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The information bit sequence \(\{111010101\}\) is to be transmitted by encoding with CRC-4 code, for which the generator polynomial is \(C(x)=x^4+x+1\). The encoded sequence of bits is _______.

1. \{1110101011100\}
2. \{1110101011101\}
3. \{1110101011110\}
4. \{1110101010100\}

Correct answer: \{1110101011100\}

Solution

For CRC-4 with generator \(x^4+x+1\), append four zeros to the data and divide by the generator polynomial using modulo-2 arithmetic. The remainder is \(1100\), so the transmitted codeword is the original data followed by \(1100\).

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