Floating Point: What do "Bits Precision" and "Decimal Precision" Mean and How To Convert Between Them?
Both of the two answers (JRE and Spehro Pefhany) are okay except IEEE floating point has an extra feature.

I hope it is clear that 


  2.3 x 10^2 = 23 x 10^1 = 230 x 10^0


It would create more work for the hardware if all three were valid (translated into base 2). For example two different bit patterns could be the same number.

So, IEEE mandates that the top bit of the mantissa is always 1. This is a normalised representation. Each number is only ever stored as one specific bit pattern. 

Then, because the first bit is always 1, it is not stored. So the mantissa is actually 1 bit longer than stored because of this implied top 1 bit.