$(2).$ A hypothetical computer stores real numbers in floating$-$point format in $8-$bit binary words. The first bit is used for the sign of the number, the second bit for the sign of the exponent, the next two bits for the magnitude of the exponent, and the next four bits for the magnitude of the mantissa. What number does $10101111$ represent in the above given $8-$bit format?

Answer: $-7\mathrm{.}75$