BCD counter vhdl code

Basically the simulation result is doing what your code commands, which is different from the above shown reference waveform. But as you have a working code now, you are on the right track.

A first, possibly less obvious problem is brought up by performing a functional rather than a timing simulation. This causes the load signal to be ignored, if it's deasserted on the rising edge of the sensor signal. This detail suggests, that the reference waveform is a timing simulation. For small designs, I would generally suggest a timing simulation, because it shows the real hardware behaviour. By slightly increasing the pulse width of load, it should work also in functional simulation.

The second point is about initial signal states. All registers are initialized to zero by default on power-up, unless you alllow power-up don't care as a synthesis option. This means, that the led output signal must be explicitely set to '1' in your code, preferably under the reset condition.

The third, general point is about the counter operation. In the reference waveform, the counter is counting from 31 to 0, which suggests a 5 bit wide counter, not 6 bit as in your code. I don't know if the exercise is explicitely stating the width of input and output signals. A 5 bit counter would automatically overflow from 31 to 0 without writing it in your code. But it's not bad to write the condition if count = 31 then explicitely. And it's required to trigger the led action.

Finally, how about the led signal? Strictly spoken, the reference waveform is not an exact specification, because it doesn't say, what happens, when the next 32 events are counted, but the most simple assumption is to repeat the LED action. In this case, the led output can be understood as a counter overflow signal, delayed by one cycle. You need an additional flag signal (a register) to implement it in your code.

I would write it like this. I left the counter bit width open in this place by using a different zero syntax.

if count_sig = 31 then
  led_flag <= '1';
  count_sig <= (others => '0');
else
  led_flag <= '0';
  count_sig <= count_sig + 1;
end if;
led <= NOT led_flag;