A recursive radix conversion formula and its application to multiplication and division

AbstractA recursive formula for number conversion from one radix representation to another radix representation is presented. This formula differs from the existing ones in two major aspects. First, it utilizes a digit shift technique which provides faster accumulation of higher significant digits in the final result. Second, it is suitable for parallel computation, so that the length of time necessary for number conversion can be shortened. Thus the longer the digit number, the more appreciation in conversion time-saving will result.Applications of the recursive formula are studied in multiplication and division for negative radix numbers as well as for positive radix numbers. The multiplication and division presented here are especially useful for computations of η word precision, since successive bit-carrying propagation to the most significant digit hardly ever occurs