Showing papers on "Division (mathematics) published in 1973"

The Parallel Evaluation of Arithmetic Expressions Without Division

Abstract: As computers become capable of executing more arithmetic operations simultaneously, the question of compiling for such machines becomes more important.

Shape Effects on Resistance in Flood-Plain Channels

Abstract: For flow computation in flood plain channels, the flow cross section is usually divided into subsections to ensure hydraulic homogeneity. However, the question of whether or not to include the division lines as part of the wetted perimeter still remains unanswered. In this study, efforts have been made to determine division lines having zero shear stress so that they need not be included in the wetted perimeter. Laminar flow cases were solved to gain qualitative insight into the shape effects on resistance and location of division lines. For turbulent flows, division lines were determined from velocity distribution patterns; and resistance coefficients for both laminar and turbulent flows are lower than those in wide rectangular channels having the same boundary materials. New formulas are proposed for computation of discharge in both main-channel and flood-plain portions.

Time division multiplex exchange

Abstract: A decentralized time division multiplex communication system having independent exchange modules arranged to individually set up connections without the need of central control. Commonality of hardware is limited to a simple interconnection unit, and a clock allowing synchronization of all modules. Each exchange module, with its associated group of terminals, is arranged to form a time division multiplex system of first order. The exchange modules, together with the interconnection unit, are arranged to form a super-multiplex system, i.e., a time division multiplex system of second order. All bus line time division multiplex channels of all exchange modules are interspersed on the interconnection unit. To each of these bus line channels, a time slot is permanently assigned in the super-multiplex time frame.

A Simulative Study of Correlated Error Propagation in Various Finite-Precision Arithmetics

Abstract: The accumulated roundoff error incurred in long arithmetic computations involving a randomized mixture of addition, subtraction, multiplication, and division operations applied to an initial randomly generated data base is studied via simulation. Truncated and rounded floating-point arithmetic and truncated and rounded logarithmic arithmetic are simultaneously utilized for each of the computation sequences and the resulting roundoff error accumulations for these four systems are compared. The nature of the correlated errors incurred under various arithmetic operator mixes are discussed.

A Combinatoric Division Algorithm for Fixed-Integer Divisors

Abstract: A procedure is presented for performing a combinatoric fixed-integer division that satisfies the division algorithm in regard to both quotient and remainder. In this procedure, division is performed by multiplying the dividend by the reciprocal of the divisor. The reciprocal is, in all nontrivial cases, of necessity a repeating binary fraction, and two treatments for finding the product of an integer and repeating binary fraction are developed. Two examples of the application of the procedure are given.

Cmos digital division network

Abstract: A CMOS dynamic division circuit employing only transmission gates and inverters minimizes the number of units required for any particular division, which then minimizes nodal capacitance for limiting power consumption. The circuit is particularly adapted for electronic watch circuits.

Temperature sensing circuit

Abstract: One portion of a constant current is applied to one semiconductor device and the remainder to a second semiconductor device. When the temperature difference between the devices changes, the division of current also changes. An operational amplifier responsive to this division of current may be employed to drive an indicator of the temperature difference and to reestablish the original temperature difference between the devices.

Line switch controller for a time division switching system

Abstract: A time division switching system is disclosed having a memory that is selectively addressable to associate time slots with ports on a time division bus. The memory is also content addressable upon the receipt of slot number information to generate output signals identifying the ports associated with each received slot number. Output signals are extended from the memory over separate paths to line switches to close each line switch serving a call during the time slot to which the call is assigned.

Temporary memory for time division multiplex telephony system exchanges

Abstract: Information relating to interconnections made through the time division switch of a telephony exchange is recorded in binary form in a plurality of memory elements. This information includes addresses permanently assigned to interconnected equipment, the on- or off-hook status of the equipment, and the status of the connection established through each time slot. The recorded information is made to recirculate and is read out periodically to provide gating information to the time division switch.

Plato’s Method of Division

Abstract: Our main difficulty with Plato’s method of division is that we don’t know what is being divided or what it is being divided into. And until we know these things, we don’t know very much about the method of division.

Tone control system for a time division switching system

Abstract: A time division switching system is disclosed in which tones are applied to the system time division bus under control of a memory which stores a call status word unique to each time slot. During each occurrence of a slot, the status word applicable to the slot is read out of memory and applied to the tone generator. The generator decodes each word it receives and applies any tone that may be required by the word to the time division bus.

Program controlled time division switching systems

Abstract: A stored program controlled time division PBX is disclosed in which each call is associated with a unique time slot as well as a unique frame. The system closes the line switches involved on a call during each occurrence of its associated time slot and it processes information for a call only during each occurrence of the associated time frame.

A Comparison of Initially Teaching Division Employing the Distributive and Greenwood Algorithms with the Aid of a Manipulative Material.

Abstract: Division of whole numbers is traditionally accepted as a part of the elementary school mathematics program and is considered to be the most difficult of the four basic operations with whole numbers. The Greenwood algorithm is employed in most contemporary elementary textbooks to initially develop the recording process. The common usage of the Greenwood algorithm for division of whole numbers today is largely due to the study by Van Engen and Gibb, General Mental Functions Associated with Division (1956). Later, in almost all textbook series, the standard algorithm is used for the final recording process. Van Engen and Gibb, however, did not recommend converting to the standard algorithm after learning the Greenwood algorithm. This transition stage is the source of substantial difficulty for many pupils. If the standard algorithm is to be the terminal algorithm, then perhaps an approach that initially employs the standard algorithm should be used.

Some results for general cell-size- dependent branching processes

Abstract: A general model for the growth and division of cells in which the growth rate and division probability at any instant depend only on their size at that time is introduced. Conditions under which (a) the distribution of cell-size at division converges ergodically, (b) the sizes tend to 0 or ox, are exhibited, and bounds to the correlation between the sizes at division of sister cells are given in a wide class of cases.

Bit serial divider with full scale capabilities

Abstract: A circuit using standardized components and providing a given word length quotient from the same length dividend and divisor. The circuit checks the input dividend and divisor for polarity and uses logic circuitry to determine if the quotient would be an improper fraction of either polarity. If an improper fraction did result, a given limit output of one polarity or the other is provided. Otherwise, the circuit operates in a normal long division process of examining the magnitude of each partial remainder in the division process, subtracting if the remainder is larger than the divisor, inserting a digit in the quotient upon each subtraction and increasing the value of the remainder for the next examination. The circuit operates with serial bit digit word format with the least significant bit of the digit word being supplied first both to and from the circuit.

Automatic branch exchange using time division switching

Abstract: A time division branch exchange for a telephony system includes a constantly recirculating temporary memory in which equipment addresses and other information relating to active time slots is recorded. This information is decoded as the temporary memory recirculates and the output is provided to a time division switch which gates audiopaths to the equipment interconnected through each time slot. The contents of the temporary memory is updated as necessary when a piece of equipment, e.g., a station, which has changed status is scanned by a line counter.

Analyzed Binary Computing

Abstract: A single format for the representation of numbers in a computer is proposed to accommodate both exact and inexact quantities. A consistent set of rules is described for addition (subtraction), multiplication, and division of such quantities, both within their separate types, as well as in combination. Error correlation aside, the propagation of inherent errors is monitored in operations with at least one imprecise value. A definitive algorithm must, of course take into account any correlations of inherent errors; these correlations must be recognized and incorporated into the algorithm by the numerical analyst, not by the logical designer of the computer.

Method for switching pulse code modulated signals using time-division multiplex principles

Abstract: A method is described for effecting the connection of time division multiplex trunks. Through-connecting units are used which cause time channel conversion and spatial throughconnection. These through-connecting units form with a spatial switching network a time division multiplex coupling array having the known time-space construction. If on an outgoing trunk selected for a desired connection and at the output with which a connection is to be established there is no common free time position, an adjacent time position is used. The latter is made possible by means of the timing on the spatial portion of the coupling array. An intermediate storage is used to bridge the time periods between time slots. This storage is disposed at the output of the spatial portion of the time division multiplex coupling array.

Asynchronous division in cell colonies. II. Control by a non-linear oscillator

Abstract: A nonlinear control model for cell division is introduced and examined for applications to the development of asynchronous division in cell cultures. Comparison with the results of a linear control model suggests experimental alternatives which might distinguish between these two possibilities. Such experiments cannot consist of division time distributions themselves because both linear and nonlinear models are capable of fitting the same division time distribution data to within experimental error. Two interesting predictions of the nonlinear model are (1) a nonzero minimum division time, and (2) the possibility for either positive or negative correlation between mother-daughter division times.

Periodic thermal stress: optimal spacing predicted by a simple set-back model of cell division synchronization.

Abstract: Digital computer simulations have been used to make quantitative predictions based on a simple set-back model of cell division synchronization. According to the model appropriate thermal stress reverses progress within a segment of the division cycle called the set-back interval. In the simulations normally distributed cell-to-cell variations in division cycling rate between periodic thermal shocks were produced with the Monte Carlo method. The simulations have shown that reasonably good synchronization with the single shock per division strategy requires a relatively long set-back interval and small cell-to-cell variations in rate of progress through the division cycle. The simulations have shown that the degree of synchrony produced by such periodic shocks is highly dependent on the time interval between shocks—with a series of as many as seven shocks inappropriately spaced producing less synchrony than a single shock! The optimal time interval between successive thermal shocks was found approximately equal to the mode division cycle time at synchrony equilibrium multiplied by 1 plus half the fraction of the division cycle occupied by the set-back interval. Position of the set-back interval within the division cycle had little effect on synchrony at the end of the final shock.

Essentials of mathematics

Abstract: Part 1 Arithmetic: whole numbers fractions decimal fractions percentage square roots of numbers metric system of measurement number bases. Part 2 Algebra: operations with signed numbers operations with algebraic expressions multiplication and division the equation solving stated word problems special products and factoring fractions fractional equations systems of equations graphing exponents powers and roots radicals quadratic equations imaginary and complex numbers roots of equations systems involving quadratics inequalities ratio proportion variation. Part 3 Geometry: plane figures measurement of plane figures right angle circles geometric solids: prisms, cylinders, pyramids and cones spheres. Part 4 Logarithms: computation applications. Part 5 Trigonometry: trigonometric ratios tables of trigonometric ratios the right angle function of angles of any size trigonometric identities radian measure special angles composite ang