# Confusion about normalised floating point number systems

I was assigned the following question:

List all numbers that can be represented exactly in a normalised floating- point number system with base 10, two digits in the fraction, and an exponent 0 ≤ e ≤ 2. How many are there in total (including zero)?

The bit in particular that confuses me is the 'base 10' aspect. After doing some research I found that a normalised floating-point number system is supposed to have a '1' before the decimal point and the rest afterwards but that only works for binary. Also, if I am supposed to list the numbers and this is in base 10, it would seem like a really large amount to list.

So it seems I need to answer the question in binary, but I am really confused about why 'base 10' is being mentioned.

Thanks

• Don't forget the negative ones, too! – kimchi lover Oct 22 '18 at 2:55

The "leading digit is always $$1$$" trick only works in binary, and therefore you cannot use it in base ten. There is a bit of ambiguity in the question regarding whether "two digits in the fraction" means they want numbers like $$2.34 \times 10^1$$ or like $$0.34 \times 10^1.$$ In the absence of any other indication, if I had to guess, I would guess they mean $$0.34 \times 10^1$$ just because the other way is ten times as many numbers to write. But if you can ask the person who assigned this question, I would recommend you do.
Even if we only use two fractional digits (like $$0.34 \times 10^1$$), there are still a few hundred possible numbers. If you really literally must list them all, perhaps you can get them printed out by computer. A simple spreadsheet can do the job. But I suspect that only only need to list enough of them in a pattern so that it is clear how you would fill in the missing numbers (and how many there would be), much the way that if I write $$1,2,3,4,\ldots,59,60$$ you can see I have in mind the first sixty positive integers. Again, that is something to ask the person who assigned this if you can.