Showing papers on "Division (mathematics) published in 1969"

Digital division by reciprocal conversion technique

Abstract: A reciprocal conversion technique for obtaining the quotient of two numbers and the reciprocal of a number. A predetermined number of leading bits of the mantissa of the denominator is used as an entry into a table used for locating the required number of shifts and adds or shifts and subtracts to form a standard from of a denominator. Significant precision control and the semireciprocal of the normalized fraction is formed in successive multiplication steps. The reciprocal of the normalized fraction is formed and the quotient can thereafter be determined with a final multiplication step.

Communications system with frequency and time division techniques

Abstract: A communication system for a substantial number of subscribers is shown having random access capabilities without the requirement for the usual central exchange. The system uses a frequency division scheme for separating the several communication information channels. The individual subscriber units are interconnected as by means of one or more wires which are also connected to a master clock which continually generates time division digital information consisting of a plurality of pulses and unused time spaces (ones and zeros) including binary circuit code information and synchronizing pulses. A relatively limited band width is required for carrying this control information which is substantially displaced in frequency from the band containing the several communication information channels. These channels are generated by means of a frequency synthesizer in each of the subscriber units, each of which continually monitors the digital control information to determine whether its address is being called and the circuit code representing the channel of the incoming call. Similarly, outgoing calls are initiated by picking up a headset at the subscriber unit which causes an unused channel to be selected, inserting its circuit code into the digital stream and causing the frequency synthesizer in responding to this code to generate the corresponding carrier frequency. The audio information is then converted to single side band (or other) modulation of the particular carrier frequency signal.

Electronic digital slide rule

Abstract: An electronic digital slide rule in the form of a small handcarried, battery powered digital electronic calculator capable of performing substantially all of the mathematical operations performed by the conventional mechanical slide rule. The electronic digital slide rule utilizes a computing technique based on integrating for a period of time proportional to one input variable x, a fixed or variable pulse rate signal, the magnitude of which may be proportional to another input variable y, to a constant, or to some other known function. The computing technique is implemented by a pulse rate generator producing a pulsetrain representative of one factor of a function whose solution is desired. First factor input means are provided for supplying the one factor to the input of the pulse rate generation means whose output is supplied to an output integrator and timing circuit. A second factor input means is coupled to and controls at least in part operation of the output integrator and timing circuit means. The electronic digital slide rule is completed by a function selector switching means that interconnects the pulse rate generation means to the second factor input means and to the output integrator and timing circuit means in a manner to perform a selected one of a plurality of different logical operations on the first and second input factors to thereby derive a desired output solution. In preferred embodiments of the slide rule, an output indicating means is coupled to the output from the output integrator and timing circuit means for displaying the solution in legible form. The plurality of different logical operations capable of being performed by the electronic digital slide rule include the arithmetic operations of addition, subtraction, multiplication, division, squaring and square rooting, and exponential, logarithmic and trigonometric operations. In constructing the electronic digital slide rule, the first and second factor input means may comprise mechanical switches having a plurality of discrete contact positions which also serve as in input memory for retaining the value of the input first and/or second factors. It is also preferred that the electronic digital slide rule operate from a battery operated power supply means for supplying energizing power to the slide rule through a start-stop switch which energizes the slide rule only during periods of use and conserves the battery power supply during periods of non-use. It is also anticipated that the electronic digital slide rule would be fabricated from micro-miniaturized integrated circuit structures mounted on a single supporting circuit board and housed in the form of a pocket size container for easy transport and use. A preferred embodiment of the electronic digital slide rule also includes a decimal point placement indicating means for visibly indicating to the user of the device the position of the decimal point in an output solution displayed by the output indicating means.

Data correction system

Abstract: The information contained in the memory passes through an assembly of windows corresponding to various positionings, and a counter associated with each window counts the sequences of identical valences seen through each window. The result is the validation of the direction which enables the validation of the contents of a division receiving an interference signal, seen through a correction window parallel to the validated direction.

Towards an abstract mathematical theory of floating-point arithmetic

Abstract: The representation of integers by a place value sequence of digits taken from a radix polynomial is one of the profound mathematical developments of all times. It provides an elegant foundation for mathematical questions where algorithmic procedures are needed, such as how to computationally effect the operations of addition, subtraction, multiplication, division and comparison. Nevertheless, as invaluable as the place value representation system is to computational mathematics, most questions regarding the mathematical structure of the integers are usually answered with proofs which make no reference to any representational form of the integers, but are based solely on an abstract characterization of the integers.

A catalog of models for the operations of addition and subtraction of whole numbers

Abstract: The above material contains twelve headings that indicate a collection of families of models. Many of these collections consist of several families. For example, the description of the collection of number-line models refers to at least seven families. There are listed here more than 20 families of models for addition and subtraction on the whole numbers which are easily distinguished from one another. Research has revealed that there are also more than 20 well-known models for the other operations of multiplication and division of whole numbers.

Improved Method and Machine for Interconnecting Two Webs of Paper

Abstract: 1,150,439 Paper bags G J O WELINBERGER 3 May, 1966 [4 May, 1965], No 19415/66 Heading B8K [Also in Division B5] Trapezoidal filter bags are made by adhering two paper webs along stripes 2, 5, 6 and cutting the webs along the stripes

Direction Indicator Switches.

Abstract: 1,151,858 Temperature responsive actuating elements JOSEPH LUCAS (INDUSTRIES) Ltd Sept27, 1966 [Oct5, 1965], No42141/65 Heading G1D [Also in Division H1] A bi-metallic strip 11 having a printed circuit type heating resistor 14 insulatingly mounted thereon releases a latched switch (see Division H1) after a predetermined time delay Resistor 14 is a cupro-nickel foil

On Whole Number Computation.

Abstract: berg system, a method for addition, multiplication, division, and square root extraction which depends primarily upon the memorization of a great many rules and secondarily upon the use of mental arithmetic. Trachtenberg's approach to computation suggests some interesting experimentation in the teaching of whole-number arithmetic. We would like to point out some of the directions experimentation might take, in the hope that readers of this article will be stimulated to try them. One feature of the Trachtenberg system is a collection of rules for multiplication by 3, 4, 5, 6, 7, 8, and 9. In most cases this is unnecessary, since the majority of students memorize the multiplication tables with little serious difficulty. Once these tables have been memorized the usual mul-

Though This be Madness

Abstract: A he number line is a powerful tool that can be used to illustrate the arithmetical operations and their relationships. Unfortunately, when the topic of multiplication and division involving two negative numbers occurs, there seems to be little or no information regarding how to represent these problems on the number line. With the use of two interpretations for the + and signs, both multiplication and division involving negative numbers can be easily represented and their inverse nature illustrated.

Organisation of large collections of chemical structures for computer searching

Abstract: New techniques of partitioning large files of chemical structures are described which allow searches for whole structures to be concentrated on a small part of the file. Using these techniques, recognition of compounds new to the system may be accomplished without generating a unique representation of the chemical structure.The chemical structure file is arranged into molecular formula groups and the larger groups are subdivided by comparing ordered lists of the atom-bond-atom pairs present in each compound. Where a finer division is required augmented versions of the atom-bond-atom pairs are used. Analysis of a number of molecular formula groups has shown that even the largest groups can be divided into small subgroups by the augmented pair technique. In the majority of cases the subgroups contain only one or two compounds.

Improvements in or relating to Vehicle Cooling Systems

Abstract: 1,157,265 Valves HUMBER Ltd 15 July, 1966 [19 July, 19651, No 30621/65 Heading F2V [Also in Division F4] A valve for a vehicle engine cooling system (see Division F4) comprises a piston 20 movable manually between valve seats 21 and 22 to control the flow of fluid from an inlet 23 to outlets 24 and 25

Electronic analog division means

Abstract: Electronic circuit means for performing the division of one or more signals by another signal, said electronic circuit means including at least one bridge circuit including electrooptical devices therein which act as variable attenuators in the performance of one or more division operations, said circuit means also including direct-current feedback means to the electrooptical devices for control purposes.

Improvements in or relating to Hydraulic Ram Systems

Abstract: 1,155,845. Vehicle loading platforms. BURTONWOOD MECHANICAL HANDLING CO. Ltd. 19 Sept., 1966 [20 Sept., 1965], No. 40023/65. Heading B8E. [Also in Division F1] A vehicle lifting platform 35, Fig. 2, is hinged to the lower ends of a pair of spaced vertical slides 38 (only one of which is shown), each connected at its upper end by a chain passing over a sprocket wheel 40, Fig. 3, carried by an hydraulic ram (see Division F 1) to a bracket fixed to a ram guide 37. The assembly so formed is mounted on an angle plate 31 bolted to the rear of the vehicle and the whole forms a detachable unit.

No. 101 ESS 4A switch unit

Abstract: A combination of space division and time division networks makes possible an 800 to 4000 line switch unit private branch exchange for the No. 101 electronic switching system.

Improvements relating to Irons

Abstract: 1,163,440. Liquid level indication. HOOVER Ltd. Oct. 3, 1966, No. 44147/66. Heading G1H. [Also in Division D1] A water level indicator for a steam and/or spray iron (see Division D1) comprises a transparent tube 30 behind which there are a series of spaced markings 41 which appear markedly different when viewed through the liquid in the tube rather than through the empty tube. As shown, the markings are printed or painted black lines extending beyond the tube at the sides and when viewed through the liquid in the tube appear to be at an angle to their actual direction.

Reinforced sheet material

Abstract: 1,147,222. Reinforced laminates. F. HEBBERLING. 12 Jan., 1966, No. 30752/68. Divided out of 1,147,221. Heading B5N. [Also in Division D1] The subject-matter of this Specification is included in that described in Specification 1,147,221, but the claims relate to a laminated web material bonded together with an array of reinforcing strands between them, the array comprising four sets of strands in an undulating pattern, the undulations in each set being out of phase with those in each other set.

Continuously operating mixing and reaction machine

Abstract: 1,150,979. Polymerization apparatus; screw mixers. FARBENFABRIKEN BAYER A.G. 14 Dec., 1967 [14 Dec., 1966], No. 56821/67. Addition to 1,065,379. Headings B1C and B1X [Also in Division B5] The continuously operating mixing and reaction machine of 1,065,379 is modified by providing the rotating cylindrical shaft 3 with an extension in the form of a screw 5 at the discharge end to enable the machine to discharge through filters or nozzles.

Serial adder/substracter utilizing counters

Abstract: The disclosure relates to an electronic desk type calculator wherein a pair of four element counters acting together in conjunction with timing and other circuitry are capable of performing the functions of shifting, addition, subtraction, multiplication and division.