The CRC algorithm as presented in this chapter requires lots of bit manipulations. It is, however, possible to do polynomial long division taking multiple bits at a time, via a table-driven method, that enables efficient software implementations of CRC.We outline the strategy here for long division $3$ bits at a time (see Table 2.5); in practice, we would divide $8$ bits at a time, and the table would have $256$ entries. Let the divisor polynomial $C= C(x)$ be $x^{3}+x^{2}+1$, or $1101$. To build the table for $C$, we take each $3$-bit sequence, $p$, append three trailing $0$s, and then find the quotient $q= p \frown 000 \div C$,
Ignoring the remainder. The third column is the product $C \times q$, the first $3$ bits of which should equal $p$.
(b) Fill in the missing entries in the table.
