Final answer:
The 7-bit Hamming code 1011011 has an error detected by checking parity at positions 1 and 4. Adding these positions indicates the 5th bit is incorrect; flipping it results in the corrected code 1011111.
Step-by-step explanation:
To determine if the received 7-bit Hamming code (1011011) is corrupt and to correct it if possible, we first need to check the parity bits. Hamming code uses parity bits which are powers of two (1, 2, 4, etc.). For a 7-bit code, we have three parity bits at positions 1, 2, and 4, with the data bits filling in the rest.
We calculate the parity for these positions using the following:
- P1 checks bits 1, 3, 5, 7
- P2 checks bits 2, 3, 6, 7
- P4 checks bits 4, 5, 6, 7
For the given code 1011011:
- Position 1 parity checks bits 1, 3, 5, 7 (1+0+1+1), which should be even. It is odd, so there's an error.
- Position 2 parity checks bits 2, 3, 6, 7 (0+0+1+1), which is even, so no error detected here.
- Position 4 parity checks bits 4, 5, 6, 7 (1+1+1+1), which should be even. It is odd, indicating another error.
Adding the positions of errors (1+4) gives us 5, which is the bit in error.
Therefore, by flipping the 5th bit of the received code, we get the corrected code: 1011111.