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218L4S09

# 218L4S09 - ESE218 Lecture 4 Error detection and correction...

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2/5/09 ESE218 Spring 2009 Lecture 4 1 ESE218 Lecture 4. Error detection and correction. Introduction to switching algebra. Logic gates Outline ± ASCII ± Error detection and correction ± Parity bit ± Distance ± Introduction to Hamming codes ± Introduction to switching algebra ² Operators and operator precedence ² Functions of two variables ± Logic operations and gates ± AND, OR, NOT ± NAND, NOR ± XOR, XNOR ± parity generation and checking ± Gray-to-binary code conversion ± Propagation delay ± Summary

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2/5/09 ESE218 Spring 2009 Lecture 4 2 A merican S tandard C ode for I nformation I nterchange (aeski) The American Standards Association (ASA, later to become ANSI ) first published ASCII as a standard in 1963 5-bit 7-bit HEX form: 0D= 0 0001101 MSB=0 for all =>128 codes An upper case character can be changed to the corresponding lower case character by changing a single bit: 01 0 0 -> 01 1 0
2/5/09 ESE218 Spring 2009 Lecture 4 3 Parity bit Parity bit generator Parity bit checker Data = 1 1 0 0 Even parity = 0 1 1 0 0 + parity bit (0 or 1) Odd parity = 1 1 1 0 0 or Data Error if parity changed Transmission line send over

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2/5/09 ESE218 Spring 2009 Lecture 4 4 Minimum distance 000 100 010 001 101 111 110 011 used codes unused codes The MINIMUM DISTANCE is the smallest number of bits by which any two words of a binary code vary for error detecting MIN DISTANCE > 1 1 bit change 1 bit change Min distance between used codes = 2 Any single error in a code from the used code group brings it to the unused code group
2/5/09 ESE218 Spring 2009 Lecture 4 5 Error Detection: codes with parity and m-out-of-n codes 1001 0 11000 1 000000000 9 1000 0 10100 0 1 00000000 8 0111 0 10010 00 1 0000000 7 0110 1 10001 000 1 000000 6 0101 1 01100 0000 1 00000 5 0100 0 01010 00000 1 0000 4 0011 1 01001 000000 1 000 3 0010 0 00110 0000000 1 00 2 0001 0 00101 00000000 1 0 1 0000 1 00011 000000000 1 0 Odd-parity- BCD 2-out-of- 5 code One-hot assignment Decimal digit MIN DISTANCE = 2

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218L4S09 - ESE218 Lecture 4 Error detection and correction...

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