Maximal redundancy signed-digit systems

The maximal redundancy signed-digit (MAXSD) number system has the highest redundancy within the carry-absorbing signed-digit number system proposed by Avizienis in 1961. The digital values for radix R lie in [1-R, R-1]. Its compatibility with both standard nonredundant systems and binary arithmetic makes it an excellent choice far multiprecision arithmetic on binary machines. The representations for finite numbers are however nonunique and can even be unbounded in wordlength; this is resolved by algorithms for partial or complete conversion to standard nonredundant notation without explicit carry propagation.