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February 12th, 2012, 04:11 PM  #1 
Member Joined: Jan 2012 Posts: 40 Thanks: 0  binary numbers between two points of a 9 number line
Say that you have a large number consisting of only 1's and/or 0's. 1011110001101010 or anything of that type. Now say we subtract a number consisting entirely of 9's that is half the digit length of the number consisting of only 1's and/or 0's. So since the number in the example is 16 digits long, an 8 digit number, 99999999. Is there a way to know without subtracting if there will be another instance of only 1's and or 0's before the larger of the two numbers reaches 15 digits? I thought it might be a long shot but I figured I should ask. I have figured a few things out. If I mod the binary number by the 9 number I receive in this case 11212110. I can change some of the 1's and 0's and get very close to this number. Say instead of 1011110001101010 we try 1011101001101010 which is a smaller number. We get 11212020. Taking this in account we can run 1011101001101000 and receive 11212110. Is there a better method of finding out just how many times this occurs before we reach a 15 digit number?

February 12th, 2012, 04:42 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: binary numbers between two points of a 9 number line
You hve a number which can be written as the sum of a collection of distinct powers of ten, and you want to subtract a power of ten and add 1 to it. So all you need to check are two decimal places and see if they have the appropriate values (one must be 0, the other 1  which is which?).

February 12th, 2012, 05:31 PM  #3 
Member Joined: Jan 2012 Posts: 40 Thanks: 0  Re: binary numbers between two points of a 9 number line
I got the math wrong in the last post for the last few mods I did. The mod solution was off by a number. Anyways I am not sure if I know what you mean. Could you please give me an example?

February 13th, 2012, 01:14 AM  #4 
Member Joined: Jan 2012 Posts: 40 Thanks: 0  Re: binary numbers between two points of a 9 number line
I got it now thanks for the help.


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