$4.$ Consider the problem of comparing two unsigned $2-$bit binary numbers A and B to determine whether A is

greater than B $($strictly greater than; not equal$).$ Define the two bits of each number as A$1$A$0$ and B$1$B$0.$ Let Q

$=1$ if A $>$ B and Q $=0$ otherwise.

$($a$)$ Write the truth table for this function.

$($b$)$ Design a circuit, using any combination of gate types that you might prefer, to implement the truth table

from part $($a$).$ Draw the schematic.