The way most digital sound gets reproduced today, a sample-value that has 8, 12, 16, or 24 bits of precision gets sent to a Digital / Analog Converter, and transformed into an analog voltage. This gets repeated at a constant sample-rate, resulting in an analog signal. Usually, the bits of precision are treated by the D/A converter in parallel. And this poses the question, ‘Why is this format named Pulse Code Modulation?’
The reason this is sometimes referred to as PCM, is the fact that a technology once existed, in which the sample-bits were sent to a kind of analog circuit sequentially.
The fact was observed that when a capacitor was allowed to discharge over a simple resistor, the voltage decay curve was exponential, and that within a constant amount of time, the capacitor voltage would halve. That interval of time was then used as the timing constant for pulses, which were either present or absent in a digital stream, and if the pulse was present, a constant amount of charge was pumped into the capacitor, thus increasing its voltage again by a fixed difference.
This resulted in a signal-format in which the least significant bit was also the earliest, and in which therefore the most significant bit would be the one represented in the last pulse. The circuit was so simple, that it could be implemented with a vacuum tube. And thereby, some form of digital sound already existed for military use, in the early 1960s. However, the precision was limited to 6 bits. Also, suitable for military use, this form of digital sound might have sounded quite distorted. It was certainly not meant for music, but was suitable to tell troops in a battlefield situation what their orders were.
(Edit : )
As to how circuit-designers assured that the amount of charge added to the capacitor would be constant, I think they just relied on the anode voltage of the tube being much higher than the signal-amplitudes, so that if this voltage was allowed to flow through a cathode-resistor ‘down to the voltage of the capacitor’, a relatively constant amount of current would result. And the analog pulse-width of each pulse was also made uniform somehow.