# Why is 2^32 in a 32-bit system = 4GiB and not 4Gib?

I was watching this video 32-Bit vs 64-Bit - The Advantage and at 1:19 (timestamp) the narrator mentioned the 4GB memory allocation for the 32-bit system. I later found out it should've been 4GiB but am still confused about the bit vs byte part. After all, it's a 32-"bit" and not 32-"byte" system.

"32-bit" describes the size of many of the units of data that the processor can use. In this context, it refers to the size of memory addresses. A 32-bit address can address $$2^{32}$$ distinct objects; in a byte addressable system, that means it can address $$2^{32}$$ distinct bytes.
We don't give addresses to individual bits in memory, but rather groups of bits. In a byte addressable system those are bytes (ie, octets of 8 bits); you can also have a word-addressable system where you can only address groups of, say, 32 bits. In a system with 32-bit addresses addressing 32-bit words, you'd be able to use $$32 * 2^{32}$$ bits, or 17GB! But nowadays most consumer hardware in phones/computers are byte addressable.