A free-running binary counter

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module counter_bin #(parameter W = 4) (
  input  wire         clk, rst_n,
  output reg  [W-1:0] count
);
  always @(posedge clk or negedge rst_n)
    if (!rst_n) count <= {W{1'b0}};
    else        count <= count + 1'b1;     // wraps naturally at 2^W
endmodule

An N-bit counter overflows from 2ᴺ−1 to 0, so its period is 2ᴺ cycles. That counter suits power-of-two period lengths.

Modulo-M: count to M−1, then wrap

Other periods reset at the terminal count M-1, the last value before wrapping. A one-cycle pulse on that value marks each period boundary.

M may be 1 (a counter that holds 0 with tc always high): the count width is guarded as localparam int CW = (M > 1) ? $clog2(M) : 1; because $clog2(1) is 0, which would give a [-1:0] count.

The bottom row, tc, is high when count holds M-1 (the module decodes count >= M-1, which is the same thing for every legal count).

• Slots 1–5: count runs 0 through 4 and tc stays low.

• Slot 6: count is 5 and tc is high.

• Slot 7: count wraps to 0 and tc falls.

• Slots 8–11: count runs 1 through 4 and tc stays low.

• Slot 12: count is 5 and tc is high.

• Slots 13–14: count is 0 then 1 and tc stays low.

Off-by-one: the classic mistakes

Testbench

The modulo-M counter plus a testbench that checks four laps and the tc pulse.

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module counter_mod #(parameter int M = 6) (   // M must be at least 1
  input  logic                  clk, rst_n,
  output logic [(M > 1 ? $clog2(M) : 1)-1:0] count,
  output logic                  tc            // high while count >= M-1 (equals M-1 in normal operation)
);
  // M = 1 guard ($clog2(1) is 0, so [$clog2(M)-1:0] would be [-1:0]).
  localparam int CW = (M > 1) ? $clog2(M) : 1;
  always_ff @(posedge clk or negedge rst_n)
    if (!rst_n)          count <= '0;
    else if (tc)         count <= '0;          // wrap after the terminal count
    else                 count <= count + 1'b1;

  assign tc = (count >= M - 1);              // >= (not ==): a forced out-of-range count still wraps
endmodule

Related topics

• Up/down counter with reload