58. Binary Subtractor

Compute a − b by adding a + (~b + 1) (two’s complement of b). Also report borrow-out (bout) for unsigned subtraction.

Requirements

Module: sub4_2c
Inputs: a[3:0], b[3:0]
Outputs: diff[3:0], bout
Keep it fully combinational (no clocks, no delays).
You may implement with a single assign, or structurally via a 4-bit adder (with cin=1, b inverted).

Behavior

Inputs: a[3:0], b[3:0]
Outputs: diff[3:0] = a − b (mod 16) bout = 1 iff borrow occurs (i.e., a < b)
Relationship: Let {cout, diff} = a + (~b) + 1. Then bout = ~cout.

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Testbench Code

`timescale 1ns/1ps

module tb_sub4_2c;
    // 1) Inputs
    reg  [3:0] a, b;

    // 2) DUT outputs
    wire [3:0] diff;
    wire       bout;

    // 3) Expected (purely combinational, width-safe)
    wire [4:0] golden   = {1'b0, a} + {1'b0, ~b} + 5'b00001; // a + (~b) + 1
    wire [3:0] exp_diff = golden[3:0];
    wire       exp_bout = ~golden[4]; // borrow = NOT carry

    // 4) Single mismatch flag (treat X/Z as mismatches)
    wire mismatch = ({diff, bout} !== {exp_diff, exp_bout});

    // Accounting
    integer TOTAL_TEST_CASES        = 0;
    integer TOTAL_PASSED_TEST_CASES = 0;
    integer TOTAL_FAILED_TEST_CASES = 0;

    // Limits
    integer VCD_MAX_CASES   = 32; // normal printed rows
    integer ERROR_MAX_CASES = 32; // error printed rows
    integer printed_rows    = 0;
    integer printed_errors  = 0;

    // DUT (pick dataflow or structural)
    sub4_2c dut(.a(a), .b(b), .diff(diff), .bout(bout));
    // sub4_2c_struct dut(.a(a), .b(b), .diff(diff), .bout(bout));

    // VCD dump
    initial begin
        $dumpfile("tb_sub4_2c.vcd");
        $dumpvars(0,
            tb_sub4_2c.a, tb_sub4_2c.b,
            tb_sub4_2c.diff, tb_sub4_2c.bout,
            tb_sub4_2c.exp_diff, tb_sub4_2c.exp_bout,
            tb_sub4_2c.mismatch
        );
        $dumpon;
    end

    // Header + init
    initial begin
        a = 0; b = 0;
        $display("  a   b  | diff bout | exp_diff exp_bout | mismatch");
        $display("-----------------------------------------------------");
    end

    // Apply + check (drive -> wait -> read combinational mismatch)
    task apply_and_check;
        input [3:0] ta, tb_;
        begin
            a = ta; b = tb_;
            #1; // settle

            TOTAL_TEST_CASES = TOTAL_TEST_CASES + 1;
            if (!mismatch) begin
                TOTAL_PASSED_TEST_CASES = TOTAL_PASSED_TEST_CASES + 1;
                if (printed_rows < VCD_MAX_CASES) begin
                    $display("0x%1h 0x%1h | 0x%1h   %0d  |   0x%1h       %0d     |    %0d",
                             a, b, diff, bout, exp_diff, exp_bout, mismatch);
                    printed_rows = printed_rows + 1;
                end
            end else begin
                TOTAL_FAILED_TEST_CASES = TOTAL_FAILED_TEST_CASES + 1;
                if (printed_errors < ERROR_MAX_CASES) begin
                    $display("ERR: a=0x%1h b=0x%1h => diff=0x%1h bout=%0d (exp diff=0x%1h bout=%0d)",
                             a, b, diff, bout, exp_diff, exp_bout);
                    printed_errors = printed_errors + 1;
                end
            end

            // Optional: stop VCD after cap of total vectors
            if (TOTAL_TEST_CASES == VCD_MAX_CASES) $dumpoff;
        end
    endtask

    integer ia, ib;
    initial begin
        // Directed: equal, underflow/borrow, boundaries
        apply_and_check(4'h0, 4'h0); // 0 - 0
        apply_and_check(4'hF, 4'h0); // no borrow
        apply_and_check(4'h0, 4'hF); // borrow
        apply_and_check(4'h8, 4'h7); // near MSB boundary
        apply_and_check(4'h7, 4'h8); // borrow near MSB boundary
        apply_and_check(4'hA, 4'hA); // equal

        // Compact sweep (keeps prints/VCD readable)
        for (ia = 0; ia < 16; ia = ia + 1)
            for (ib = 0; ib < 16; ib = ib + 1)
                apply_and_check(ia[3:0], ib[3:0]);

        // A few randoms
        repeat (16) apply_and_check($random, $random);

        // Summary
        $display("-----------------------------------------------------");
        $display("TOTAL_TEST_CASES=%0d", TOTAL_TEST_CASES);
        $display("TOTAL_PASSED_TEST_CASES=%0d", TOTAL_PASSED_TEST_CASES);
        $display("TOTAL_FAILED_TEST_CASES=%0d", TOTAL_FAILED_TEST_CASES);
        $display("ALL_TEST_CASES_PASSED=%s", (TOTAL_FAILED_TEST_CASES==0) ? "true" : "false");
        #2 $finish;
    end
endmodule