Fill in the missing entries in the table

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Reference no: EM131046279

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 2.6); 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 x3 + x2 +1, or 1101. To build the table for C, we take each 3-bit sequence, p, append three trailing 0s, and then find the quotient
q = p ?000÷C, ignoring the remainder. The third column is the product C × q, the first 3 bits of which should equal p.

(a) Verify, for p = 110, that the quotients p ?000 ÷ C and p ?111 ÷ C are the same; that is, it doesn't matter what the trailing bits are.

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(b) Fill in the missing entries in the table.

(c) Use the table to divide 101 001 011 001 100 by C. Hint: The first 3 bits of the dividend are p = 101, so from the table the corresponding first 3 bits of the quotient are q = 110. Write the 110 above the second 3 bits of the dividend, and subtract C×q = 101 110, again from the table, from the first 6 bits of the dividend. Keep going in groups of 3 bits. There should be no remainder.

Reference no: EM131046279

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