The binary representation 201 is 1100 1001
. The corresponding mantissa part of the floating point number is

The exponent is not shown. Instead, the binary point is shown (between the bits marked 7 and 8). The leading bit 1
is not actually stored in the IEEE format$, so it is shown outside the 52 bits allocated for the mantissa.
The next double precision number after 201 can be obtained#, by setting 1
in the least significant bit. That bit position is marked by the x
in the figure.
Now take the difference of the two numbers and you will immediately get the result as a power of 2. That power is P. P is a negative integer.
To get an even better visualisation, rename the bits from 1 to 52 shown in the figure to the powers of 2 represented by those bits (i.e, 6, 5, 4, ... 0 \$\ \bullet\ \$ -1, -2, -3, ...).
$ There may be some exceptions.
#This statement is not proved here. Any error in this solution will probably be in this assumption.