Electronic – Triangular waveform to square waveform circuit

You've got a whole lot of things mixed up:

• First off, the DE0 Nano has an ADC, not a DAC. It converts analog voltages to digital values, not the other way around.

• You can't write an integer to a single pin, it doesn't make any sense. A GPIO pin can be either a zero or a one. To output a parallel signal, you need to declare a std_logic_vector and assign a set of pins.

• R8 is the input of a 50MHz clock. You'll probably want to divide that down quite a bit before you try to generate an audio frequency sine wave.

• Even if the ADC was actually a DAC (it's not), you can't simply assign numbers to the pins it's connected to. You need to read the datasheet to understand how to communicate with a device. For the ADC, here's the datasheet, note that it communicates via a serial data stream (compatible with SPI).

• I2C and audio don't really mix. You might be thinking of I2S, which is digital, serial, often multichannel, audio. I2C is typically too slow/not appropriate for audio. If you want to learn more about I2C, the Wikipedia page is pretty straightforward. If you want to learn about I2S, read up on I2S, and then get yourself an I2S DAC.

So, with all this in mind: if you want to output audio, instead of trying to use the non-existent DAC on the DE0 Nano, use PWM to output an analog voltage. You can use a PLL to get a high-frequency PWM frequency so that it can be very easily filtered (simple RC LPF) to get a passable audio signal.

To go along with some of the other answers: An "ideal" 50% duty cycle square wave will have infinite harmonics at the odd-integer frequencies above the fundamental frequency. As you change the duty cycle, there will be a shift of even-integer frequency harmonics added in, etc. Modifying the value of R2 in your circuit not only changes the frequency but also the duty cycle at the same time, so you will observe not only the Pulse Width Modulation effect (and frequency change) but also the change in the resulting harmonics.