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Digital switching uses binary values — 0 or 1, on or off in electrical terms. To do this, the analogue sound signal must be sampled many times per second, its strength (amplitude) measured, and converted to a binary number.
Digital telephone systems standardise on 8 bits (1 byte) per sample. Human voice typically runs up to about 3–4kHz; for accurate transmission, the sampling rate must be twice this, so digital telephone systems sample at 8kHz (8,000 times per second).
With 8 bits, the biggest number representable is 0 to 255 — each sound sample is measured against one of 256 levels and stored as an 8-bit binary number.
At 8,000 of these 8-bit numbers per second, data travels through the network at 64,000 bits per second (64 kbit/s) — 8,000 × 8 = 64,000. On a dial-up line, this is the maximum theoretical data rate for data transmission.
Getting this speed requires an end-to-end digital link — a digital line all the way from the local exchange to your computer, commonly called ISDN (Integrated Services Digital Network). With a standard phone line, the local exchange does an analogue-digital conversion, with the "last mile" from exchange to phone remaining analogue. This conversion, plus the conversion in your modem, loses efficiency — which is why old dial-up connections on a standard line typically maxed out around 48kbit/s.
Digital exchanges forward these 8-bit numbers from one line to another using solid-state switches built from transistors and capacitors on an integrated circuit.