1958 FACOM 128B Japanese Relay Computer, still working [video]

One of the particularly interesting parts about this computer is that it comes quite a significant amount of time after valve/tube-based computer systems, and in fact some time after the first prototype transistor computers. It was made by Fujitsu, who at the time produced telephone switches, so reused a lot of telephone switching equipment, including a crossbar-switch-based main memory.

Numbers are stored in floating point, with 8 decimal digits in the mantissa and 2 in the exponent, encoded in an interesting bi-quinary representation (for each decimal digit, this uses five bits to represent a unary 1, 2, 3, 4 or 5, then a single bit to represent +0 or +5) with 69 bit words. Instructions use a 72 bit word length.