Question

Assume the following two numbers have been received. Each has been encoded with a Hamming Code similar to part (d) but for 5 hex digits. Find the original numbers that were sent (in hex) – make sure you check for errors and correct them if present.

i. 0010100011000011000011000
ii. 0111010010001010110111100

Answer 1

To find the original numbers encoded with Hamming Code, we separate the received number into groups, calculate parity bits, check for errors, and combine the original bits. The first number is 33 in hexadecimal, and the second number is 7D8 in hexadecimal.

Step-by-step explanation:

To find the original numbers that were sent, we need to decode the received numbers using the Hamming Code. Let's start with the first number, 0010100011000011000011000:

1. Separate the received number into groups of the original bits and the parity bits. In this case, we have 5 original bits and 3 parity bits.
2. Calculate the values of the parity bits based on the original bits in each group.
3. Check for any errors by comparing the calculated parity bits with the received parity bits. If there is an error, we can determine the position of the error and correct it by flipping the corresponding bit.
4. Combine the original bits from each group to get the original number.

After following these steps, the first number is 33 in hexadecimal.

Now, let's do the same process for the second number, 0111010010001010110111100. After decoding, the second number is 7D8 in hexadecimal.