1376 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



The binary message is 



00110011100110. 



For this example, the quinary components (quinary information digits) 

 of decimal digits are chosen odd if the corresponding digit of the binary 

 example is 1, even if that digit is 0. The binary and c{uinary components 

 are then combmed by the rules of the reflected ciuibinary code to form 

 the decimal digits 7 2 9 4 7 6. For example, the cjuinary and binary 

 components of the fifth digit are 2 and 0, respectively; the decimal digit 

 which has these components is 4, the fifth decimal digit of the message. 

 Consider the binary case. Suppose that the message is mutilated in 

 transmission so that the tenth digit is received incorrectly. The message 

 is mutilated from 



001100111001 10 

 to 



00110011110110. 

 The decoder and corrector calculates the corrector by 



14 



Cj = ^ Xidj mod 2. (53) 



!=1 



In this formula, Cj is the jth digit of the corrector and .r/ the received 

 value of Xi . In this example the corrector is 1 1 0, which means that 

 the tenth digit, which has this characteristic, is wrong and should be 

 changed to 0. 



The corresponding error in the decimal example is a change in the 

 fifth digit from 4 to 3. If the message 7 2 9 3 7 6 is received, the 

 resolver and quinary to binary converter delivers the message 



00110011110110 



to the decoder instead of 



00110011100110 



corresponding to the correct message. The corrected binary message is 

 produced at the output of the decoder and corrector. When the quinar}^ 

 and binary components of the fifth digit are examined by the quinary 

 correction circuit, the following inputs exist: 



Received quinary digit 1 (Odd) (quinary component of 



Corrected binary digit 



derived from quinary (Bi) 



Corrected binary digit 



from same decimal number {B-i). 



received decimal 3) 



