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.
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:
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Write the bit stream as the dividend, including any leading zeros if necessary: 10011101.
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Append the divisor, which is x^3+1, to the dividend. The divisor is represented as 1001 in binary form.
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Perform the division operation, starting from the leftmost bit of the dividend.
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Divide the leftmost four bits of the dividend (1001) by the divisor (1001). The result is 1, with no remainder.
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Write down the result (1) as the first bit of the CRC code word.
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Move to the next bit of the dividend (0011) and repeat the division process.
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Divide 0011 by 1001. The result is 0, with a remainder of 0011.
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Write down the result (0) as the next bit of the CRC code word.
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Move to the next bit of the dividend (0110) and repeat the division process.
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Divide 0110 by 1001. The result is 0, with a remainder of 0110.
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Write down the result (0) as the next bit of the CRC code word.
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Move to the next bit of the dividend (1100) and repeat the division process.
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Divide 1100 by 1001. The result is 1, with a remainder of 0011.
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Write down the result (1) as the next bit of the CRC code word.
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Move to the next bit of the dividend (0011) and repeat the division process.
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Divide 0011 by 1001. The result is 0, with a remainder of 0011.
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Write down the result (0) as the next bit of the CRC code word.
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Move to the next bit of the dividend (0110) and repeat the division process.
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Divide 0110 by 1001. The result is 0, with a remainder of 0110.
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Write down the result (0) as the next bit of the CRC code word.
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Move to the next bit of the dividend (1100) and repeat the division process.
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Divide 1100 by 1001. The result is 1, with a remainder of 0011.
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Write down the result (1) as the next bit of the CRC code word.
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Move to the next bit of the dividend (0011) and repeat the division process.
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Divide 0011 by 1001. The result is 0, with a remainder of 0011.
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Write down the result (0) as the last bit of the CRC code word.
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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.
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