Fully redundant decimal addition and subtraction using stored-unibit encoding
Decimal computer arithmetic is experiencing a revived popularity, and there is quest for high-performance decimal hardware units. Successful experiences on binary computer arithmetic may find grounds in decimal arithmetic. For example, the traditional fully redundant (i.e., the result and both of the operands are represented in a redundant format) and semi-redundant (i.e., the result and only one of the operands are redundant) binary addition schemes have influenced the design and implementation of similar decimal arithmetic units. However, special comparison and correction steps are required when decimal arithmetic algorithms are implemented on binary hardware. To circumvent these difficulties, alternative encodings of decimal digits and a variety of decimal arithmetic algorithms have been examined by many researchers over decades. In this paper we offer a new redundant decimal digit set [?8, 9] and a fully redundant addition/subtraction scheme. The proposed digit set, faithfully encoded as a mix of posibits, negabits, and unibits, is shown to obviate the need for any compare-to-9 operations and leads to minimal penalty subtraction using the addition circuitry. Moreover, conversion from the standard BCD encoding to the proposed stored-unibit encoding is possible with the latency of one logic level. However, the reverse conversion, like any other redundant to nonredundant conversion, involves carry propagation.
stored-unibit encoding decimal computer arithmetic fully redundant addition redundant number systems semi-redundant addition