Final answer:
A 12-bit Hamming code with a hexadecimal value of 0xE4F can be represented as 0xF in hexadecimal. With 4 check bits, the maximum number of data bits that can be coded is 11.
Step-by-step explanation:
In this question, we are given a 12-bit Hamming code with a hexadecimal value of 0xE4F. To find the original value in hexadecimal, we need to remove the parity bits and keep only the data bits. The Hamming code has 8 data bits, so the original value can be represented as 0xF.
For part (b), we are asked about the maximum number of data bits that can be coded with 4 check bits. The number of check bits can be calculated using the formula 2^r ≥ m + r + 1, where r is the number of check bits and m is the number of data bits. Solving this equation, we find that for 4 check bits, we can code a maximum of 11 data bits.