2.3 Binary Codes for Decimal Numbers ReturnNext Code: A set of n-bit strings in which different bit strings represent different numbers or other things.

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Presentation transcript:

2.3 Binary Codes for Decimal Numbers ReturnNext Code: A set of n-bit strings in which different bit strings represent different numbers or other things is called a code. Code Word: A particular combination of n bit-values is called a code word. BCD: Binary-coded decimal (BCD) which encodes the digits 0 through 9 by their 4- bit unsigned binary representations

NextBackReturn DD Ex-3Biquinary1-out-of Binary Codes for Decimal Numbers

NextBackReturn Unused code words (Pseudo Code) …… 2.3 Binary Codes for Decimal Numbers

NextBackReturn Examples: 1. (1001) 8421BCD =( ? ) 10 (1001) 8421BCD =1  8+0  4+0  2+1  1=(9) (1011) 2421BCD =( ? ) 10 (1011) 2421BCD =1  2+0  4+1  2+1  1=(5) 10 Weighted Code: 8421 code and 2421 code are weighted codes. The weights for the BCD bits are 8,4,2,1 and 2,4,2, Binary Codes for Decimal Numbers

(1011) 242 complement = (0100), it ’ s a 2421 code word for decimal digit 4. NextBackReturn Self-Complementing Code: The 2421 code and the excess-3 have the advantage that they are self-complementing. But excess-3 code is not weighted. Example: What is the 9s ’ complement code of (1011) 2421 ? Is the complement code a 2421 code word? 2.3 Binary Codes for Decimal Numbers

NextBackReturn The biquinary code and 1-out-of-10 code use more than the minimum number of bits in a code. The potential advantage is an error-detecting property. Example: Any errors can be detected in the following codes? ( ) biquinary, ( ) biquinary, ( ) 1-out-of Binary Codes for Decimal Numbers

BackReturn Packed- BCD Representation: Each decimal digit is represented four bits. So one 8-bit byte may represent the value from 0~99; 12 bits may represent the value from 0~999; and so on. Example: ( ) 8421 =( ? ) 10 ( ) 8421 =(94) Binary Codes for Decimal Numbers