218L3S09 - ESE218 Lecture 3 Binary codes: Decimal codes....

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2/3/09 ESE218 Spring 2009 Lecture 3 1 Outline ± Decimal codes ² Binary-coded decimals (BCD) ² Addition of BCD ² BCD with sign ² Self-complementing codes ² Excess-3 ² 2421 ± Gray code ± Codes for serial transmission ± Summary ESE218 Lecture 3 Binary codes: Decimal codes. Gray code. Codes for serial transmission.
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2/3/09 ESE218 Spring 2009 Lecture 3 2 Binary coded decimals 0101 5 0100 4 0011 3 1000 8 0111 7 0110 6 0000 0 BCD Digits 0010 2 - 9 1 6 unused codes 1001 0001 17 10 = 0001 0111 BCD 25 10 = 0010 0101 BCD + 0011 1100 11 carry Result of a bit-by-bit addition is not a BCD number 0110 = +6 if sum > 9 + 0011 0010 1 1 carry 42 10 = 0100 0010 BCD Weighted code
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2/3/09 ESE218 Spring 2009 Lecture 3 3 BCD clock What time is it?
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2/3/09 ESE218 Spring 2009 Lecture 3 4 Negative BCD numbers 0101 5 0100 4 0011 3 1000 8 0111 7 0110 6 0000 0 BCD Digits 0010 2 - 9 1 6 unused codes 1001 0001 00 = 0 0000 0000 01 = +1 0000 0001 02 = +2 0000 0010 .. 97 = -3 1001 0111 98 = -2 1001 1000 99 = -1 1001 1001 +2 0000 0010 -1 1001 1001 1011 1 0110 0110 <- add 6 +1 1 0000 0001 carry discarded + + Presented as 10’s complements <- not a BCD <- add 6
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2/3/09 ESE218 Spring 2009 Lecture 3 5 9’s and 10’s complements 000 001 002 003 999 998 997 996 001 002 003 999 998 997 996 10’s complement = 1 + 9’s complement 3-digit decimal numbers with sign: -100…+ 99 -1 -2 -3 -4 +1 +2 +3 +1 099 900 900 099 000 Two zeros Digital systems obtain 10’s complements from 9’s complements because…
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218L3S09 - ESE218 Lecture 3 Binary codes: Decimal codes....

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