A cardinalised binary representation for exponentiation

This paper introduces the Cardinalised Binary Representation (CBR) of integers. A family of algorithms for converting binary integers to their CBR equivalents is described. Characteristics of the resulting representation is analyzed and exploited to achieve performance improvement for large integer exponentiation operations. This paper demonstrates that the CBR is a more general scheme than the well known Binary Redundant Representation (BRR) [1], and shows that both software and hardware CBR exponentiation algorithms operate more efficiently than that of BRR.