Endian-ness: Bits in a Byte vs. Bytes in Memory

Question

When we say a specific architecture is either little-endian or big-endian, we are referring to the whether numerical significance is stored from left-to-right or right-to-left in memory. My question is: does this ordering refer to how bits or ordered in a byte, or how bytes are ordered in a memory?

For example, consider the number 6000=1770h=0001011101110000b. If both bits in a byte and byte in memory are little-endian, this would be stored as

00001110 11101000 = 0E E8,

if bits in a byte were big-endian, but bytes in memory were little-endian, this would be stored as (for what it's worth, this happens to be how Visual Studio seems to be telling me that memory is organized in x64 architecture)

01110000 00010111 = 70 17,

if bits were little-endian, but bytes were big-endian, this would be stored as

11101000 00001110 = 0E E8,

and finally, if bits were big-endian, but bytes were little-endian, this would be stored as

00010111 01110000 = 17 70

(Hopefully I did that right.)

So then, what do the terms "little-endian" and "big-endian" actually refer to? Do the terms refer to the ordering of bits in a byte, or the ordering of bytes in memory, or both? Furthermore, if VS tells me that, for example, 7C, is 'in' a given particular byte, do they mean that the bits that make up that byte in computer memory are literally 0111 1100, or do they just mean that the value stored in that byte is 7Ch=124, but or may not be actually represented as 7c=01111100 depending on whether or not the underlying architecture happens to be little-endian?

Answer 1

The ordering of bits in a byte is invisible. Since you can't address individual bits, there would be no difference between the two cases. However, you can address individual bytes, so there it does make a difference.

If we're expressing 6000 in byte-addressible memory, the high byte is 23 decimal (6000 divided by 256) and the low byte is 112 decimal (6000 mod 256). We could store this as 23,112 or 112,23. There are no other options. Only the ordering of bytes is an open choice, and this is what endianness refers to.

Answer 2

In memory, little-endian or big-endian is not so much left-to-right or right-to-left issue as one of addressing. In little endian, the least significant portion of data is stored in the lower addressed locations and the reverse with big endian.

The ordering occurs independently at 2 levels. As most machines address more than 1 bit at a time (recall some graphic CPUs that did have bit addresses), the address will locate a group of bits, typically 8 bits. So if the bits at address 10 are less significant than the bits at address 11, it is a little endian machine. This is generalized as byte endian-ness. The processor's characteristics define this.

The endian-ness of the group of bits, the bit endian-ness, is significant if there is a way to address them in some fashion. Some processors provide operations that use a bit level address within the byte (or word). If your programming language directly allows you to use that or hides that is another question.

In C there are bit fields such as

union u {
  unsigned char uc;
  struct s {
    int a :1;
    int b :7;
  };
};

This code is non-portable because of bit endian-ness. u.uc = 7 may result in u.s.b also being 7 or something else. Typically the byte endian-ness and bit endian-ness are the same. But the compiler controls the above example.

Bit endian-ness is also significant in serial communication. As 1 bit is sent/received sequentially, its construction to/from memory needs endian-ness definition.

Conclude:
Big-endian and little endian most often refer to the "byte" level addressing. The endian-ness of the bit is typically either the same or of select importance to the programmer.

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BTW, your example of "If both bits in a byte and byte in memory are little-endian, this would be stored as

00001110 11101000 = 0E E8

I would suggest is not correct as the left side and right side are using different endian-ness. Had you used the same endian-ness, you may conclude

00001110 11101000 = 07 71

For fun consider:

01000000 (big endian) has value "sixty-four" (A big endian word)
10110000 (little endian) has value "thirteen".  (Thirteen is little endian word)