Division Instructions Research Articles

Making Offline and Online Work Procedures for Vision Glasses Optical Store in Surabaya

Vision Glasses is a Surabaya-based eyewear shop selling high-quality, affordable glasses, lenses, and eyewear accessories. This thesis intends to discuss the existing managerial issue in Vision Glasses, namely work performance. This research employs theory of constraints and the theory of work procedure by Boutros & Purdie. After collecting the data from the owner and employees of Vision Glasses, the writer discovers that Vision Glasses needs to apply a work procedure which contains rules or guidelines such as the policy, customer-service ethics, and division instructions for the employees and as a guideline for the company to discipline the employees or deal with internal conflict.

Young Children Intuitively Divide Before They Recognize the Division Symbol.

Children bring intuitive arithmetic knowledge to the classroom before formal instruction in mathematics begins. For example, children can use their number sense to add, subtract, compare ratios, and even perform scaling operations that increase or decrease a set of dots by a factor of 2 or 4. However, it is currently unknown whether children can engage in a true division operation before formal mathematical instruction. Here we examined the ability of 6- to 9-year-old children and college students to perform symbolic and non-symbolic approximate division. Subjects were presented with non-symbolic (dot array) or symbolic (Arabic numeral) dividends ranging from 32 to 185, and non-symbolic divisors ranging from 2 to 8. Subjects compared their imagined quotient to a visible target quantity. Both children (Experiment 1 N = 89, Experiment 2 N = 42) and adults (Experiment 3 N = 87) were successful at the approximate division tasks in both dots and numeral formats. This was true even among the subset of children that could not recognize the division symbol or solve simple division equations, suggesting intuitive division ability precedes formal division instruction. For both children and adults, the ability to divide non-symbolically mediated the relation between Approximate Number System (ANS) acuity and symbolic math performance, suggesting that the ability to calculate non-symbolically may be a mechanism of the relation between ANS acuity and symbolic math. Our findings highlight the intuitive arithmetic abilities children possess before formal math instruction.

Fast Random Integer Generation in an Interval

In simulations, probabilistic algorithms, and statistical tests, we often generate random integers in an interval (e.g., [0, s )). For example, random integers in an interval are essential to the Fisher-Yates random shuffle. Consequently, popular languages such as Java, Python, C++, Swift and Go include ranged random integer generation functions as part of their runtime libraries. Pseudo-random values are usually generated in words of a fixed number of bits (e.g., 32b, 64b) using algorithms such as a linear congruential generator. We need functions to convert such random words to random integers in an interval ([0, s )) without introducing statistical biases. The standard functions in programming languages such as Java involve integer divisions. Unfortunately, division instructions are relatively expensive. We review an unbiased function to generate ranged integers from a source of random words that avoids integer divisions with high probability. To establish the practical usefulness of the approach, we show that this algorithm can multiply the speed of unbiased random shuffling on x64 processors. Our proposed approach has been adopted by the Go language for its implementation of the shuffle function.

Using the Concrete–Representational–Abstract Sequence to Teach Conceptual Understanding of Basic Multiplication and Division

To meet increasingly complex mathematics standards in late elementary school, students must conceptually understand and be fluent in the operations of multiplication and division. This includes understanding the operations’ inverse relation. The purpose of the study was to investigate the effects of alternating concrete–representational–abstract (CRA) multiplication and division instruction on students’ mastery of unknown facts and on their conceptual understanding. Fourth through sixth-grade students with learning disabilities who had failed to master all multiplication facts participated in the study. The researchers used a mixed method design, measuring accuracy and fluency of facts with a multiple probe across students design and qualitative methods to capture changes in students’ explanations of their computation. The researchers demonstrated a functional relation between CRA instruction and accuracy and fluency in multiplication and division. Qualitative results indicated differences in students’ understanding of the operations. Implications of the results will be discussed further.

Design on Embedded Processor with Configurable Divider

By analyzing Cortex-M3 Instruction Set and AHB Bus protocol, a Cortex-M3 Instruction Set compatible 32-bit RISC embedded microprocessor with built-in an optimized 5+2-stage pipeline was realized in this paper. The performance of the 32-bit RISC processor is optimized by deepening pipeline and optimizing functional modules compared with Cortex-M3. According to division instructions, a configurable hardware divider in different realization ways was realized for different applications. The design of the system architecture was completed using Verilog hardware description language (Verilog HDL) and Top-down methodology. The logic function was corrected by VCS simulation FPGA verification. Design Compiler synthesis result shows that, the maximal dominant frequency of the RISC embedded microprocessor could be up to 95MHz with the 0.18um CMOS process of SMIC, and is improved by 31.94% compared with STM32 Cortex-M3 (72MHz).

Improved Division by Invariant Integers

This paper considers the problem of dividing a two-word integer by a single-word integer, together with a few extensions and applications. Due to lack of efficient division instructions in current processors, the division is performed as a multiplication using a precomputed single-word approximation of the reciprocal of the divisor, followed by a couple of adjustment steps. There are three common types of unsigned multiplication instructions: we define full word multiplication (umul), which produces the two-word product of two single-word integers; low multiplication (umullo), which produces only the least significant word of the product; and high multiplication (umulhi), which produces only the most significant word. We describe an algorithm that produces a quotient and remainder using one umul and one umullo. This is an improvement over earlier methods, since the new method uses cheaper multiplication operations. It turns out that we also get some additional savings from simpler adjustment conditions. The algorithm has been implemented in version 4.3 of the gmp library. When applied to the problem of dividing a large integer by a single word, the new algorithm gives a speedup of roughly 30 percent, benchmarked on AMD and Intel processors in the x86_64 family.

A parallel residue-to-binary conversion algorithm without trial division

In recent years, the conversion of residue numbers to a binary integer has been intensively studied. The Chinese Remainder Theorem (CRT) is a solution to this conversion problem of a number to the Residue Number System with a general moduli set. This paper presents a new division-free conversion approach for the conversion of residue numbers to a binary integer. The algorithm differs from others employing a great number of division instructions by using shift instructions instead. These simple instructions keep the power consumption lower. This algorithm can also be implemented with a lookup table or upon a vector machine. Both make the conversion process efficient. This division-free algorithm employs the concept of Montgomery multiplication algorithm. There are two variations of Montgomery algorithm proposed, which are algorithms MMA and IMA. The algorithm MMA is to transform the input number into the output presentation of Montgomery algorithm. Algorithm IMA is therefore inverse the computation of Montgomery algorithm to obtain the multiplicand. These two algorithms are in the complexity of O( n), where n is ⌈log 2 q i ⌉. q i is a modulus. The proposed algorithm for converting the residues to a binary integer therefore runs on O( n × log m) times on O( m) processors. There are O(log m) iterations of O( n) complexity. Compared with the traditional conversion algorithm, the advantages of this proposed algorithm are not only in employing simpler operations but also in performing fewer iterations.

Using Explicit and Strategic Instruction to Teach Division Skills to Students With Learning Disabilities

Students with mathematics learning disabilities (LD) exhibit difficulties with retrieval and cognitive skills that impede their ability to perform basic mathematical skills. Instruction in mathematical procedures (i.e., procedural knowledge) is necessary to help students learn and apply skills such as basic facts and whole-number computation. Division is a skill that is identified in curriculum across the grade levels; yet, it is a skill that is often taught last in instructional sequences because of its complexity and prerequisite knowledge. Reviews of research have revealed that students with LD benefit from a combined model of academic instruction that includes both explicit and strategic instructional procedures. This article presents an overview of division instruction and a sample of interventions for teaching division that include explicit and strategic instructional procedures, which are found in the combined model of teaching.

Design of a cycle-efficient 64-b/32-b integer divisor using a table-sharing algorithm

In new generations of microprocessors, the superscalar architecture is widely adopted to increase the number of instructions executed in one cycle. The division instruction among all of the instructions needs more cycles than the rest, e.g., addition and multiplication. This makes the division instruction an important cycles-per-instruction figure for modern microprocessors. In this paper, a radix-16/8/4/2 divisor is proposed, which uses a variety of techniques, including operand scaling, table partitioning, and, particularly, table sharing, to increase performance without the cost of increasing complexity. A physical chip using the proposed method is implemented by 0.35-/spl mu/m single poly four metal (1P4M) CMOS technology. The testing measurement shows that the chip can execute signed 64-b/32-b integer division between 3-13 cycles with a 80-MHz operating clock.

Descriptive analysis of fifth grade division instruction in basal mathematics programs: Violations of pedagogy

The purpose of this article was to examine the teaching of division in two fifth-grade mathematics basal series published prior to the current National Council of Teachers of Mathematics (NCTM) Standards (1989) and recent editions of the same basals published after the standards were in effect. In this article, six pedagogical variables gleaned from effective teaching practices are presented followed by a narrative description of the extent to which the late 1980s' and early 1990s' editions of two basal mathematics programs applied these variables in designing instructional sequences. The present analysis revealed substantial pedagogical deficits in the two programs' 1980 and 1990 editions: prior knowledge was rarely addressed, content was introduced too rapidly, coherence of information taught was lacking, teaching demonstrations were often not explicit and straightforward, and practice and review were often inadequate.

Improving the division instruction of application-specific RISCs

This paper presents the development and application of a signed radix-4 division algorithm to a RISC architecture, where the internal ALU Manchester Carry adder is used to maintain the partial remainder in irredundant form. There are division algorithms which are faster than the one described in this paper, however, they usually make use of a redundant representation of the partial remainder and require carry-save adders which are not normally used in the integer execution unit of RISCs. The method presented in this contribution employs 3x divisor multiples and uses a reduced next divisor multiple estimate table which is implemented by a small and fast logic. Alternative radix-4 schemes with quotient digits {-2,-1,0,1,2} require large and slow PLAs for quotient digit generation. Additionally, there is no need for positive and negative quotient registers because quotient bits are generated on-the-fly by a small-sized logic, concurrently with partial remainder formation. This method also deals directly with signed two's complement numbers, eliminating the need for additional instructions for sign conversion. The application of this radix-4 division algorithm provides a two-bits-at-a-time division instruction, instead of the traditional single bit approach used in some RISCs. The speedup achieved can be very important in many numeric intensive applications, in which the use of floating-point units is not essential.

Implementing high integrity systems: the VIPER microprocessor

The author describes the development of VIPER and points out some of the practical problems encountered over the four years of the project. Informal proofs of correctness, carried out in the early stages of the project, are outlined. A peer review group criticized the lack of multiplication and division instructions in VIPER 1. This deficiency is corrected in VIPER 2, and the performance is increased to 3 MIPs.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The architecture of RIG: A RISC for image generation in a multi-microprocessor environment

RIG is a fast Reduced Instruction Set Processor suitable for Real-Time Image Generation (RTIG) Geometric Computations. It is designed to be used in a parallel processing architecture, so that high polygon throughput can be achieved. RIG is a 16 MIPS processor that can execute the geometric computations required in RTIG at least ten times faster than a MC68000-12Mhz microprocessor due to the following innovations and characteristics: • • A novel “Data Ready” technique, in which data is available without waiting for external memory. Data is transferred in burst mode (via DMA) directly into processor internal registers in parallel with processing. • • “Indices” to the General-Purpose Registers instead of “Register Windows” schemes, as a fast and efficient parameter passing mechanism in procedure calls. • • Fast multiplication and division instructions together with a three-staged pipeline architecture with “data forwarding”. • • Extremely fast interaction with a parallel processing system with minimum overhead.

Fast Simulation of Turing Machines by Random Access Machines

We prove that a $T(n)$ time-bounded, $S(n)$ space-bounded and $U(n)$ output-length-bounded Turing machine can be simulated in $O(T(n) + (n + U(n))\log \log S(n))$ time by a random access machine (with no multiplication or division instructions) under the logarithmic cost criterion.

Enhancing Self-Efficacy and Achievement Through Rewards and Goals: Motivational and Informational Effects

This experiment compared the effects of performance-contingent rewards and proximal goals on children's task motivation, self-efficacy, and skillful performance. Children deficient in division skills received division instruction and solved problems. Some children were offered rewards based on their actual performances (rewards only); others pursued proximal performance goals (goals only); and children in a third condition received rewards and goals (rewards + goals). Although the three experimental treatments led to equally rapid problem solving during training, combining rewards with goals resulted in the highest self-efficacy and division performance. Future research should investigate whether proximal goals and performance-contingent rewards enhance self-efficacy through a common informational process. Implications for teaching are discussed.

On some decision problems for RAM programs

We look at some decision problems for programs using the RAM (random access machine) model of computation. Under this model, each instruction takes one step to execute. We obtain positive as well as negative results. For example, we show that there is an algorithm to determine given a positive integer k and a program P with one input variable over the instruction set { x ← 0, x ← x + 1, x ← x ← 1, x ← x + y, x ← x − y, x ← x ∗ y, x ← x y , if p( x) then halt, halt, if p( x) then goto l, goto 1}, where x y is integer division and p( x) is a predicate of the form x < 0, x = 0, x ≠ 0, x > 0, whether P halts on all integer inputs in at most k steps. The problem is also decidable for multi-input programs with no multiplication and division instructions. In contrast, the problem is undecidable for programs with two input variables over the instruction set { x ← 0, x ← x + 1, x ← x − y, x ← x y , if x = 0 then halt, halt}, even when only total programs (i.e., no division by 0 occurs during any computation) are considered. This last result also holds when x ← x y is replaced by multiplication, x ← x ∗ y, but the number of input variables needed is large.

The floating point unit of the Golem B computer

The Golem B computer is a fast machine using emitter-coupled logic and multi-layer circuits. The autonomous floating point arithmetic unit obtains its instructions and operands from buffers loaded ahead of need. Its main part, for 56-bit fractions, uses two 4-operand adder complexes with stored carries.In multiplication instructions, 4 bits of the multiplier are used to form a new partial product in each pass through an adder complex. Division instructions use a base-4 non-restoring algorithm. Addition favours the case of equal or nearly equal exponents, but 112 sum bits are accumulated for all exponent differences.An effort has been made to provide instructions and number formats that will aid the writing of compilers and operating systems.

Algorithm for computer control of a digital plotter

An algorithm is given for computer control of a digital plotter. The algorithm may be programmed without multiplication or division instructions and is efficient with respect to speed of execution and memory utilization.