There are many different kinds of problems for which high precision calculation can be useful. The most common situation involves a computation that is numerically unstable, so that using double precision is not sufficient to get the final result as accurately as it is needed. We will use the term “significant digits” to mean the number of equivalent decimal digits of precision, as opposed to t...

signed digit (sd) number systems provide the possibility of constant-time addition, where inter-digit carry propagation is eliminated. such carry-free addition is primarily a three-step process; adding the equally weighted sds to form the primary sum digits, decomposing the latter to interim sum digits and transfer digits, which commonly belong to {–1, 0, 1}, and finally adding the transfers to...

This paper presents mathematical foundtions of the Overlap Resolution Number System (ORNS) which employs signed Continuous Valued Digits (CVD’s). ORNS is a redundant Number System employing residue arithmetic. In contrast to the implementation of arithmetic by binary or multiple-valued logic circuits, arithmetic operations in this novel number system are performed by analog digit manipulation c...

Heterotopic or transpositional replantation of digits is technically feasible with results similar to those of conventional replantation procedures. Occasionally in multiple digital amputations not all the digits may be replanted in their correct place as a result of complex injuries proximal to the amputation zone or severe damage to important fingers. In these circumstances the amputated digi...