# lec5 - CSE20 Lecture 5 CK Cheng UC San Diego 1 Residual...

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1 CSE20 Lecture 5 4/12/11 CK Cheng UC San Diego

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Residual Numbers (NT-1 and Shaum’s Chapter 11) Introduction Definition Operations Range of numbers 2
Introduction Applications: communication, cryptography, and high performance signal processing Goal: Simplify arithmetic operations (+, -, x) when bit width n is huge, e.g. n= 1000. Note no division is involved. Flow: 3 Number x Residual number (x 1 , x 2 , …, x k ) +, -, x operations for each x i under m i Chinese Remainder Theorem Mod Operation Moduli (m 1 , m 2 , …, m k ) Results

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Definition Mod (Modular) operation. Given integer x and d (d> 0), find q and r such that x = q*d+r, 0<= r <d, where q: quotient, d: divisor, and r: remainder. We define x%d= r. Conversion to residual system: Given moduli (m 1 , m 2 , …, m k ), where all m i are mutually prime, transform integer x to (r 1 , r 2 , …, r k ), where r i =x%m i 4
Definitions mutually (or relatively) prime if their greatest

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## This note was uploaded on 12/11/2011 for the course CSE 20 taught by Professor Foster during the Fall '08 term at UCSD.

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lec5 - CSE20 Lecture 5 CK Cheng UC San Diego 1 Residual...

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