Counting active binary combinations
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Hi,
I am trying to solve a problem to no avail. I have a 64-bit binary string. The problem requires that only 8-to-16 of these bits can be active (equal to 1). How would I determine the number of such combinations for which this can be true?
I thought I had the solution when I formed the equation:
x=((2^n)-1)*(m-n+1);
Where:
x = number of unique combinations (?),
m = bit string length (64 here), and
n = length of active range (16-8 = 8 here).
However, this only gave the answer for when the active bits were within an 8-bit range of each other in the bit string length. The actual answer must consider situations where those 8-to-16 bits can be anywhere in the 64-bit string.
Please help!
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James Tursa
2017-9-19
You are choosing a combination of 64 bits taken 8-to-16 at a time. So add them up:
s = 0;
n = 64;
for k=8:16
s = s + nchoosek(n,k);
end
A big number
7.1325e+14
2 个评论
Walter Roberson
2017-9-19
Right. Or is the question about verifying that a particular given combination only has 8 to 16 bits set??
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