Computer arithmetic architectures with redundant number systems

Redundant arithmetic number systems are gaining popularity in computationally intensive environments particularly because of the carry-free addition/subtraction properties they possess. This property has enabled arithmetic operations such as addition, multiplication, division, square root, etc., to be performed much faster than with conventional binary number systems. In this paper, some of the recent contributions to the area of design of redundant arithmetic based addition, multiplication, division, and square root algorithms and architectures are briefly discussed. Also, only the use of bit/digit-parallel implementation for architectures is discussed so that the enhancement in speed through the use of redundant arithmetic becomes immediately apparent as opposed to the use of bit/digit-serial architectures, where the primary justification for their use is to conserve area. A new radix 2 division algorithm using over-redundant radix 2 quotient digits and requiring a 2 digit quotient selection function is also presented.