Is there a way to compare both signed and unsigned binary words?
There is no circuit with a single output that can do greater/equal/less comparisons on both signed and unsigned values without some input that specifies whether the operands should be interpreted as signed or unsigned.

One approach is to subtract one operand from the other and look at two important carries: the carry into the MSB and the carry out of the MSB. Depending on how your subtractor works you may see different behavior from these two signals when there is an underflow for signed vs. unsigned operands.

You can also look at the sign of the result compared to the signs of the operands. For example, suppose you compute \$A - B\$ with two unsigned operands. You can zero extend the operands and then perform the subtraction. If the result is negative then \$B &gt; A\$. If the result is zero then \$A = B\$. Else, \$A &gt; B\$.

This sounds like a homework question so I'll leave you to work out the details. Even if it's not homework, it's a great learning opportunity.