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Computer Arithmetic
Published in Joseph Cavanagh, Digital Design and Verilog HDL Fundamentals, 2017
Division can be considered as the inverse of multiplication in which the dividend, divisor, and quotient correspond to the product, multiplicand, and multiplier, respectively. Division employs the same general principles as multiplication. Multiplication is an add-shift operation, whereas division is a shift-subtract/add operation. In division, the result of each subtraction determines the next operation in the division sequence. There can be no overflow in multiplication because the product can never exceed 2n bits. In division, however, the dividend may be so large compared to the divisor that the value of the quotient exceeds n bits.
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 (÷).
Students’ ability to determine the truth value of mathematical propositions in the context of operation meanings
Published in International Journal of Mathematical Education in Science and Technology, 2022
Multiplication and division have many meanings conceptually. They have more conceptual features than addition and subtraction. Meanings for multiplication and division were expressed by researchers under different names (Souviney, 1994; Van de Walle et al., 2013). In this study, the classification stipulated by Haylock and Cockburn (2014) was considered. According to this classification, the multiplication has repeated addition and scale meanings. At the heart of the repeated addition meaning is a key phrase in the form of ‘many groups of many things’. The scale meaning of multiplication is also referred to in some studies as the comparison meaning (Holmes, 1995; Kılıç, 2013; Tertemiz, 2017; Van de Walle et al., 2013). This meaning is a quantity magnified by a multiplier. Division operation has four meanings of equal sharing, inverse of multiplication (grouping), ratio, and repeated subtraction. Equal sharing is the key expression in the equal sharing meaning. A set of 12 objects is arranged into three groups, the answer is the number of objects in each group for 12:3 in this meaning. The reverse multiplication meaning can be called ‘grouping’ because it is intended to find the number of groups that can be obtained for a given magnitude. For 12:3, 12 objects are organized into groups of three, and the answer is the number of groups. The idea that division is the inverse of multiplication suggests that division has repeated subtraction meaning similar to the multiplication’s repeated addition meaning. The ratio meaning of division is also the inverse of the scale meaning of multiplication. In problem posing researches on four basic operations, it was found that students had more difficulty in multiplication and division than addition and subtraction; they posed exercise and problems related to different operations (Kılıç, 2013; Tertemiz, 2017).