IEEE754 representation in hexadecimal? In class, I've heard hexadecimal representation for IEEE754 mentioned and described in 32bit length as a format that consists of one bit for sign, normalized 6-digit fraction (with an implied leading zero) and biased (+64) 7bit exponent, leading me to believe it's not just a made up spec. 

However, googling the actual IEEE754-2008 standard, I've found only 5 basic formats for base 2 and base 10 in it (binary32, binary64, binary128, decimal64, decimal128) and some more interchange formats for these two bases, but no mention of representation in base 16. Could that specification be some rejected proposal which is difficult to find now or am I missing something here?
Hexadecimal notation is just a shortcut writing one hexadecimal digit instead of four bits. For example 1A is exactly the same as 00011010. So eight hexadecimal digits give you the same as the binary32 format. 

What you describe may be that someone takes one sign bit, 2 hex digits for the 8 bit exponenent, and 6 hex digits for the 23 bit mantissa. That would be possible but a bit misleading.