How to calculate floating point numbers?

Question

Here are two locations in memory:

 0110 | 1111 1110 1101 0011
 0111 | 0000 0110 1101 1001

Interpret locations 6 (0110) and 7 (0111) as an IEEE floating point number. Location 6 contains bits [15:0] and location 7 contains bits [16:31].

Floating Point -
   Locations 6 and 7: 0000 0110 1101 1001 1111 1110 1101 0011
   The number represented is 1.101 1001 1111 1110 1101 0011 × 2^(-114) 

Is my answer correct?
I am unsure exactly what the [16:31] and [15:0] relate to/mean?

Answer 1

The [16:31] and [15:0] refer to locations in the binary representation of a $32$-bit integer. You have interpreted this correctly.

When in doubt about technical problems, always consult Wikipedia an expert.

In your case the number is 0 || 00001101 || 101 1001 1111 1110 1101 0011

The sign is positive.

The biased exponent is 1101 $ = 13$, so the actual exponent is $13 - 127 = -114$, assuming single precision.

So the answer you have is correct: $$2^{-114} \times (1.101 1001 1111 1110 1101 0011)_2$$