SOEN228w-11week2

# SOEN228w-11week2 - • Gate representations • Map...

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SOEN228 week2 Codes Boolean Algebra

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Codes BCD XS3 2421 Cyclic Error Detection Error Correction
Codes representing decimal numbers BCD 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 XS3 0011 0011 0100 0101 0110 0111 1000 1001 1010 1011 2421 0000 0001 0010 0011 0100 1011 1100 1101 1110 1111 CYCLIC 0000 0001 0011 0010 0110 1110 1010 1011 1001 1000

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Error detecting with Parity bits BCD without parity DDDD 0000 0001 0010 0011 0100 0101 0110 0111 1000 BCD Hamming even parity P 1 P 2 D 3 P 4 D 5 D 6 D 7 00 0 0 000 11 0 1 001 01 0 1 010 10 0 0 011 10 0 1 100 01 0 0 101 11 0 0 110 00 0 1 111 11 1 0 000 00 1 1 001
Hamming Parity combinations for each bit position Parity bits P 3 P 2 P 1 000 001 010 011 100 101 110 111 Bit position Correct 1 2 3 4 5 6 7

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Demonstration of Hamming error detection P 1 P 2 D 1 P 3 D 2 D 3 D 4 parities number 1 0 0 1 0 1 1 P1cover 1 0 0 1 0 P2cover 0 0 1 1 0 P3cover 1 0 1 1 1 Even Parity over bits: 0 is ok, 1 is incorrect • P 3 P 2 P 1 = 100: bit 4 is an error
Boolean Algebra Postulates Definitions Duality Theorems Truth Tables Canonical Forms

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Unformatted text preview: • Gate representations • Map Simplification • Incompletely Specified Functiond Fundamental Definitions Duality Precedence Truth Tables Truth tables Canonical Forms: Representation of functions Minterms Representations of minterms Maxterms Representation of Maxterms Relationship of canonical forms Standard Gate Symbols And Or not(inverter) Gate realisation of Simplified expression Karnaugh Map Simplification with maps Example • Gate realisation Maxterm realisation 4 variable map Combinations of 4 variables Combinations of 4 variables Combinations of 4 variables Incompletely Specified Functions Example unspecified terms...
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SOEN228w-11week2 - • Gate representations • Map...

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