Signedness

Abstract: An arithmetic unit for multiplying and accumulating signed binary data and indicating an occurrence of a signed arithmetic overflow includes a multiplier-accumulator and an overflow flag register. The multiplier-accumulator receives and selectively multiples and accumulates signed binary data, and provides output data representing the multiplied and accumulated data and a sign bit representing its polarity, i.e. positive or negative. The flag register provides two "sticky" flag bits for indicating whether a signed arithmetic overflow (positive or negative) of the multiplied and accumulated data has occurred. The flag bits are "sticky" in that once a flag has been set, it cannot be reset by another arithmetic overflow condition. Instead, it must be specifically reset. The sign bit is used to selectively set one of the two sticky flag bits to a true state to indicate the direction (positive or negative) of the first arithmetic overflow. The sticky flag bits have mutually exclusive true states in that once a flag bit has been set true, the other flag bit cannot be set true until both flag bits have been specifically reset.

Abstract: When performing fixed point multiplication with 32 bit operands for example, the product is, in general, represented by a 64 bit number. However, a typical microprocessor may compute the product to only 32 bits. Therefore, the possibility of overflow exists. The present invention provides an indication as to the status of the upper (most significant) 32 bits of the product. This indication may include both "carry" and "overflow" flags, which are unsigned and signed overflow, respectively. The inventive technique is implemented in hardware that is used in conjunction with a Booth recoding multiplier.

Abstract: This paper proposes a new method of encoding numbers by variable-length byte-strings. The primary property of the encoding is that the lexicographic comparison of the encoded numbers corresponds correctly to the order of the real numbers. The encoding is space-efficient. Further, unlike the fixed-length representations of numbers (fixed-point, floating-point, etc.,) the encoded numbers are not limited in their magnitude or the number of their significant digits. The paper also elaborates the application of the encoding method to the storage of numeric data in databases. The proposed application for databases is a uniform format for all the numbers, regardless of their types and attributes (fields). All the numbers are represented in a form of lexicographically-comparable byte-strings. This form simplifies the data management software (only one format to deal with at the physical database level) and hardware (when associative memory and storage devices etc. are used); makes the applications more flexible (by removing limitations on the sizes of numbers); and is space-efficient for all numbers while being especially concise for those numbers that are used more frequently in databases.

Abstract: Conventionally, there are four common ways to represent negative numbers, namely, 1's-complement, 2's-complement, signed-magnitude, and excess-2m-1. In all these representations except the last one (excess-2m-1), 1 is used as the sign bit to denote negative numbers. However, in a recently reported magnetic bubble device, using 1 as the sign bit for negative numbers may cause problems when two numbers are compared. In this paper we define a new number representation (called Bl's-complement), and we propose a simple, read-free device for converting numbers represented in any of the above standard representations to either the excess-2m-1 or the Bl's-complement representation.