The binary waveform is derived using pulse-width modulation (PWM), pulse density modulation (sometimes referred to as pulse frequency modulation), sliding mode control (more commonly called "self-oscillating modulation" in the trade.) or discrete-time forms of modulation such as delta-sigma modulation.
The most basic way of creating the PWM signal is to use a high speed comparator ("C" in the block-diagram above) that compares a high frequency triangular wave with the audio input. This generates a series of pulses of which the duty cycle is directly proportional with the instantaneous value of the audio signal. The comparator then drives a MOS gate driver which in turn drives a pair of high-power switches (usually MOSFETs). This produces an amplified replica of the comparator's PWM signal. The output filter removes the high-frequency switching components of the PWM signal and recovers the audio information that the speaker can use.
DSP-based amplifiers which generate a PWM signal directly from a digital audio signal (e. g. SPDIF) either use a counter to time the pulse length or implement a digital equivalent of a triangle-based modulator. In either case, the time resolution afforded by practical clock frequencies is only a few hundredths of a switching period, which is not enough to ensure low noise. In effect, the pulse length gets quantized, resulting in quantization distortion. In both cases, negative feedback is applied inside the digital domain, forming a noise shaper which has lower noise in the audible frequency range.