Binary Logic for Residue Arithmetic Using Magnitude Index

We consider a residue number system using n pairwise relatively prime moduli m
1
,⋯,m
n
to represent any integer X in the range M/ 2≤X>M/2, when M = ∏mi. The moduli m
i
are chosen to be of the 2-1 type, in order that the residue arithmetic can be implemented by means of binary registers and binary logic. Further, for each residue number X, a magnitude index P
x
is maintained for all arithmetic operations. We investigate the properties of such a system and derive the addition, subtraction, multiplication, sign determination, and overflow detection algorithms. The proposed organization is found to improve the operation times for sign detection and overflow detection operations, while rendering multiplication to be a difficult operation.