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Fractions
Published in John Bird, Basic Engineering Mathematics, 2017
The simple rule for division is change the division sign into a multiplication sign and invert the second fraction. For example,23÷34=23×43=89 $$ \begin{aligned} {\text{ For} \text{ example,} }\frac{2}{3}\div \frac{3}{4} = \frac{2}{3}\times \frac{4}{3} =\frac{ \mathbf 8 }{ \mathbf 9 } \end{aligned} $$
Parallel Computation of Quotients and Partial Remainders to Design Divider Circuits
Published in Hafiz Md. Hasan Babu, VLSI Circuits and Embedded Systems, 2023
Division is one of the four basic operations of arithmetic, the others are addition, subtraction, and multiplication. The division of two natural numbers is the process of calculating the number of times, one number is contained within one another. In mathematics, the word “division” means the operation which is the opposite of multiplication. The symbol for division can be a slash (, a line (—), or the division sign (÷).
RNS Comparison via Shortcut Mixed Radix Conversion: The Case of Three 4-Moduli Sets {2 n + k , 2 n ± 1, m} (m ϵ {2 n + 1 ± 1, 2 n − 1 − 1})
Published in IETE Journal of Research, 2023
Z. Torabi, G. Jaberipur, S. A. Mirnaseri
Unlike the residue-parallel addition and multiplication in residue number system (RNS), implementation of comparison, division, sign and overflow detection cannot be distributed between the parallel computation channels. Therefore, should one of the aforementioned difficult RNS operations appear in the sequence of RNS-friendly add and multiply operations, the straightforward action is to convert the corresponding operands to binary, perform the desired difficult operation, and convert the obtained binary result back to RNS, if necessary. In case of comparison, this method may be designated as R&C, where almost all of the previously proposed RNS comparison algorithms [1–2] have failed to exhibit better figures of merit than R&C. On the other hand, devising a faster-than-R&C RNS comparator (e.g. [2–5]) is expected to widen the spectrum of RNS applications. The works of [2] and [5] regard the 3-moduli set , where [2] does a partial reverse conversion via the mixed radix conversion (MRC [6]) method, and [5] compares the RNS operands via dynamic range partitioning (DRP). However, the comparator in [3] regards the 4-moduli set , also worked on in [4], where it is noted that both comparators, although faster than R&C, consume more area. Nevertheless, two other comparators for , and are offered in [4], where all figures of merit are better than R&C.
Teaching redundant residue number system for electronics and computer students
Published in International Journal of Mathematical Education in Science and Technology, 2022
Since RNS converts large numbers to smaller residues according to its moduli, arithmetic operations are realized in parallel on the moduli without any carry propagation between them. Therefore, RNS can support high-speed, carry-limited, and parallel arithmetic operations. The number system is appropriate for applications that are only composed of addition, subtraction, and multiplication. Other arithmetic operations like division, sign detection, and magnitude comparison are difficult operations in RNS (Parhami, 2009).
Algebra discourses in mathematics and physics textbooks: comparing the use of algebraic symbols
Published in International Journal of Mathematical Education in Science and Technology, 2023
Helena Johansson, Magnus Österholm
To answer our research questions, each unit of analysis was examined with respect to different aspects. In order to empirically reveal the construction of symbolic sequences (RQ1), the following aspects were used to capture the complexity or size of sequences: total number of algebraic objects and total number of different algebraic objects; total number of equal signs; total number of algebraic objects and total number of different algebraic objects in sequences with more than one equal sign; total number of mathematical operations and total number of different mathematical operations, as well as which operations; and also the use of special types of symbols by examining the total number of algebraic objects that included an index (e.g. b2, ex), that were preceded by capital delta (e.g. Δh, Δtb) and that included Greek letters (except Δ). These special types of symbols are known, from experience, to occur frequently in physics, and therefore it is relevant to empirically determine if they are more common in physics than in mathematics. Operations are here used with a broader meaning than what is formally counted as mathematical operations. It is, for example, distinguished between addition signified by the plus symbol and addition signified by the summation symbol. It is also distinguished between different situations that include the division sign, where the operation ‘division’ relates to all situations where there are no variables in the denominator, and the operation ‘inverse proportionality’ relates to situations with a number in the numerator and a variable in the denominator. The above aspects are chosen to capture fundamental aspects of the construction of symbolic sequences, but they also relate to some specific statements in previous research about symbols in mathematics and physics (e.g. the number of used symbols, Heck & van Buuren, 2019).