Sometimes I need to generate a clock at a lower frequency than the main clock driving the FPGA. If the ratio of the frequencies is a power of 2, the logic is easy. If the ratio is an integer N, then a divide-by-N counter is only a little harder. But if the ratio isn't an integer, a little (and I mean a little) math is required.

Note that the new clock will have lots of jitter: there's no escaping that. But it will have no drift, and for some applications that's what counts.

If you have a clock A at frequency a, and want to make a clock B at some lower frequency b (that is, b < a), then something like:

d = 0;
forever {
Wait for clock A.
if (d < 1) {
d += (b/a);
} else {
d += (b/a) - 1; /* getting here means tick for clock B */
}
}

but comparison against zero is easier, so subtract 1 from d:

d = 0;
forever {
Wait for clock A.
if (d < 0) {
d += (b/a);
} else {
d += (b/a) - 1; /* getting here means tick for clock B */
}
}

want an integer representation, so multiply everything by a:

d = 0;
forever {
Wait for clock A.
if (d < 0) {
d += b;
} else {
d += b - a; /* getting here means tick for clock B */
}
}

For example. I just bought a bargain batch of 14.1523MHz oscillators from BG but I need to generate a 24Hz clock.

So a=14152300 and b=24:

d = 0;
forever {
Wait for clock A.
if (d < 0) {
d += 24;
} else {
d += 24 - 14152300; /* getting here means tick for clock B */
}
}

For a hardware implementation I need to know how many bits are needed for d: here it's 24 bits to hold the largest value (-14152300) plus one more bit for the sign. In VHDL this looks like:

signal d, dInc, dN : std_logic_vector(24 downto 0);
process (d)
begin
if (d(24) = '1') then
dInc <= "0000000000000000000011000"; -- (24)
else
dInc <= "1001010000000110110101100"; -- (24 - 14152300)
end if;
end process;
dN <= d + dInc;
process
begin
wait until A'event and A = '1';
d <= dN;
-- clock B tick whenever d(24) is zero
end process;