/*
This Verilog module implements a digital circuit that divides a 9-bit number by 7 and produces both the quotient and remainder. Think of it like a specialized calculator that can only do division by 7.

The circuit takes one input: a 9-bit number 'n' (which can represent values from 0 to 511). It produces two outputs: a 9-bit 'quotient' (the result of dividing n by 7) and a 3-bit 'remainder' (what's left over after the division).

The algorithm works through a clever iterative process that avoids actual division operations (which are complex in digital hardware). Instead, it uses three stages of simpler additions:

In the first stage, it splits the input number into two parts: the upper 6 bits (q1) and lower 3 bits (r1), then adds them together. The second stage takes this result and again splits it into upper bits (q2) and lower bits (r2), adding them together. The third stage does one final split and addition with q3 and r3.

The final step combines all the quotient parts (q1 + q2 + q3) and checks if the remainder needs adjustment. If the remainder equals 7 (binary 111), it increases the quotient by 1 and sets the remainder to 0, since having a remainder of 7 means we can fit in one more complete division by 7.

This method is based on a mathematical property where dividing by 7 can be done through repeated additions of smaller parts, making it much simpler to implement in digital hardware than traditional division. The circuit effectively transforms what would be a complex division operation into a series of simpler additions and bit manipulations.
*/
module div_mod_7(
    input wire [8:0] n,
    output wire [8:0] quotient,
    output wire [2:0] remainder
);
    // First iteration
    wire [5:0] q1 = n[8:3];
    wire [2:0] r1 = n[2:0];
    wire [6:0] rem1 = q1 + r1;

    // Second iteration
    wire [3:0] q2 = rem1[6:3];
    wire [2:0] r2 = rem1[2:0];
    wire [4:0] rem2 = q2 + r2;

    // Third iteration
    wire [1:0] q3 = rem2[4:3];
    wire [2:0] r3 = rem2[2:0];
    wire [2:0] rem3 = q3 + r3;

    // Final quotient sum
    wire [7:0] quotient_sum = q1 + q2 + q3;

    // Final check and output assignment
    assign quotient = (rem3 == 3'b111) ? quotient_sum + 1 : quotient_sum;
    assign remainder = (rem3 == 3'b111) ? 3'b000 : rem3[2:0];
endmodule
