Division (mathematics)

About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.

Operation-specific effects of numerical surface form on arithmetic strategy.

Abstract: Educated adults solve simple addition problems primarily by direct memory retrieval, as opposed to by counting or other procedural strategies, but they report using retrieval substantially less often with problems in written-word format (four + eight) compared with digit format (4 + 8). It was hypothesized that retrieval efficiency is relatively low with word operands compared with digits and that this promotes a shift to procedural backup strategies. Consistent with this hypothesis, Experiment 1 demonstrated greater word-format costs on retrieval usage for addition than subtraction, which was due to increased counting for addition but not subtraction. Experiment 2 demonstrated greater word-format costs on retrieval for division than multiplication, which was due to increased use of multiplication-fact reference to solve division problems. Format-related strategy shifts away from retrieval reflected both the efficiency of retrieval for a given operation and the availability of viable alternative strategies. The results demonstrate that calculation processes are not abstracted away from problem surface form. The authors propose that retrieval efficiency for arithmetic connects diverse performance and strategy-related effects across key arithmetic factors, including arithmetic operation, numerical size, and numeral format.

Integer multiplication and division on the HP Precision Architecture

Abstract: In recent years, many architectural design efforts have focused on maximizing performance for frequently executed, simple instructions. Although these efforts have resulted in machines with better average price/performance ratios, certain complex instructions and, thus, certain classes of programs which heavily depend on these instructions may suffer by comparison. Integer multiplication and division are one such set of complex instructions. This paper describes how a small set of primitive instructions combined with careful frequency analysis and clever programming allows the Hewlett-Packard Precision Architecture integer multiplication and division implementation to provide adequate performance at little or no hardware cost.

Loop carrier system for telecommunication and data services

Abstract: A versatile loop communication system is disclosed wherein recurring frames of the ring carrier signal are divided by a movable partition into a dynamically allocated time division channel portion and a data packet communication portion. A common signal channel, in the ring carrier frame, is used to logically connect and disconnect stations for either circuit or packet communication on a common bus extending from terminals located in the loop. The loop controller automatically forms a contiguous group of time division channels or signal bytes at one end of the ring carrier frame. The format of the time division multiplexing channels is such that dynamic time slot interchanges of signal bytes are produced by the controller without the necessity of counting circuitry in the terminals to identify specific channel locations. The dynamic time slot interchange or byte displacement function is provided by additional memory arrangements both for the signals being transported by the ring and control functions in the time division switch located in the controller. The remaining portion of the frame serves as a shared channel for packet header switched data. In order to provide a flexible basis for packet switching, the controller assigns address tags and retains a map of the system.

Fluid conveying apparatus

Abstract: 1,163,392. Pumping oil between land and ship. FMC CORP. 8 Jan., 1968 [18 Jan., 1967], No. 1017/68. Heading B8E. [Also in Division F2] Oil is delivered between fixed land-based pipe 20 and port 48 carried by ship 12 by means of the pipes 28, 40 and 44 connected by universal joints. The pipe 28 slides horizontally around circle 30 by means of slide 36 so that the set of pipes may be turned through 360 degrees. Additionally, the pipes 28 and 40 are provided with air-tight sleeves 56 and 58 to reduce their weight.