• Communications of Mathematical Education
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• v.35 no.4
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• pp.505-525
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• 2021

In this study, we investigated how multiplication by 2-digit numbers had been taught in elementary mathematics textbooks of Korea, Japan, Singapore, and USA. As a result of analysis, we found as follows. Korean textbooks do not teach the multiplication by 10 and the multiplication by power of 10, but Japanese, Singapore, and US textbooks explicitly teach related content. In the '×tens' teaching, Japanese and American textbooks teach formally the law of association of multiplication applied in the process of calculating the partial product of multiplication. The standard multiplication algorithm generally followed a standard method of recording partial product result according to the law of distribution, but the differences were confirmed in the multiplication model, the teaching method of the law of distribution, and the notation of the last digit '0'. Based upon these results, we suggested some proposals for improving the multiplication teaching.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.4
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• pp.637-637
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• 1997

In this paper, format conversion filters are proposed, which have advantages in hardware implementation compared to the ones proposed in MPEG-4 Video Verification Model. since each coefficients of the proposed filters is constrained to have less than two non-zero digits in minimal signed digit representation, multiplication of input and the coefficient can be implemented by a single adder. As a result, the proposed filters have advantages in hardware complexity and speed, compared to the filters which are usually implemented by integer multiplier or carry save adders. Six kinds of filters are proposed in MPEG-4 Video Verification Model for size conversion of 2:1, 4:1, 5:3 and 5:6. We design 5 filters for the same purpose and compare the performance. The remaining one is very simple to implement. For comparing the filtering performance, we first compare the results of sine wave frequency conversion as an indirect but meaningful comparison. Second. We compute the PSNR of the images obtained from the proposed filters and the ones proposed by MPEG, with reference to the images obtained by using double precision arithmetic and high order filter. The results show that the performance of the proposed filters is almost the same as that of the filters proposed by MPEG. In conclusion, the peroformance of the proposed filters is comparable to that of the ones in MPEG-4, while requiring lower hardware complexity and providing high operating speed.