Ignoring the issue of "normal conversation", it must be before 1973 or so. I was a COBOL programmer back then, and I still have some of my IBM IBM 360/370 "cheat cards". In around 1965, I remember hearing about base
12, duodecimal, (referencing Hammurabi?), and in 1967, we covered various bases in math class. I don't remember if we went to base 16, but I'm sure we didn't cover it in the context of a shorthand for binary.I remember writing an EBCDIC-to-ASCII converter in COBOL, then later writing an ASCII-to-Baudot(6 bit)-to-ASCII converter in PL/M.
I hate being old...
RB