Fully Redundant Decimal Arithmetic
Fully Redundant Decimal Arithmetic
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DOI：
10.1109/arith.2009.23
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发表时间：
2009-06
期刊：
影响因子：
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通讯作者：
S. Gorgin;G. Jaberipur
中科院分区：
文献类型：
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作者：
S. Gorgin;G. Jaberipur
在通用数字处理器的设计和实现中，所有基本的基10算术运算的硬件实现正在发展成为一个新的趋势。部分乘积和余数的冗余表示分别在乘法和除法硬件算法中很常见。更频繁的加/减运算的无进位实现，以及提高乘法和除法的速度的副产品，可以通过冗余数表示来实现。然而，冗余结果到传统表示的转换需要较慢的进位传播，如果结果以冗余格式保存以供稍后用作其他算术运算的操作数，则可以避免这种情况。考虑到与冗余二进制相反的冗余十进制表示法不一定需要额外的存储，我们有动力开发一种完全冗余十进制算术的框架，其中所有操作数和结果都属于相同的冗余十进制数系统，并且可以存储并在以后用作进一步的十进制运算的操作数。在本文中，我们提出了一种新的更快的十进制带符号数字加/减单元，并展示了它如何有效地用于十进制乘法器和除法器的设计，其中所有操作数和结果都用相同的冗余数字集[-7，7]表示。
Hardware implementation of all the basic radix-10 arithmetic operations is evolving as a new trend in the design and implementation of general purpose digital processors. Redundant representation of partial products and remainders is common in the multiplication and division hardware algorithms, respectively. Carry-free implementation of the more frequent add/subtract operations, with the byproduct of enhancing the speed of multiplication and division, is possible with redundant number representation. However, conversion of redundant results to conventional representations entails slow carry propagation that can be avoided if the results are kept in redundant format for later use as operands of other arithmetic operations. Given that redundant decimal representations, contrary to redundant binary, do not necessarily require extra storage, we are motivated to develop a framework for fully redundant decimal arithmetic, where all operands and results belong to the same redundant decimal number system and can be stored and later used as operands of further decimal operations. In this paper, we present a new faster decimal signed digit add/sub unit and show how it can be efficiently used in the design of decimal multipliers and dividers, where all operands and results are represented with the same redundant digit set [–7, 7].