Abstract
For efficient optoelectronic implementation of parallel algorithms, a novel digit-set-restricted modified signed-digit (MSD) arithmetic based on content-addressable-memory is presented. With the introduction of the reference digits, carry propagation is avoided by restricting digit sets of the intermediate carry and sum into {-1,0} and {0,1}, respectively. The two-step MSD addition schemes based on the nonrestricted and the digit-set-restricted reference digits are investigated. Previous algorithms require 16 or 12 minterms, and in those algorithms reduction of the minterms is based on utilizing the bit-by-bit complement property for nonzero outputs, i.e., the minterms generating a positive output are exactly the bit-by-bit complement of those generating a negative output. In our new algorithm, without using the complement property for the nonzero outputs, only 12 minterms for all the outputs are required. More significantly, since no complement operation is involved, the optical system needs no additional reflecting unit and mask, which makes the proposed algorithms more practical and efficient. Thus, compared with the most recently reported 16 or 12-minterm recoded MSD adders with two optical units, our approach shows superiority in terms of the number of minterms and the system complexity. An incoherent correlator based optoelectronic shared-content-addressable-memory processor is used to perform the arithmetic operations. Only one set of minterms needs to be stored independent of the operand length. A proof-of-the-principle experiment is demonstrated.