The IBM 1620 had an unusual architecture in that it did decimal
arithmetic operating on variable-length strings of BCD-encoded decimal
digits. It thus didn't really have a word length at all. It also
didn't have a proper ALU--it did arithmetic by table lookup. The
internal code name for the machine was CADET, which was said to stand
for "Can't Add, Doesn't Even Try". Arithmetic on variable-length
decimal strings was a feature carried over to the System/360/370 and
also the DEC VAX.
Have there been other commercially sold computers without a fixed word length?
-Paul W.