The generator function G for your Layer 2 Protocol’s Cyclic Redundancy Check is 1001. You have received the data D, 101000011. Answer the following questions with reference to G and D. You may assume that any error detection bits are found after the data bits. Has this data been transmitted correctly? Provide all working required to justify your answer.
Try an answer before revealing the guidance below.
Key Concepts
- Modulo-2 (XOR) division
- Remainder
- Zero remainder means no detected error
Answer Approach
- Divide the full received string 101000011 by 1001 using XOR long division.
- Alternatively, recompute the CRC for the data bits 101000 and compare.
- A non-zero remainder means an error was detected.
Full Answer
Answer status: Draft answer (unofficial). Revision notes, not an official marking scheme.
Divide 101000011 by 1001 (mod 2): 1010 ⊕ 1001 = 0011 → bring down to 0110 → 1100 ⊕ 1001 = 0101 → 1010 ⊕ 1001 = 0011 → 0111 → 1111 ⊕ 1001 = 0110. The remainder is 110, not 000, so an error has been detected and the data was not transmitted correctly. Check: the correct CRC for data 101000 is 101000000 mod 1001 = 101, which differs from the received 011.
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