Am I correct in understanding the a 1 bit D/A outputs a pulse width with a DC value equal to the desired analog value?
Essentially, that's right. You then place a crude analog filter on the output, and voila - you've got a nice analog output.
In practice a '1 bit DAC' (also called 'bitstream DAC' or 'multi-stage acoustic noise-shaping [MASH]') is a
Delta-sigma modultator. This uses clever digital logic to create a high-frequency pulse-width modulated output from a digital input. (The naive method. Switch on output. Count from 0 to x. Switch off output. Count to max. repeat. Is impractical).
The advantages of the DS modulator approach are:
It's cheap - High-precision DACs must be built with tolerances equal to their precision - so a 16 bit DAC needs to be built with resistors accurate to within 0.001%. This means special manufacturing techniques - like laser trimming, and special design features like on-die sapphire heat-spreaders to ensure that all the DAC resistors are at the same temperature. The crude '1 bit DAC' needs no expensive factory adjustments, and the digital algorithm ensures absolute linearity and virtually zero distortion.
It 'spreads the quantization noise'. Any DAC/ADC introduces noise due to the 'steppiness' of the output - this noise is spread evenly over the frequency band of the DAC (e.g. 48 kHz). In a DSM (which may operate at many MHz), however, the digital processing 'shapes' the noise so that it mainly falls in the high frequencies, which are in the MHz range and totally inaudible, and leaves the audio range ultra pure. The result, is that a DSM DAC introduces virtually no noise in the audio range - a unique property of the DSM DAC.
The advantages of a DSM DACs/ADCs for audio are overwhelming, and they are now virtually the only audio technology available. However, many manufacturers have now dropped the '1 bit' design, and may use 2-4 bit DACs in their DSMs, as these higher performance components dramatically improve the performance of the DSM as a whole.