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Bit steam 10011101 is to be transmitted using the standard CRCmethod with divisor value x3+1. Generate the CRC code word.

Question

Bit stream 10011101 is to be transmitted using the standard CRC method with divisor value x^3 + 1. Generate the CRC code word.

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Solution

To generate the CRC code word for the given bit stream 10011101 using the standard CRC method with a divisor value of x^3+1, follow these steps:

  1. Write the bit stream as the dividend, including any leading zeros if necessary: 10011101.

  2. Append the divisor, which is x^3+1, to the dividend. The divisor is represented as 1001 in binary form.

  3. Perform the division operation, starting from the leftmost bit of the dividend.

    • Divide the leftmost four bits of the dividend (1001) by the divisor (1001). The result is 1, with no remainder.

    • Write down the result (1) as the first bit of the CRC code word.

    • Move to the next bit of the dividend (0011) and repeat the division process.

    • Divide 0011 by 1001. The result is 0, with a remainder of 0011.

    • Write down the result (0) as the next bit of the CRC code word.

    • Move to the next bit of the dividend (0110) and repeat the division process.

    • Divide 0110 by 1001. The result is 0, with a remainder of 0110.

    • Write down the result (0) as the next bit of the CRC code word.

    • Move to the next bit of the dividend (1100) and repeat the division process.

    • Divide 1100 by 1001. The result is 1, with a remainder of 0011.

    • Write down the result (1) as the next bit of the CRC code word.

    • Move to the next bit of the dividend (0011) and repeat the division process.

    • Divide 0011 by 1001. The result is 0, with a remainder of 0011.

    • Write down the result (0) as the next bit of the CRC code word.

    • Move to the next bit of the dividend (0110) and repeat the division process.

    • Divide 0110 by 1001. The result is 0, with a remainder of 0110.

    • Write down the result (0) as the next bit of the CRC code word.

    • Move to the next bit of the dividend (1100) and repeat the division process.

    • Divide 1100 by 1001. The result is 1, with a remainder of 0011.

    • Write down the result (1) as the next bit of the CRC code word.

    • Move to the next bit of the dividend (0011) and repeat the division process.

    • Divide 0011 by 1001. The result is 0, with a remainder of 0011.

    • Write down the result (0) as the last bit of the CRC code word.

  4. The resulting CRC code word is 10000110.

Therefore, the CRC code word for the given bit stream 10011101 using the standard CRC method with a divisor value of x^3+1 is 10000110.

This problem has been solved

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