Parallel negabinary signed-digit arithmetic operations: one-step negabinary, one-step trinary, and one-step quaternary addition algorithms

摘要

In this paper, we are proposing more efficient one-step negabinary signed-digit algorithms for the addition/subtraction operations. It is shown that by using digits grouping of the negabinary signed-digits, a huge reduction of the number of the symbolic substitution computation rules involved in the arithmetic computations will be achieved. Further, to increase the information storage density, one-step trinary negabinary (using base = -3) and negabinary quaternary (using base = -4) signed-digit will be proposed. The proposed algorithms are very suitable for optical implementation. Various holographic and nonholographic methods based on symbolic substitution content addressable memory (CAM) are suggested for optoelectronic implementation. Among them, the method of joint spatial encoding technique and incoherent optical correlator to act as a shared CAM will be presented.