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.