It starts with the telegraph. TDM (time-division multiplexing) was patented in 1853 by Moses G. Farmer, [pictured] a telegraph operator who was employed as a technician to maintain a network of telegraph lines north of Massachusetts. Farmer was trying to interlace samples from multiple telegraphy sources, and convey them over a single telegraph cable. He at least proved the viability of future duplex and quadruplex systems. This was borne out by the work of W. M. Miner in 1903. He successfully multiplexed multiple telegraph signals. He managed to achieve a sample rate of 3500–4300 Hz.
But this was not PCM. It was PAM (pulse-amplitude modulation) In PAM the data is encoded in the amplitude of a series of signal pulses. PCM reuires an A-to-D conversion (analog to digital) First the analog signal amplitude is sampled at a known time interval. The amplitude of the signal at each sample is rounded off to a power of 2 (2,4,8,16 etc) a process is called quantization. This is represented by binary digits three, four, five, or six binary digits (aka bits) respectively. So the output is now just a string of binary numbers. See the chart below:
In 1926 Paul M. Rainey at Western Electric patented a facsimile machine which transmitted its signal via PCM. It was using a 5-bit encoded PCM. It was never sold commercially but the idea was taking hold. This was it's first use transmitting an image. Though telegraph and fax are both both used to transmit text, the fax sends an image with text on it. The telegraph sends dots and dashes directly correlating to alphanumeric characters. A fax can send non text data. You can fax a xerox image of your middle finger which I have done on occasion. Alec Reeves invented PCM on his own in 1937 unaware of any prior work. He was a British expat working at the International Telephone and Telegraph in France. He patented the concept in 1938 but no working model. His U.S. patent # 2,272,070 was granted in 1943. More here. He lived long enough to see it used in WWII by the allies, though it was so top secret he probably didn't know until after the war. SIGSALY went into service in 1943 and was in military-only use until 1946.