What's the sum of 10000.101 and 1100.001?

The answer is 28.75 but don't know why. First I thought these were binary numbers but they can't have decimal places, right? And without the digits past the decimal the sum in decimal is 28. What gives?

I'm not going to do the math, but solve for X below, and work from there. It may give you something. (The smallest base it could be in is Base 9.)

.101X + .001X = .75


(Of course, if the actual sum is a larger number with the 75 after or to the right of the "decimal point", this may not help.)

If this doesn't give any possible answer, try reading those numbers in different bases. Then again, the answer may not be in a different base at all.

It's pure binary.

No, there is no decimal point in the binary system -- but there is a an analogous binary point. In the decimal system the first digit after the decimal point represents 1/10's, the next digit represents 1/100's, etc. Similarly in the binary system, the first digit after the binary point represents 1/2's, the second digit 1/4's, the third digit 1/8's, etc.

So your first binary number (10000.101) represents 16 + 1/2 + 1/8.

The second binary number (1100.001) represents 8 + 4 + 1/8.

Add them together and you get 28.75
In binary, this sum is written 11100.11

I assumed the answer given (28.75) was in the same base. (I should have worked it out.)

Thanks Prof!