$1.$ Perform the following base conversions.

a$.10101\_2=\_\_\_\_\_\_\_10$

b$.61\_10=\_\_\_\_\_\_\_\_2$

c$.563\_10=\_\_\_\_\_\_\_5$

d$.755\_10=\_\_\_\_\_\_\_16$

$2.$ Represent the following decimal numbers in binary using the three $8-$bit formats: signed magnitude, one's complement and two's complement formats.

a$.113$

b$.91$

$3.$ Show how each of the following decimal floating point values would be stored using IEEE$-754$ single precision. Show the result as a string of $0$s and $1$s$,$ and indicate where are the sign bit, the exponent, and the significand.

a$.-11\mathrm{.}25$

b$.2\mathrm{.}625$