For each the following scenarios:

- build the truth table;

- derive the corresponding boolean expression, and simplify it to the extent possible; and

- construct the digital circuit using logisim, and embed the png image.

1)

Given four inputs: a, b, c & d, where (a, b) represents a 2-bit unsigned binary number X; and (c, d)

represents a 2-bit unsigned binary number Y (i.e. both X and Y are in the range #0 to #3).

The output is z, which is 1 whenever X > Y, and 0 otherwise (this circuit is part of a "2-bit comparator").

For instance, if a = 1, b = 0 (i.e. X = b10 => #2); c = 0, d = 1 (i.e. Y = b01 => #1); then z = 1, since b10 > b01