ERROR DETECTING AND CORRECTING CODES 



151 



Table I 



Etc. 



to give the position of any error in a code symbol, any position which has 

 a 1 on the right of its binary representation must cause the first check to 

 fail. Examining the binary form of the various integers we find 



1 = 1 



3 = 11 



5 = 101 

 7 = 111 



9 = 1001 



Etc. 



have a 1 on the extreme right. Thus the first parity check must use positions 



1,3,5,7,9, ••• . 



In an exactly similar fashion we find that the second parity check must 

 use those positions which have I's for the second digit from the right of their 

 binary representation, 



2 = 10 



3 = 11 



6 = 110 



7 = 111 



10 = 1010 



11 = 1011 

 Etc., 



