Negative Radix Research Articles

On Classes of Positive, Negative, and Imaginary Radix Number Systems

A unified approach to a broad class of finite number representation systems is proposed. This class contains aDl positive and negative radix systems and other well-known number systems. In addition, it can be extended to include imaginary radix number systems. The proposed approach enables us to develop a single set of algoritims for arithmetic operations.

Negative radix transformation algorithms and a sequential logic machine for bidirectional binary implementation

The purpose of this paper is twofold: to give a positive integer algorithm for transforming both negative and positive numbers between equal magnitude radices of opposite sign; to implement a sequential logic machine for bidirectional conversion of radix 2 numbers which requires no “a priori” or “a posteriori” knowledge of the sign digit and which automatically generates the properly signed data and its complement, when required, on a digit-by-digit basis starting with the least significant digit.

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

A 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.

Two-way converter logic for positive and negative binary numbers†

This paper describes a hardware implementation of a two-way converter logic by which conversion between numbers from positive to negative binary representation is possible. Index terms: (i) Negative radix, (ii) Positive radix, (iii) Two-way conversion.

Complementary Two-Way Algorithms for Negative Radix Conversions

This paper describes two sets of algorithms in positive radix arithmetic for conversions between positive and negative integral radix representation of numbers. Each set consists of algorithms for conversions in either direction; these algorithms are mutually complementary in the sense they involve inverse operations depending upon the direction of conversion. The first set of algorithms for conversion of numbers from positive to negative radix (negative to positive radix) proceeds serially from the least significant end of the number and involves complementation and addition (subtraction) of unity on single-digit numbers. The second set of algorithms for conversion of numbers from positive to negative radix (negative to positive radix) proceeds in parallel starting from the full number (the most significant end of the number) and involves complementation and right (left) shift operations. The applications of these algorithms to integers, mixed integer-fractions, floating-point numbers, and for real-time conversions are given.

Negative Radix Conversion

Adoption of a negative radix for number representation results in a system that is totally indifferent to the sign of the number. Compared to the sign-magnitude representation, the approach considered here requires one extra digit.

Subtraction by Minuend Complementation

In performing the operation of subtraction in additive systems, a popular practice is to complement the subtrahend and add. A second method of performing subtraction, which seems to have been overlooked, is to complement the minuend, add it to the subtrahend, and complement the result. In many cases, this second method is more awkward; however, in two instances it seems to be worthy of consideration. The first instance, surprisingly enough, concerns BCD systems, where minuend complementation can compare favorably with more conventional methods of BCD subtraction. The second instance concerns negative radix numbers where the technique of minuend complementation seems to offer definite advantages.

Conversion from Positive to Negative and Imaginary Radix

Conversion from Positive to Negative and Imaginary Radix