My entry to this contest is a bit late, but hopefully it goes through. The entry is a class D amplifier made entirely out of discrete digital logic components. I took great pains not to use op amps or transistors or any active devices besides logic gates. Though the amplifier outputs square waves, the process to generate them is entirely analog. As such, this design is an example of using digital gates in an analog way.
The first stage part is a square wave generator which gets turned into a triangle wave by an integrator. The square wave frequency of 333khz is generated using a basic 2 NAND gate oscillator made from 4011UBE chips. Note that it has to be the unbuffered version, because the buffered one tends to oscillate during transitions. The square wave is integrated using a resistor and capacitor circuit similar to an op amp integrator, except the op amp is replaced with a 74hcu04 inverter. There is a potentiometer (VR1) to tune the integrator. The triangle wave then goes into a "comparator" which is another 74hcu04 inverter acting similar to an op amp summing amplifier, except with no feedback.
The other signal which goes into the comparator is the input signal, which in this case is an electric guitar going through a preamp made of 4011UBE amplifiers, which look like op amp inverting amplifier (its seems like inverting logic gates almost work like op amps with the non inverted inputs grounded...) There is a potentiometer (VR2 in schematic) which biases the input to be in the middle of the amplifiers output to get a good AC voltage swing.
The triangle wave and the input are now summed together, which causes the comparator to cut up the input signal into a square wave with pulse widths proportional to its amplitude. This is the principle on which a class D amplifier works on.
The output of the comparator is buffered and inverted several times and complementary inputs are fed into 74hc244 buffers, with all the inputs connected together, and all the outputs connected together into an LC filter, which low passes the square wave back into the original input signal, except amplified. Unfortunately, this filter is not done correctly for this build because I could not get proper inductors due to hurricane Sandy hitting the east coast. As such, I just used what I had. Also, the speaker is 16 ohms for the video because it is louder and works better with the filter.
Here are some pictures and a video:
Now with video!