Question

Generate the HC for the data 01001011

a. using even parity check
b. receiver receives 010111010110 bits of HC. Check if this is correct using an even parity check.

Answer 1

To generate the Hamming Code for 01001011, parity bits are inserted at positions corresponding to powers of two, resulting in a final Hamming code of 011010001001011. When checking received data 01101010010110, errors are identified if the recalculated parity bits do not match, suggesting altered transmission.

Step-by-step explanation:

Generating Hamming Code for Data Using Even Parity:

To generate the Hamming Code (HC) for the data 01001011 using an even parity check, we start by determining the positions of the parity bits. These are positioned at the powers of 2 (i.e., positions 1, 2, 4, 8, etc.). Inserting placeholder parity bits (P) into the data sequence, we get P1, P2, 0, P4, 1, 0, 0, P8, 1, 0, 1, 1. After calculating the parity bits to satisfy even parity, the final Hamming code becomes 011010001001011.

Checking Received Data for Errors:

When the receiver gets the 01101010010110 bits, it will check the parity by recalculating to identify if there are any errors. If the parity bits do not match, it indicates that there is an error in the transmission. After applying even parity check calculations, any discrepancy from expected parity values would suggest that one or more bits were altered during transmission. In this case the received data does not match the calculated Hamming code indicating an error.