Design a circuit that compares the two-bit integers (x₁x₀)₂ and (y₁y₀)₂, returning an output of 1 when the first 2-bit number is larger and an output of 0 otherwise.

a) (3 points) Construct the truth table.

b) (4 points) Find the output Boolean function in the canonical sum-of-product format and the canonical product-of-sum format, respectively.

c) (4 points) Using K-Map to find the simplified output Boolean function.

d) (4 points) Construct the circuit for the obtained Boolean function in part (c).