Let $a=1\mathrm{.}0*2^9,b=-1\mathrm{.}0*2^9$ and $c=1\mathrm{.}0*2^1.$ First convert the numbers to the floating$-$point

model $($the representation uses a $14-$bit format, $5$ bits for the exponent with a bias of $15,$ a

normalized mantissa of $8$ bits, and a single sign bit for the number$),$ perform the following

calculations, paying close attention to the order of operations. What can you say about the

algebraic properties of floating$-$point arithmetic in our finite model? Do you think this

algebraic anomaly holds under multiplication as well as addition?

$b+(a+c)=$

$(b+a)+c=$