How to determine the maximum RAM capacity for an operating system?

Problem Detail: 

I was curious to know what limits the max RAM capacity for an OS while reading about microprocessors being 32-bit and 64-bit. I know that limit for 32-bit OS is 4GB and for 64-bit OS is 16 Exabytes, but my question is how do we get there? I found this calculation:

$\qquad 2^{32} = 4\,294\,967\,296$

and

$\qquad \frac{4\,294\,967\,296}{1024 \cdot 1024}\,\mathrm{B} = 4\,096\, \mathrm{MB} = 4\, \mathrm{GB}$.

It's different for 64-bit:

$\qquad 2^{64} = 18\,446\,744\,073\,709\,551\,616$

and

$\qquad \frac{18\,446\,744\,073\,709\,551\,616}{1024 \cdot 1024}\mathrm{B} = 16\,\mathrm{EB}$.

What I don't understand is how the calculation of bits turned into bytes and reached the results 4GB and 16EXB?

Asked By : Neeraj

Answered By : Neeraj

1. First of all, in computer architecture, 32-bit/64-bit computing is the use of processors that have datapath widths, integer size, and memory addresses widths of 32/64 bits (four/eight octets). Also, 32-bit/64-bit CPU and ALU architectures are those that are based on registers, address buses, or data buses of that size(due to design decisions that may differ in different CPU/OS).

2. Secondly, there is a confusion that is created when calculating the maximum RAM capacity for 32/64 bit OS/microprocessor. The 32-bit/64-bit address/machine word is usually considered as containing a single byte word and not byte (e.g a byte word might be a floating point number of 32/64 bits depending on the architecture & a byte on the other hand is 8 bits) but since we do all our memory calculations in terms of bytes the result her too is in terms of bytes. Hence, bytes is the unit written where

1byte = 1 byteword = 1 address space/machine word

So if we have 4,294,967,296 addresses that means we can address as much byte words and hence the total capacity of RAM in a 32-bit OS is 4GB, similarily for 64-bit OS the calculations are of addresses with one byteword each and later written in terms of bytes.

I hope this should make it pretty clear. Thank you for your inputs and replies.

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Question Source : http://cs.stackexchange.com/questions/19619