Combinational digit-set converters for hybrid radix-4 arithmetic

Two pure combinational radix-4 digit-set converters for use in hybrid arithmetic are presented. The conventional to minimally redundant balanced signed-digit set converter is very simple and has zero cost and delay in terms of gates. The balanced to conventional digit-set converter performs the conversion “on the fly” with the generation of the balanced signed-digits, from the most significant to the least significant one; it has an O(1) delay (i.e. constant and independent of the length n of the number), an O(n²) cost and a regular structure suitable for VLSI implementation. A review of the principles of hybrid addition/subtraction was previously presented (N. Takagi et al., 1985)