A new $16-$bit standard for storing floating point numbers, called bfloat$16,$ has become popular in the last couple of years for use in machine learning programs. It is a truncated form of single precision floating point $($which uses $32$ bits$)$ but is different to half precision floating point $($which also uses $16$ bits$).$ Please read the Wikipedia ar$-$ ticle https:$//$en$.$wikipedia.org$/$wiki$/$Bfloat$16\_$floating$-$point$\_$format before at$-$ tempting the questions below. The article is self contained, so it is not necessary to first know the details of single precision floating point.

For the questions below, show how you obtain your answer $-$ do not use an on$-$line con$-$ verter!

$($A$)$ What is the value $($expressed in decimal notation$)$ of the number stored in bfloat$16$ format as BADE$16?$