Residue number system Totally Explained

Everything about Residue Number System totally explained

A residue number system (RNS) represents a large integer using a set of smaller integers, so that computation may be performed more efficiently. It relies on the Chinese remainder theorem of modular arithmetic for its operation, a mathematical idea from Sun Tsu Suan-Ching (Master Sun’s Arithmetic Manual) in the 4th century AD.

Defining a residue number system

A residue number system is defined by a set of N integer constants, ť ^i m_i for

i>0

and

0leq x^*_i

Note that after conversion from the RNS to AMRS, the comparison of numbers becomes straightforward.

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