I have a music player which is only able to play sound with one a bit-depth of one. I can produce this by taking a song and simply boosting the signal $+100\textrm{ dB}$.
Is there another approach which produces a better sounding result?
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$\begingroup$ what kinda "music player" do you have? something that plays back recorded audio? like a CD or MP3 player? is it a SACD $\endgroup$ – robert bristow-johnson Jun 15 '16 at 1:53
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You could try PWM or Delta-Sigma modulation. The result will depend on the sample-rate of your music player, and the frequency content of the sound you are trying to play back. You can get good results if you can use a high sample-rate and an "aggressive" noise-shaping filter in Delta-Sigma modulation. A Python based toolbox is available here.
The format used on Super Audio CD (SACD) is one bit.
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1$\begingroup$ 1-bit PWM was done on the Apple II via software timing loops and on the original Mac using hardware counters for audio and music synthesis of waveforms of greater bit depths. $\endgroup$ – hotpaw2 Jun 15 '16 at 0:23
