Why are Bytes talked about in powers of 2?

Question

2^10 = 1KB, 2^20 = 1MB, etc. etc.

Except, a byte is 8 bits so I do not understand why we are using powers of 2 as an explanation. To talk about Bits in powers of 2 I can completely understand but with Bytes, I am totally lost. Many textbooks / online resources talk about it in this way, what am I missing here?

By the way, I understand 2^10 = 1024 which is approximately 10^3 = 1000. What I don't understand is why we justify the use prefixes and bytes using powers of 2.

Answer 1

I'll ask the question you're really asking: Why don't we just use powers of 10?

To which we'll respond: why should we use powers of 10? Because the lifeforms using the computers happen to have 10 fingers?

Computers break everything down to 1s and 0s.

1024 in binary = 10000000000 (2^10), which is a nice round number.

1000 in binary = 1111101000 (not an even power of 2).

If you are actually working with a computer at a low level (ie looking at the raw memory), it is much easier to think using numbers that get represented as round numbers in the way they are stored.

Answer 2

From your question, I think that you understand about powers of two and measuring bytes. If not, the other answers explain that.

Is your question is why not use bits rather than bytes since bits are truly binary?

The reason that memory, disk space, etc is described in bytes rather than bits has to do with the word addressability of early computers. The bit, nibble and byte came about as workable amounts of memory in simple computers. The first computers had actual wires that linked the various bits together. 8-bit addressability was a significant step forward.

Bytes instead of bits is just a historical convention. Networks measurements are in (mega) bits for similar historical reasons.

Wikipedia has some interesting details.