Signed Digit Research Articles

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 New Explanation of the Reflected Binary Code

Reflected binary (RB) code words plus an even parity check can be considered as signed digit (SD) representations of the corresponding natural binary (NB) code words. The SD code words allow a simple serial conversion with the least significant bit leading of their digits forming the RB code words into the NB code words.

Decimal Adder with Signed Digit Arithmetic

Addition algorithm, decimal adder with signed digit arithmetic p presented here was designed to establish the following facts: the redundant representation of a decimal digit xi by a 5-bit binary number Xi=3xi leads to a logical design of extreme simplicty; it is possible to form an additional algorithm for the adder so that it can be used to transform numbers written in a conventional decinal form into a signed digit form, and vice versa.