Quiz: how long does it take to transfer a 1 TiB file over a gigabit ethernet connection assuming no overhead? Answer: about 1100 seconds, since network bandwidth is also measured in base 10.
Incorrect. You confused bit and bytes.
A 1 TiB file is 1024^4=1,099,511,627,776 bytes.
A gigabit connection can transfer (again assuming no overhead) 1,000,000,000 bits, or 125,000,000 bytes per second.
So the answer is 1,099,511,627,776 / 125,000,000 = ~8796 seconds
Powers of 2 only need to be used when measuring bits. So 1 Kb/s is 1024 bits per second, but 1 kHz is 1000 Hz. I have no reason to be confused about my scope sample rate or CPU frequency since neither is a measure of bits or bits per second.
Incorrect. (Data) bits have nothing to do with it per se. Ethernet is using bit rates based on base 10, so there nothing in that particular example that warrants use of base 2, per se.
Where base 2 comes from is the physical layout of memory chips. You have an array of memory locations with a number of rows and number of columns which will both be a power of 2. This follow naturally from the way the address lines are used. A number of address bits (n) will be fed into a demultiplexer which will output one of 2^n rows or columns. There is no such "intrinsic reason" to use binary prefixes in the example "1024 bits per second". 1024 is just an arbitrary data rate. The array size of solid state memories is not arbitrary, but by design.
Just to be clear, I wouldn't want to force anyone to use binary prefixes. What I would encourage people to do is use whatever prefixes they use correctly. k, M, G, T are base 10 prefixes, period. If you use them for RAM, you ought use them correctly and say for example "4.3 GB", as described in my previous post.
Historically they could get away with it since the difference between 1 kB and 1 kiB is only 2.4%, but differences get larger now we're talking about TBytes and up.
This is an important point. For those may not get it, the difference between the binary and decimal prefixes increase for the bigger prefixes, since it accumulates for every multiplication by 1024.
ki = 1024 -> 2.4% difference
Mi = 1048576 -> 4.9% difference
Gi = 1073741824 -> 7.4% difference
Ti = 1099511627776 -> 10% difference
And it grows - no joke - exponentially.