How do you convert sound signals to binary?

By using an analog to digital conversion. To achieve this, samples of the waveform are taken at regular intervals. The human ear is capable of hearing audio frequencies up to 20 KHz, thus the sampling frequency needs to be at least twice as high in order to reproduce the highest frequencies without introducing too much distortion. Typically, samples are taken at a rate of at least 44,100 samples per second per channel for CD quality audio.

The amplitude of each sample is then scaled and converted to a signed integer. CD quality audio uses 16 bits per channel thus the waveform amplitudes are scaled to integers in the range -32,767 to +32,767. Thus CD quality stereo audio consumes 2 * 44,100 * 16 bits every second, which is 176,400 bytes per second. Thus 60 minutes of audio consumes approx. 605 MB.