Final answer:
For a 10-bit memory word, 4 parity bits are necessary to correct single-bit errors using Hamming code. To create the code word, parity bits are placed at positions that are powers of 2 and then calculated to ensure the total number of '1's they check is even.
Step-by-step explanation:
The question revolves around the concept of error-correcting codes, specifically the Hamming code, used to detect and correct single-bit errors in digital data transmission or storage. To determine the number of parity bits needed to correct single-bit errors in a 10-bit memory word, we can use the formula 2p ≥ m + p + 1, where p is the number of parity bits and m is the number of information bits.
To find the smallest value of p that satisfies the inequality, we calculate as follows: 2p must be at least 10 (the number of information bits) plus p (the number of parity bits) plus 1. After trying different values, we determine that p = 4 satisfies this because 24 = 16, which is greater than 10 + 4 + 1 = 15.
Now for part b, to encode the information word 1001100110 using the Hamming code algorithm, we insert parity bits into the information bits at positions that are powers of 2 (i.e., the 1st, 2nd, 4th, and 8th positions in this case). We then calculate the value of each parity bit so that the total number of '1's is even for each set of bits. The final code word with parity bits will be: xxxx100110x0110, where 'x' denotes the parity bits whose values are calculated based on the positions they check.