• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.12
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• pp.20-35
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• 2016

In this paper, in order to reduce the delay and area of the partial product accumulation (PPA) of the parallel decimal multiplier, a tree architecture that composed by multi-operand decimal CSAs and improved CLA is proposed. The proposed tree using multi-operand CSAs reduces the partial product quickly. Since the input range of the recoder of CSA is limited, CSA can get the simplest logic. In addition, using the multi-operand decimal CSAs to add decimal numbers that have limited range in specific locations of the specific architecture can reduce the partial products efficiently. Also, final BCD result can be received faster by improving the logic of the decimal CLA. In order to evaluate the performance of the proposed partial product accumulation, synthesis is implemented by using Design Complier with 180 nm COMS technology library. Synthesis results show the delay of the proposed partial product accumulation is reduced by 15.6% and area is reduced by 16.2% comparing with which uses general method. Also, the total delay and area are still reduced despite the delay and area of the CLA are increased.

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.243-256
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• 2005

Abacus numerals were developed using the concept of the binary system to form decimal numerals. This would allow addition, subtraction, multiplication, and division to be performed based solely on the knowledge of the 14 forms of the numerals and three simple rules. These numerals were taught to 260 elementary school pupils of 3rd and 4th grade. After 90 minutes of instruction, they, nearly all, were able to understand principles to add, and to subtract, and partly to multiply using Abacus Numerals. Protected Abacus Numerals are proposed against forgery. An International Numeration System is proposed based on the form of Abacus Numerals to facilitate international communication. A new type of abacus is proposed.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.6
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• pp.55-60
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• 2023

When performing the multiplication m×r=p of two binary numbers m and r on a computer, there is a shift-and-add(SA) method in which no time-consuming multiplication is performed, but only addition and shift-right(SR). SA is a very simple method in which when the value of the multiplier r_i is 0, the result p is only SR with m×0=0, and when r_i is 1, the result p=p+m is performed with m×1=m, and p is SR. In SA, the number of SRs can no longer be shortened, and the improvement part is whether the number of additions is shortened. This paper proposes an SA method to minimize addition based on the fact that setting a smaller number to r when converted to a binary number to be processed by a computer can significantly reduce the number of additions compared to the case of setting a smaller number to r based on the decimals that humans perform. The number of additions to the proposed algorithm was compared for four cases with signs (-,-), (-,+), (+,-), and (+,+) for some numbers in the range [-127,128]. The conclusion obtained from the experiment showed that when determining m and r, it should be determined as a binary number rather than a decimal number.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.445-458
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• 2010

This study intends to investigate the process of the development of quantity concept and how to deal with the quantity calculus in elementary school, and to find out the implication for improving the curriculum and mathematics textbooks of Korea. There had been the binary Greek categories of discrete number and continuous magnitude in quantity concept, but by the Stevin's introduction of decimal, the unification of these notions became complete. As a result of analyzing of the curriculum and mathematics textbooks of Korea, there is a tendency to disregard the teaching of quantity and its calculus compared to the other countries. Especially multiplication and division of quantity is seldom treated in elementary mathematics textbooks. So these should be reconsidered in order to seek the direction for improvement of mathematic teaching. And Korea's textbooks need the emphasis on the quantity calculus and on constructing quantity concept.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.11
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• pp.2002-2007
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• 2006

The path search method in the telematics system should consider traffic flow of the roads as well as the shortest time because the optimal path with minimized travel time could be continuously changed by the traffic flow. The existing path search methods are not able to cope efficiently with the change of the traffic flow. The search method to use traffic information also needs more computation time than the existing shortest path search. In this paper, a method for efficiency improvement of path search is implemented and its performance is evaluated. The method employs the fixed grid for adjustable heuristic to traffic flow. Moreover, in order to simplify the computation of estimation values, it only adds graded decimal values instead of multiplication operation of floating point numbers with due regard to the gradient between a departure and a destination. The results obtained from the experiments show that it achieves the high accuracy and short execution time as well.