Multiple precision arithmetic
David Pope, Marvin L. Stein · Communications of the ACM · 1960
Let us return to the consideration of a single bit position.If the parity bit is not zero, but the Hamming check bits are all zero, the overwhehning probtfl)ility is that the parity bit is in error.If the parity bit is zero, but the tiararuing bits are not all zero, a multiple error in this position is indicated and no correction is possible.If the parity bit is not zero and the Hamming bits are not zero, then the hypothesis of a single error nmy be tested.Construct a binary word, 0, in which h0 is the unit; bit, h~ is the 2 bit, he is the f bit, etc.If p > N' a multiple error is indicated, but if p -, or t.h~l,i; there ~rre trt worst single errors, a.ll of which have b(~en co> retted, the record is ready to be pa, ck(~d and rciurn(>d to its original q rr'mgemeni re'My for use.IlJ{;t;EI(EN ( ' .ES 1. tLt~.mx(:.R. W. Error detecting trod error cocrecthtg ~odcs.Bell Sll,'gem.Tech.J. 29, No. 2, (Al)ril /!}50).2. SHAIIE Distribution ?g(,138 (/kugust 15, I!)(i()).