1348 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1957 



Table II — Quibinary Code 



tion of the mixed digit might be used, letting the quinary component of 

 the mixed digit convey information and the binary component a check. 

 (Table II.) 



The information source generates blocks of decimal digits followed by 

 one quinary digit. The messages are then generated in the following 

 way : record all decimal information digits as information message digits 

 and take their sum; if the sum is even, the binary component, z, of the 

 mixed digit is 0, otherwise it is 1. The quinary component, |/, of the mixed 

 digit is taken directly from the information source and combined with 

 the calculated binary part by the rules of the quibinary code to form 

 the mixed decimal digit. Thus, a;, the value of the mixed digit, is given 

 by the formula : 



X = 2\j -\- z. 



(1) 



For example, if the decimal digits of a message are 289 and the quinary 

 digit of the message is 3, the mixed digit is 7, and the message is 2897. 

 The sum of the decimal information digits is 19, which is odd, so that 

 the binary component of the mixed digit is 1 ; this is combined with the 

 quinary component, 3, bj^ the rules of the quibinary code table, to form 

 decimal digit 7. The requirement that the sum of all digits be even is 

 satisfied by the binary component of the mixed digit, and the informa- 

 tion associated with the mixed digit is contained in the quinary com- 

 ponent. 



This method is easily extensible to any other number base and is also 

 extensible to the case of slightly larger but still restricted errors (such 

 as ±1 or ±2), provided that the maximum single error is less than 



(& - l)/2. 



From the preceding example, it is apparent that mixed digits can be 

 usefully employed in error detection codes. The use of mixed, check and 



