1378 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



Table XIV — Decimal Digit Conveying Three Binary Digits 



parity check digits if a simple reflected binary code correspondence be- 

 tween binary and decimal digits is maintained as shown in Table XIV. 



An extension of this idea is the encoding of the original information 

 (i.e., the information that is shown coming out of the information source 

 in Fig. 2) in some error detection or correction code. For example, the 

 decimal to reflected quibinary code resolver will cause both components 

 to be incorrect if an error of ±2 in a decimal digit occurs. In this case, 

 the system shown in Fig. 2 will automatically make a correction on the 

 decimal digit of either +2 or —2 dependuig upon the value of the re- 

 ceived decimal digit, and provided a double error correction binary 

 code is used. Such a correction wall be incorrect about half the time. If 

 the received binary digit is compared to the corrected binary digit and 

 the received quinary digit is compared to its corrected odd or even digit, 

 an error of ±2 can be detected without changing the code. If one extra 

 binary check digit, treated as an information digit by the encoder and 

 decoder, is transmitted in the message, this binary digit can convey the 

 information necessary for determining the sign for a correction of dz2, 

 provided that only one such correction is required for any one message. 

 A rule for determining the value of this digit is: 



Be = if X) Qi = (0 or 1) mod 4, 



i=l 

 n 



5e = 1 if 53 Qi = (2 or 3) mod 4, 



(54) 



where g, represents the zth quinary information digit, and Be represents 

 the special check digit. If the received message contains one error of ±2 

 on a digit, two possible corrections may be made on the quinary compo- 

 nent of this digit; ±1. Obviously, only one of these corrections will 

 satisfy the equation for determining Be since the two possible corrected 

 values of q are two units apart. 



