Comment by variaga
1 day ago
Big-endian matches the way we commonly write numbers, but if you have to deal with multiple word widths or greater than word-width math I find little-endian much more straightforward because LE has the invariant that bit value = 2^bit_index and byte value = 2^(8byte_index).
E.g. a 1 in bit 7 on a LE system always represnts 2^7 for 8/16/32/64/ whatever bit word widths.
This is emphatically not true in BE systems and as evidence I offer that IBM (natively BE), MIPS natively BE) and ARM (natively LE but with a BE mode) all have different mappings of bit and byte indices/lanes in larger word widths* while all LE systems assign the bit/byte lanes the same way.
Using the bit 7 example
- IBM 8-bit: bit 7 is in byte 0 and equal to 2^0
- IBM 16-bit: bit 7 is in byte o and equal to 2^8
- IBM 32-bit: bit 7 is in byte 0 and equal to 2^25
‐ MIPS 16-bit: bit 7 is in byte 1 and equal to 2^7
- MIPS 32-bit: bit 7 is in byte 3 and is equal to 2^7
- ARM 32-bit BE: bit 7 is in byte 0 and is equal to 2^31
Vs. every single LE system, regardless of word width
- bit N is in byte (N//8) and is equal to 2^N
(And of course none of these match how ethernet orders bits/bytes, but that's a different topic)
Not that it typically matters in a practical sense* (Unless you're writing to a register for a device)...
However I've always viewed Little Endian as 'bit 0' being on the left most / lowest part of the string of bits, but Big Endian 'bit 0' is all the way to the right / highest address of bits (but smallest order of power).
If encoding or decoding an analog value it makes sense to begin with the biggest bit first - but that mostly matters in a serial / output sense, not for machine word transfers which are (at least in that era were) parallel (today, of course, we have multiple high speed serial links between most chips, sometimes in parallel for wide paths).
Aside from the reduced complexity of aligned only access, forcing the bus to a machine word naturally also aligns / packs fractions of that word on RISC systems, which tended to be the big endian systems.
From that logical perspective it might even make sense to think of the RAM not in units of bytes but rather in units of whole machine words, which might be partly accessed by a fractional value.