Consider two 4-bit binary numbers A and B. Bits of A are a3, a2, a1, and a0, and bits of B are b3, b2, b1, and b0. A is greater than B if a3 is 1 and b3 is 0, but if a3 and b3 are the same, then if a2 is 1 and b2 is 0, we can determine that A is greater than B. This evaluation continues until a0 and b0 are considered. If a0 and b0 are equal then A and B are equal. Using discrete gates and Verilog gate primitives build a 4-bit comparator that generates a 1 on its GT output when its 4-bit input A is greater than its B input, and a 1 on its EQ output when A and B are equal. Use the generate statement and other Verilog iterative logic support structures. The code should be as simple as possible.

Here's a possible implementation of the 4-bit comparator in Verilog:

module comparator(
    input [3:0] A,
    input [3:0] B,
    output GT,
    output EQ
);

genvar i;
wire [3:0] eq_wire;

assign GT = (A[3] > B[3]) || ((A[3] == B[3]) && (A[2] > B[2])) || 
            ((A[3:2] == B[3:2]) && (A[1] > B[1])) || 
            ((A[3:1] == B[3:1]) && (A[0] > B[0]));

assign eq_wire[3] = (A[3] == B[3]);
for (i = 2; i >= 0; i--) begin
    assign eq_wire[i] = eq_wire[i+1] && (A[i] == B[i]);
end
assign EQ = eq_wire[0];

endmodule

The comparator module takes two 4-bit binary inputs A and B, and outputs two 1-bit signals GT and EQ. GT is high (1) if A is greater than B, and EQ is high (1) if A and B are equal.

The comparator uses a generate statement to create a wire eq_wire that stores the result of the equality comparison between A and B. The generate statement creates a loop that iterates over the bits of A and B from the most significant to the least significant, and computes the equality of each pair of bits using logical AND and stores the result in eq_wire.

The GT output is computed using a series of conditional statements that check the bits of A and B in order of decreasing significance. If a bit in A is greater than the corresponding bit in B, or if A has a higher-order bit set to 1 while B has it set to 0, then A is greater than B.

The EQ output is computed using the eq_wire wire, which stores the result of the equality comparison between A and B. The EQ output is high if all bits of A and B are equal.