$2\mathrm{.}10$a$-$c and e $2\mathrm{.}10$ Suppose we would like to build function $Y=2x+3$ where

X denotes a $3-$bit unsigned value $(x2x10{)}_2$ and $Y=y4..y0$

is a $5-$bit value in hardware. Construct its truth table where

input bits are $x2,x1,$ and $x0$ and output bits are $y4$ through

$y0.$ Then do the following for output $y2($you may repeat

this for the other outputs$)$:

a$.$ Determine the canonical SOP expression for output

bit $y2.$

b$.$ Write the min$-$terms for $y2.$

c$.$ Use K$-$map and find a minim

d$.$ Draw a minimal NAND circuit for $y2.$

e$.$ Compare the number of transistors required to

implement the canonical and the minimal SOP

expressions.

$2\mathrm{.}11$ Repeat Problem $2\mathrm{.}10$ but this time use POS expressions for

$y2.$

$2\mathrm{.}12$ Repeat Problem $2\mathrm{.}10b$ through $d$ but this time use $3-$bit

$2\text{'}$s complement values for $x$ and output $y4.$

$2\mathrm{.}13$ Repeat Problem $2\mathrm{.}12b$ through $d$ but this time use POS

expressions for $y4.$

$2\mathrm{.}14$ Find a minimal SOP expression for each of the following

functions using K$-$maps:

a$.f(w,x,y,z)=(0,2,8,10)+{}_d(12,14)$

b$.g(a,b,c,d)=(5,7,13,15)+{}_d(6,14)$

c$.h(w,x,y,z)=||(0,2,8,10)+|{|}_d(12,14)$

d$.t(a,b,c,d)=||(5,7,13,15)+|{|}_d(6,14)$