General division algorithms for residue number systems /
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| Other Authors: | , , |
| Format: | Thesis Book |
| Language: | English |
| Published: |
1992.
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| Subjects: | |
| Online Access: | Link to OAKTrust copy |
| Abstract: | This dissertation presents a new approach, for the division in a Residue Number System (RNS). A parity checking technique has been developed to compare number and detect overflows in the RNS. Based on the parity checking technique, an unsigned RNS division algorithm is proposed. In this division algorithm, first the upper bound and lower bound of the quotient is searched, and then a binary search is applied to find the quotient. Based on this division algorithm, a 16-bit RNS divider is designed and implemented by the Verilog program. The unsigned division algorithm is further extended to a signed RNS division algorithm, with sign-magnitude representation. The analysis and experiment show that our approach is practical and efficient. Traditionally, the RNS is confined to integers (fixed-point. numbers). Due to the trend of requesting large numbers in computations, the fixed-point RNS is not satisfying for the future generation of computers. In this dissertation, we proposed a new concept for the floating-point RNS. The mantissa and exponent are in the RNS format in this new system. The operations of both the mantissa and exponent are RNS operations. The arithmetic operations of addition, subtraction, multiplication, and division are described. No mixed-radix number conversion is required. The floating-point RNS can significantly increase the range of the number represented by RNS, and hence the area of the RNS applications. |
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| Item Description: | Typescript (photocopy). Vita. "Major subject: Electrical Engineering." |
| Physical Description: | x, 193 leaves : illustrations ; 29 cm |
| Bibliography: | Includes bibliographical references. |