One-step high-radix signed-digit arithmetic units based on classified joint spatial encoding

A simple one-step fully-parallel high-radix signed-digit arithmetic is proposed for parallel optical computing based on new joint spatial encodings. The high-radix signed-digit arithmetic operations are based on classifying the neighboring input digit pairs into various groups in order to reduce the computation rules. A new joint spatial encoding technique is developed to present both the operands and the computation rules. This technique increases the spatial bandwidth product (SBWP) of the spatial light modulators (SLM) of the system. It will be shown that our one-step TSD and QSD arithmetic units are much simpler and better than all previously reported high-radix signed-digit techniques.