Question

A 12-bit Hamming code whose Hexadecimal value is 0xE4F arrives at the receiver. What was the original value in Hex. Assume 1-bit error at most. b) ( 2 points) The code in part (a) needs/has 4 check bits to correct a single bit error. What is the maximum number of data bits that can be coded with r=4 check bits?

Answer 1

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.

Answer 2

The original value in Hex is 0xE0F. The maximum number of data bits that can be coded with 4 check bits is 11.

Step-by-step explanation:

The hexadecimal value 0xE4F represents a 12-bit Hamming code. To find the original value, we need to convert it back to binary and then correct any errors. The binary representation of 0xE4F is 111001001111. By checking the parity bits, we find that the error is in the third bit. Correcting the error, we get the binary value 111000001111, which is equivalent to the hexadecimal value 0xE0F.

In part (b), a 12-bit Hamming code with 4 check bits can correct a single-bit error. To find the maximum number of data bits that can be coded with 4 check bits, we use the formula 2^r - r - 1, where r is the number of check bits. In this case, 2^4 - 4 - 1 = 11 data bits can be coded.