Consider a $16-$bit floating$-$point representation based on the IEEE floating$-$point format:

the highest bit is used for the sign bit,

the sign bit is followed by $4$ exponent bits, which are then

followed by $11$ fraction bits.

$(1)$What is the largest positive normalized number with the above floating$-$point format? Write the number in binary form.

$(2)$Compute the decimal value of the bit vector $0$x$6$D$80$ with the above floating$-$point format. Write the result in decimal format.