Codes in binary system
BCD codes,for decimal digit;
Gray code,for numbers in binary system;
ASCII code,for characters;
Key point,
Use n bits,we can make 2n different words;
To make n code-words,you must use
bits.
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BCD codes
Binary codes for decimal digits ( Table 2-9 )
BCD codes
Express 10 digit ( 0—9),use 4 or more bits,
many different way for coding
8421 code
Natural code,just lake 4-bit
binary numbers;
Each digit is weighted;
It has 10 valid code words
and 6 invalid code words.
BCD codes
Each digit is weighted;
Self-complementing;
Use MSB to express
higher/lower part;
It has 10 valid codes and
6 invalid codes.
2421 codes
BCD codes
Excess-3 code
Its digit is not weighted;
Self-complementing ;
8421 code +,0011”,
BCD codes
1-out-of-10 code
One hot code;
It is very useful in
control systems.
BCD codes
Examples:
use BCD code for decimal numbers A = 19.46
8421 code,A = 0001 1001,0100 0110
2421 code,A = 0001 1111,0100 1100
Excess-3 code,A = 0100 1100,0111 1001
Key point
Each decimal digit is coded by a 4-bits string!
BCD codes
Biquinary code,7-bits;
first 2 bits for higher/lower range;
last 5 bits is one hot code in the range.
error-detecting property !
Gray codes
Target,code for continues changed numbers (in
binary system) to prevent wrong code happened
in transition time;
Property,In each pair of successive code words,
only one bit changes.
Gray codes
From binary number to Gray code
The length is same,the MSB is same;
From left to right,if a bit in binary system is same as
its left bit,the gray code is 0,if it is different,the gray
code is 1.
Examples:
binary number,1001 0010 0110 0011
Gray codes,1101 1011 0101 0010
Codes for other things
Character codes,ASCII,7-bits string,128 code
words;
p.54 Table 2-11
Example,How are you!
1001000 1101111 1110111 0100000 1100001 1110010
1100101 0100000 1111001 1101111 1110101 0100001
Codes for other things
Codes for actions,conditions or states:
Use n bits,we can make 2n different words;
To make n different words,we must use
bits.
p.55 Table 2-12
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Codes in digital circuit
Parallel codes
use n-line to transmit an n-bits code words ;
transmit an n-bits code words in one time period;
Serial codes
use one line to transmit an n-bits code words ;
transmit an n-bits code words in n time period;