#$04-2024-1006-704$

CSCI $150$

$3.(5$pt$)$ Combinational Circuit designs

A$.$ A comparator is a component that compares the value of two numbers, and determine whether one is greater than the other, or equal to one another. You need to design a $1$ bit comparator, with $x,Y$ as $1$ bit inputs, $G,E$ as $1$ bit outputs, where $G=1$ if $x>Y,E=1$ if $x=Y.$ Draw the truth table, then write down the boolean expressions after optimisation. $(2\mathrm{.}5$pt$)$

B$.$ Design a $2$bit comparator using two $1$ bit comparators, where $x$ and $Y$ are $2$bit inputs. $(2\mathrm{.}5$pt$)$