Parallel Arithmetic on Optical Computers by Redundant Binary Number Representation

A parallel arithmetic, suitable for optical computers, can be obtained using two main approaches 1) residue number system1,2 and 2) redundant number representations3,4. In fact using of both approaches it is possible to build totally parallel adders operating by symbolic substitution (SS)2,5–7 and in constant time (the adding time is independent of the length of the operand digit strings, N). Using a residue number system, the size of the SS Truth Tables required for the carry-free addition heavily increases with numerical range involved1,2, and these tables depend on the digit position. On the contrary, additions of redundant numbers can be performed in constant time by small SS Truth Tables which are independent of the digit positions