Question $1-$ Criterion A$.1$

$($a$)$ Using Karnaugh Maps design a $2-$bit magnitude digital comparator. A magnitude digital comparator is a combinational circuit that compares two binary numbers in order to find out whether one binary number is equal, less than or greater than the other binary number. You need to design a circuit for which you will have two inputs one for A$,$ other two inputs for B and three output terminals, one for $\backslash (\backslash$mathrm$\{$A$\}>\backslash$mathrm$\{$B$\}\backslash )$ condition, one for $\backslash (\backslash$mathrm$\{$A$\}=\backslash$mathrm$\{$B$\}\backslash )$ condition and one for the $\backslash (\backslash$mathrm$\{$A$\}<mi>\backslash </mi>$mathrm$\{$B$\}\backslash )$ condition $($refer to Figure $1).$

$(3$ marks$)$

$($b$)$ Implement the logical functions obtained in Question $1($a$)$ using only CMOS NOR or NAND gates. Provide a detailed schematic diagram of your implementation including input pull down resistors, input switches, output signalling LEDs and power supply connections.