here formula_4 is the original message polynomial and formula_5 is the degree-formula_2 generator polynomial. the bits of formula_7 are the original message with formula_2 zeroes added at the end. the crc 'checksum' is formed by the coefficients of the remainder polynomial formula_9 whose degree is strictly less than formula_2. the quotient polynomial formula_11 is of no interest. using modulo operation, it can be stated that