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If one of the code words of a Hamming (7, 4) code is 0001011, which of the following cannot be the valid codeword in the same group?
- a)0011101
- b)0101100
- c)0011010
- d)1110100
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If one of the code words of a Hamming (7, 4) code is 0001011, which of...
The minimum bits change between any valid Hamming codes is 3.
Analysis:
The change of bits between the given code: 0001011 and option C code: 0011010 is two bits change only.
So 0011010 can’t be a valid Hamming code of the same group.
Analysis:
The change of bits between the given code: 0001011 and option C code: 0011010 is two bits change only.
So 0011010 can’t be a valid Hamming code of the same group.
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If one of the code words of a Hamming (7, 4) code is 0001011, which of...
Understanding Hamming (7, 4) Code
Hamming codes are used for error detection and correction in digital data transmission. The (7, 4) code means 4 bits of data are encoded into 7 bits by adding 3 parity bits.
Codeword Structure
In a (7, 4) Hamming code:
- Data bits: 4
- Parity bits: 3
- Total bits: 7
The codeword must satisfy specific parity check equations based on the positions of the parity bits.
Given Codeword: 0001011
This codeword can be analyzed to determine its validity within the Hamming code structure. The parity bits at positions 1, 2, and 4 ensure that the entire codeword meets the parity check conditions.
Checking Validity of Other Codewords
To find a codeword that cannot belong to the same group, we need to evaluate the following codewords against the parity conditions:
- a) 0011101
- b) 0101100
- c) 0011010
- d) 1110100
Examining Option C: 0011010
1. Calculate Parity: For codeword 0011010, the parity bits must be checked:
- P1, P2, and P4 are used to check the parity of the bits they cover.
2. Check Parity Conditions:
- P1 checks bits 1, 3, 5, 7: 0 + 1 + 0 = 1 (Should be even, but it's odd)
- Hence, the first parity check fails.
3. Conclusion: Since option C fails the parity check, it cannot be a valid codeword in the Hamming (7, 4) code group.
Final Answer
Thus, the codeword 0011010 (Option C) cannot be a valid codeword in the same group as 0001011.
Hamming codes are used for error detection and correction in digital data transmission. The (7, 4) code means 4 bits of data are encoded into 7 bits by adding 3 parity bits.
Codeword Structure
In a (7, 4) Hamming code:
- Data bits: 4
- Parity bits: 3
- Total bits: 7
The codeword must satisfy specific parity check equations based on the positions of the parity bits.
Given Codeword: 0001011
This codeword can be analyzed to determine its validity within the Hamming code structure. The parity bits at positions 1, 2, and 4 ensure that the entire codeword meets the parity check conditions.
Checking Validity of Other Codewords
To find a codeword that cannot belong to the same group, we need to evaluate the following codewords against the parity conditions:
- a) 0011101
- b) 0101100
- c) 0011010
- d) 1110100
Examining Option C: 0011010
1. Calculate Parity: For codeword 0011010, the parity bits must be checked:
- P1, P2, and P4 are used to check the parity of the bits they cover.
2. Check Parity Conditions:
- P1 checks bits 1, 3, 5, 7: 0 + 1 + 0 = 1 (Should be even, but it's odd)
- Hence, the first parity check fails.
3. Conclusion: Since option C fails the parity check, it cannot be a valid codeword in the Hamming (7, 4) code group.
Final Answer
Thus, the codeword 0011010 (Option C) cannot be a valid codeword in the same group as 0001011.
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If one of the code words of a Hamming (7, 4) code is 0001011, which of the following cannot be the valid codeword in the same group?a)0011101b)0101100c)0011010d)1110100Correct answer is option 'C'. Can you explain this answer?
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