• Journal of the Korean School Mathematics Society
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• v.5 no.1
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• pp.111-122
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• 2002

The purpose of this study was to examine high school second graders' understanding of the basic nature of logarithm, the major type of error they made about logarithmic function and the cause of such an error, and to seek ways to instruct it better. For that purpose, three research questions were posed: 1. Investigate how much high school students in their second year comprehend the nature of logarithm. 2. Analyze what type of error they make about logarithmic function. 3. Analyze the cause of their error according to the selected error models and how it could be taught more efficiently. The findings of this study were as below: First, the natural science students had a better understanding of the basic nature of logarithm than the academic students. What produced the widest gap between the two groups' understanding was applying the nature of logarithm to the given problems, and what caused the smallest gap was the definition of logarithm and the condition of base. Second, the academic students had a poorer understanding of the basic nature of logarithmic function graph and of applying the nature of logarithm to the given problems. Third, the natural science students didn't comprehend well the basic nature of logarithmic function graph, the nature of characteristics and mantissa. Fourth, for all the students from academic and natural science courses, the most common errors were caused by the poor understanding of theorem or nature of the ［E4] model. Fifth, the academic students made more frequent errors due to the unfamiliar signs of the ［El］ model, the imperfect understanding of theorem or nature of the ［E4］ model, and the technical part of the ［E6］ model. Sixth, the natural science students made more frequent errors because of the improper problem interpretation of the ［E2］ model and the logically improper inference of the ［E3］ model.

• Journal of the Institute of Electronics Engineers of Korea TE
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• v.39 no.4
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• pp.355-355
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• 2002

In this paper, we designed a FPU(floating point unit) that it is very important and requires of high density when digital audio is designed. Almost audio system must support the multi-channel and required for high quality. A floating point arithmetic function in MPEG-2 AAC that implemented by hardware is able to realtime decoding when DSP realization. The reason is that MPEG-2 AAC is compatible to the Audio field of MPEG-4 and afterwards. We designed a FPU by hardware to increase the speed of a floating point unit with much calculation part in the MPEG-2 AAC Decoder. A FPU is composed of a multiplier and an adder. A multiplier used the Radix-4 Booth algorithm and an adder adopted 1's complement method for speed up. A form of a floating point unit has 8bit of exponent part and 24bit of mantissa. It's compatible with the IEEE single precision format and adopted a pipeline architecture to increase the speed of a processor. All of sub blocks are based on ISO/IEC 13818-7 standard. The algorithm is tested by C language and the design does by use of VHDL(VHSIC Hardware Description Language). The maximum operation speed is 23.2MHz and the stable operation speed is 19MHz.