I just restart the C programming study. Now, I'm studying the memory storage capacity and the difference between bit and byte. I came across to this definition. There is a calculation to a 32 bits system. I'm very confused, because in this calculation 2^32 = 4294967296 bytes and it means about 4 Gigabyte. My question is: Why 2 raised to 32 power results in a number in bytes instead of bits ?
Thanks for helping me.
There are two ways to look at this:
A 32-bit integer can hold one of 2^32 different values. Thus, a uint32_t can represent the values from 0 to 4294967295.
A 32-bit address can represent 2^32 different addresses. And as Scott said, on a byte-addressable system, that means 2^32 different bytes can be addressed. Thus, a process with 32-bit pointers can address up to 4 GiB of virtual memory. Or, a microprocessor with a 32-bit address bus can address up to 4 GiB of RAM.
That description is really superficial and misses a lot of important considerations, especially as to how memory is defined and accessed.
Fundamentally an N-bit value has 2N possible states, so a 16-bit value has 65,536 possible states. Additionally, memory is accessed as bytes, or 8-bit values. This was not always the case, older machines had different "word" sizes, anywhere from 4 to 36 bits per word, occasionally more, but over time the 8-bit word, or "byte", became the dominant form.
In every case a memory "address" contains one "word" or, on more modern machines, "byte". Memory is measured in these units, like "kilowords" or "gigabytes", for reasons of simplicity even though the individual memory chips themselves are specified in terms of bits. For example, a 1 gigabyte memory module often has 8 gigabit chips on it. These chips are read at the same time, the resulting data combined to produce a single byte of memory.
By that article's wobbly definition this means a 16-bit CPU can only address 64KB of memory, which is wrong. DOS systems from the 1980s used two pointers to represent memory, a segment and an offset, and could address 16MB using an effective 24-bit pointer. This isn't the only way in which the raw pointer size and total addressable memory can differ.
Some 32-bit systems also had an alternate 36-bit memory model that allowed addressing up to 64GB of memory, though an individual process was limited to a 4GB slice of the available memory.
In other words, for systems with a singular pointer to a memory address and where the smallest memory unit is a byte then the maximum addressable memory is 2N bytes.
Thankfully, since 64-bit systems are now commonplace and a computer with > 64GB of memory is not even exotic or unusual, addressing systems are a lot simpler now then when having to work around pointer-size limitations.
We say that memory is byte-addressable, you can think like byte is the smallest unit of memory so you are not reading by bits but bytes. The reason might be that the smallest data type is 1 byte, even boolean type in c/c++ is 1 byte.
