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Topic: 7 Boolean Questions (Read 2716 times) |
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continuum
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7 Boolean Questions
« on: Aug 29th, 2002, 7:44pm » |
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With 7 bits, you can have 4 of information (a number between 0 and 15) and 3 of redundance. If at most one of the 7 bits is changed you can find out which was by the break in the redundance.
b0, b1, b2, b3 of information
a0, a1, a3 of redundance
b0 xor b1 xor b2 xor a0 = 0
b0 xor b1 xor b3 xor a1 = 0
b0 xor b2 xor b3 xor a2 = 0
Shouldn't it be in the CS section? Or there are other solutions?
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wayne
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So what are the question?
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Jonathan_the_Red
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Re: 7 Boolean Questions
« Reply #2 on: Sep 20th, 2002, 11:40am » |
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on Sep 20th, 2002, 7:11am, wayne wrote:| So what are the question? |
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Highlight the below to read:
Considering your number's representation in binary:
1. Is the least significant bit (bit 0) set?
2. Is bit 1 set?
3. Is bit 2 set?
4. Is bit 3 set?
5. Of bits 0, 1, and 2, are an odd number set?
6. Of bits 0, 1, and 3, are an odd number set?
7. Of bits 0, 2, and 3, are an odd number set?
Highlight below to see how to determine the number from the answers:
Look at the answers to questions 5, 6, and 7. See if they're consistent with the answers to questions 1, 2, 3, and 4.
If exactly one of 5, 6, and 7 is inconsistent with 1, 2, 3, 4, that's the question that was answered incorrectly. 1, 2, 3, and 4 were all answered correctly, and you can calculate the number.
If more than one of 5, 6, and 7 is inconsistent with 1, 2, 3, or 4, whichever bit is common to all of the inconsistent "parity" questions was answered incorrectly. (That is, if all three of 5, 6, 7 are inconsistent, question 1 was answered incorrectly. If only 5 and 6 are inconsistent, question 2 was answered incorrectly, and so on)
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