Exercise $5\mathrm{.}31$ Convert the following two$$s complement binary fixed$-$point

numbers to base $10.$ The implied binary point is explicitly shown to aid in your

interpretation.

$($a$)0101\mathrm{.}1000$

$($b$)1111\mathrm{.}1111$

$($c$)1000\mathrm{.}0000$ Exercise $5\mathrm{.}32$ Repeat Exercise $5\mathrm{.}31$ for the following two$$s complement binary

fixed$-$point numbers.

$($a$)011101\mathrm{.}10101$

$($b$)100110\mathrm{.}11010$

$($c$)101000\mathrm{.}00100$

Exercise $5\mathrm{.}34$ Add the following IEEE $754$ single$-$precision floating$-$point

numbers.

$($a$)$ C$0123456+81$C$564$B$7$

$($b$)$ D$0$B$10301+$ D$1$B$43203$

$($c$)5$EF$10324+5$E$039020$

Exercise $5\mathrm{.}51$ Implement the following functions using a single $163$ ROM. Use

dot notation to indicate the ROM contents.

$($a$)$ X $=$ AB$+$BCD$+$AB

$($b$)$ Y $=$ AB$+$BD

$($c$)$ Z $=$ A$+$B$+$C$+$D