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POMost binary combinations from 4 bits, with single change per bit
 

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    <p>I have 4 binary bits</p> <pre><code>Bit 3 Bit 2 Bit 1 Bit 0 </code></pre> <p>Normally the answer is simple: 2^4, or 16 different combinations; and it would looks something like the following:</p> <p>0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111</p> <p>However, The LSB (Bit 0) changes state every iteration.</p> <p>I need an algorithm where the state of a bit only changes once through all the iterations; i.e, I need all my bits to act like the MSB (Bit 3).</p> <p>How can I do this?</p> <h3>Edit</h3> <p>It seems that most people are converging to there being only 5 possible solutions. However this assumes there is a starting point for the value and an ending point. This doesn't matter so I'm going to give a real world scenario to better explain.</p> <p>Suppose I have an digital alarm clock that gives me 4 outputs. Each output can be programmed to go on at a certain time and off at a certain time and are programmed independent of each other, eg. I can program output 1 to go on at 1 am and off at 3 am, while I can program output 2 to go on at 7 pm and off at 2 am. There are no restrictions to how long each output can stay on. </p> <p>Now I want to hook this alarm clock to a computer and get as close as possible to the current correct time. i.e If the clock says the time is 2:15 pm, my computer knows that the alarm is within the 12 pm to 6 pm range for example. I want to be able to get the smallest possible range. Whats the smallest possible range I can get?</p>
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    1. USdarudude
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    1. COThis is a very interesting problem. I'm trying to figure it out now, I like challenges. =) Do you know if it is possible, or is it a prove/disprove?
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      1. USAndrei Krotkov
    2. COBits are normally numbered in a way that LSB is bit 0, let me edit that for you. :)
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    3. CO@Andrei: I have come up with a solution, but didn't state it in the question cause I want to see what other people come up with. I actually have to use this in some computer interfacing.
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      1. USdarudude
 

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