the base 10 system of the calculator.