ABSTRACT
In the oldest number systems, numbers were represented by enumeration. For large numbers, this representation is not optimal. The modern number system, the g-adic system, originated in India and came through the orient (Arabian numbers). It can be shown that a finite set of numbers can be represented uniquely by an k-tupel of remainders. Logic is the basis for realizing numeric or nonnumeric operations. Implementation of logic includes the hardware aspects (devices and interconnects) and the underlying logic. Binary multiplication is performed by a convolution of the bit patterns. The result appears in the so called ’mixed binary’ form that has to be converted to binary form involving a carry propagation. Boolean equations in this logic also are converted into a form that only involves NOR-operations. Like in spatial filtering logic, the logic device is used to code the input. The mechanism of pattern recognition and substitution can be implemented with regular arrays of logic gates and regular optical interconnects.
