Where did the octal/hex notations come from?
After all of this time, I've never thought to ask this question; I understand this came from c++, but what was the reasoning behind it:
- Specify decimal numbers as you normally would
- Specify octal numbers by a leading 0
- Specify hexadecimal numbers by a leading 0x
Why 0? Why 0x? Is there a natural progression for base-32?
Answer
C, the ancestor of C++ and Java, was originally developed by Dennis Richie on PDP-8s in the early 70s. Those machines had a 12-bit address space, so pointers (addresses) were 12 bits long and most conveniently represented in code by four 3-bit octal digits (first addressable word would be 0000octal, last addressable word 7777octal).
Octal does not map well to 8 bit bytes because each octal digit represents three bits, so there will always be excess bits representable in the octal notation. An all-TRUE-bits byte (1111 1111) is 377 in octal, but FF in hex.
Hex is easier for most people to convert to and from binary in their heads, since binary numbers are usually expressed in blocks of eight (because that's the size of a byte) and eight is exactly two Hex digits, but Hex notation would have been clunky and misleading in Dennis' time (implying the ability to address 16 bits). Programmers need to think in binary when working with hardware (for which each bit typically represents a physical wire) and when working with bit-wise logic (for which each bit has a programmer-defined meaning).
I imagine Dennis added the 0 prefix as the simplest possible variation on everyday decimal numbers, and easiest for those early parsers to distinguish.
I believe Hex notation 0x__ was added to C slightly later. The compiler parse tree to distinguish 1-9 (first digit of a decimal constant), 0 (first [insignificant] digit of an octal constant), and 0x (indicating a hex constant to follow in subsequent digits) from each other is considerably more complicated than just using a leading 0 as the indicator to switch from parsing subsequent digits as octal rather than decimal.
Why did Dennis design this way? Contemporary programmers don't appreciate that those early computers were often controlled by toggling instructions to the CPU by physically flipping switches on the CPUs front panel, or with a punch card or paper tape; all environments where saving a few steps or instructions represented savings of significant manual labor. Also, memory was limited and expensive, so saving even a few instructions had a high value.
In summary: 0 for octal because it was efficiently parseable and octal was user-friendly on PDP-8s (at least for address manipulation)
0x for hex probably because it was a natural and backward-compatible extension on the octal prefix standard and still relatively efficient to parse.