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The final code after encoding data bits 1101 into 7-bit even parity Hamming Code is
- a)1110101
- b)1011101
- c)1010101
- d)0110101
Correct answer is option 'C'. Can you explain this answer?
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The final code after encoding data bits 1101 into 7-bit even parity Ha...
The given question belongs to the field of electronics and communication engineering and specifically deals with Hamming Code. Hamming Code is a technique used for error detection and correction in data transmission.
To understand the answer, let's break down the steps involved in encoding the data bits using Hamming Code:
1. Identify the number of parity bits required:
- The number of parity bits needed is determined by the formula 2^r ≥ m + r + 1, where r is the number of parity bits and m is the number of data bits.
- In this case, we have 4 data bits (1101), so we need to find the smallest value of r that satisfies the equation. By substituting different values of r, we find that r = 3 is the minimum value that satisfies the equation.
2. Insert the data bits into the encoded bit positions:
- The data bits are inserted into the encoded bit positions, leaving spaces for the parity bits.
- The data bits are placed in the positions that are powers of 2 (1, 2, 4, 8, etc.), starting from the leftmost position.
- In this case, the data bits 1101 are inserted into the positions 1, 2, 4, and 8, respectively.
3. Calculate the value of each parity bit:
- Each parity bit is responsible for checking a specific set of bits, including itself.
- The value of each parity bit is determined by performing an XOR operation on the bits it checks.
- The parity bits are placed in the positions that are not powers of 2.
- In this case, the parity bits are placed in positions 3, 5, and 6, respectively.
4. Determine the value of each parity bit:
- The value of each parity bit is determined by counting the number of 1s in the positions it checks.
- If the count is even, the parity bit is set to 0. If the count is odd, the parity bit is set to 1.
- In this case, the count of 1s in positions 3, 5, and 6 is 2, 2, and 1, respectively.
- Therefore, the parity bits are set to 0, 0, and 1, respectively.
5. Combine the data bits and parity bits to form the final encoded code:
- The data bits and parity bits are combined to form the final encoded code.
- In this case, the final encoded code is 1010101.
Therefore, the correct answer is option 'C' (1010101).
To understand the answer, let's break down the steps involved in encoding the data bits using Hamming Code:
1. Identify the number of parity bits required:
- The number of parity bits needed is determined by the formula 2^r ≥ m + r + 1, where r is the number of parity bits and m is the number of data bits.
- In this case, we have 4 data bits (1101), so we need to find the smallest value of r that satisfies the equation. By substituting different values of r, we find that r = 3 is the minimum value that satisfies the equation.
2. Insert the data bits into the encoded bit positions:
- The data bits are inserted into the encoded bit positions, leaving spaces for the parity bits.
- The data bits are placed in the positions that are powers of 2 (1, 2, 4, 8, etc.), starting from the leftmost position.
- In this case, the data bits 1101 are inserted into the positions 1, 2, 4, and 8, respectively.
3. Calculate the value of each parity bit:
- Each parity bit is responsible for checking a specific set of bits, including itself.
- The value of each parity bit is determined by performing an XOR operation on the bits it checks.
- The parity bits are placed in the positions that are not powers of 2.
- In this case, the parity bits are placed in positions 3, 5, and 6, respectively.
4. Determine the value of each parity bit:
- The value of each parity bit is determined by counting the number of 1s in the positions it checks.
- If the count is even, the parity bit is set to 0. If the count is odd, the parity bit is set to 1.
- In this case, the count of 1s in positions 3, 5, and 6 is 2, 2, and 1, respectively.
- Therefore, the parity bits are set to 0, 0, and 1, respectively.
5. Combine the data bits and parity bits to form the final encoded code:
- The data bits and parity bits are combined to form the final encoded code.
- In this case, the final encoded code is 1010101.
Therefore, the correct answer is option 'C' (1010101).
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Community Answer
The final code after encoding data bits 1101 into 7-bit even parity Ha...
Hamming (7, 4) code: It is a linear error-correcting code that encodes four bits of data into seven bits, by adding three parity bits.
Example: It is used in the Bell-Telephone laboratory, error-prone punch caret reader to detect the error and correct them.
Hamming code:
P1 = d1 ⊕ d2 ⊕ d4
P2 = d1 ⊕ d4 ⊕ d3
P3 = d2 ⊕ d4 ⊕ d3
Example: It is used in the Bell-Telephone laboratory, error-prone punch caret reader to detect the error and correct them.
Hamming code:
P1 = d1 ⊕ d2 ⊕ d4
P2 = d1 ⊕ d4 ⊕ d3
P3 = d2 ⊕ d4 ⊕ d3
Given data 1101 i.e.
d1 = 1, d2 = 1, d3 = 0, d4 = 1
We can write:
P1 = d1 ⊕ d2 ⊕ d4 = 1 ⊕ 1 ⊕ 1 = 1
P2 = d1 ⊕ d4 ⊕ d3 = 1 ⊕ 1 ⊕ 0 = 0
P3 = d2 ⊕ d4 ⊕ d3 = 1 ⊕ 1 ⊕ 0 = 0
Then transmitted final code is
i.e. 1010101
Option 3 correct.
d1 = 1, d2 = 1, d3 = 0, d4 = 1
We can write:
P1 = d1 ⊕ d2 ⊕ d4 = 1 ⊕ 1 ⊕ 1 = 1
P2 = d1 ⊕ d4 ⊕ d3 = 1 ⊕ 1 ⊕ 0 = 0
P3 = d2 ⊕ d4 ⊕ d3 = 1 ⊕ 1 ⊕ 0 = 0
Then transmitted final code is
i.e. 1010101
Option 3 correct.
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The final code after encoding data bits 1101 into 7-bit even parity Hamming Code isa)1110101b)1011101c)1010101d)0110101Correct answer is option 'C'. Can you explain this answer?
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