Re-writing the same answer as that of Arjun Sir (correct me if I am wrong anywhere)
The Floating point representation given in the question is not that of IEEE-754. The equation of the given representation is:
$0.M X 2^{Exponent-Base}$
The 0 in 0.M is not implicit, but explicit
Now, given number -7.5
$(-7.5)_{10} = (-111.1)_{2} = -0.1111 * 2^{3} \rightarrow\left[1\right]$
Now, base is given as 16 with excess 64, that is
$16^{x-64} = 2^{4(x-64)} = 2^{4x-256} \rightarrow\left[2\right]$
Here, x is the exponent. Now from equation 1 and 2, we get
$4x-256=3$
$x\approx 65$
Now, equation 1 becomes:
$-0.1111 * 2^{65-64}$
This gives S=1, M = 011110000000000000000000 and E = 1000001
$(1\; 01111\underbrace{000\dots0}_{\text{19 zeroes}} \; 1000001)_2 = (BC000041)_{16}$