QuestionMay 5, 2025

Which of the following is the hamming code for the 8 bit ASCII character B. Use even parity for the calculation 010010011010 010010011001 010010010010 010000010001

Which of the following is the hamming code for the 8 bit ASCII character B. Use even parity for the calculation 010010011010 010010011001 010010010010 010000010001
Which of the following is the hamming code for the 8 bit ASCII character B. Use even parity for the calculation 010010011010 010010011001 010010010010 010000010001

Solution
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Answer

010010010001 Explanation 1. Identify ASCII for 'B' The ASCII code for 'B' is 66, which in binary is 01000010. 2. Determine Hamming Code Structure A 12-bit Hamming code with even parity includes 8 data bits and 4 parity bits. The positions of the parity bits are powers of 2 (1, 2, 4, 8). 3. Place Data Bits Insert the data bits into positions not reserved for parity: _ _ 0 _ 1 0 0 0 _ 1 0. 4. Calculate Parity Bits - **Parity bit 1** covers bits 3, 5, 7, 9, 11: 0 + 1 + 0 + 1 + 0 = 2 (even), so p1 = 0. - **Parity bit 2** covers bits 3, 6, 7, 10, 11: 0 + 0 + 0 + 0 + 0 = 0 (even), so p2 = 0. - **Parity bit 4** covers bits 5, 6, 7, 12: 1 + 0 + 0 + 0 = 1 (odd), so p4 = 1. - **Parity bit 8** covers bits 9, 10, 11, 12: 1 + 0 + 0 + 0 = 1 (odd), so p8 = 1. 5. Construct Final Hamming Code Combine parity and data bits: 010010010001.

Explanation

1. Identify ASCII for 'B'<br /> The ASCII code for 'B' is 66, which in binary is 01000010.<br /><br />2. Determine Hamming Code Structure<br /> A 12-bit Hamming code with even parity includes 8 data bits and 4 parity bits. The positions of the parity bits are powers of 2 (1, 2, 4, 8).<br /><br />3. Place Data Bits<br /> Insert the data bits into positions not reserved for parity: _ _ 0 _ 1 0 0 0 _ 1 0.<br /><br />4. Calculate Parity Bits<br /> <br />- **Parity bit 1** covers bits 3, 5, 7, 9, 11: 0 + 1 + 0 + 1 + 0 = 2 (even), so p1 = 0.<br />- **Parity bit 2** covers bits 3, 6, 7, 10, 11: 0 + 0 + 0 + 0 + 0 = 0 (even), so p2 = 0.<br />- **Parity bit 4** covers bits 5, 6, 7, 12: 1 + 0 + 0 + 0 = 1 (odd), so p4 = 1.<br />- **Parity bit 8** covers bits 9, 10, 11, 12: 1 + 0 + 0 + 0 = 1 (odd), so p8 = 1.<br /><br />5. Construct Final Hamming Code<br /> Combine parity and data bits: 010010010001.
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