This got me thinking, and I went digging even further into historic mainframes. These rarely used eight-bit bytes, so calculating memory size on them is a little funny. But all had more than 256 bytes.
Whirlwind I (1951): 2048 16-bit words, so 4k bytes. This was the first digital computer to use core memory (and the first to operate on more than one bit at a time).
EDVAC (designed in 1944): 1024 44 bit-words, so about 5.6k.
ENIAC (designed in 1943): No memory at all, at least not like we think of it.
So there you go. All but the earliest digital computer used an address space greater than eight bits wide. I'm sure there are some micro controllers and similar that have only eight bit address spaces, but general purpose machines seem to have started at 12-bits and gone up from there.
Whirlwind I (1951): 2048 16-bit words, so 4k bytes. This was the first digital computer to use core memory (and the first to operate on more than one bit at a time).
EDVAC (designed in 1944): 1024 44 bit-words, so about 5.6k.
ENIAC (designed in 1943): No memory at all, at least not like we think of it.
So there you go. All but the earliest digital computer used an address space greater than eight bits wide. I'm sure there are some micro controllers and similar that have only eight bit address spaces, but general purpose machines seem to have started at 12-bits and gone up from there.