Random-Access Memory: Is there a difference in RAM sizes between 32 bit and 64 bit machines

When we talk a 32-bit or 64-bit machine, the 32 and 64 actually refers word-length of a processor; i.e. the maximum number of bits the processor can operate upon at a time. A 32-bit processor, for instance, has 32-bit registers, and does operations (like addition or logical-AND) on 32-bit numbers.

Theoretically speaking, the word-length has no influence on the amount of RAM usable by the system. The maximum amount of addressable memory is determined by the address-length of the processor - put simply, using an n-bit address, a [Math Processing Error]-byte memory can be addressed.

In real machines, 32-bit machines typically can address a maximum of 4GB of RAM while 64-bit machines can go up to petabyte ranges. This is because the address-length of 32-bit machines are typically 32 bits (translating to [Math Processing Error] = 4096 bytes = 4 GB) while 64-bit machines, being relatively modern, feature 64 (or even 128 in some cases) address lines, giving 16PB of addressable memory.

 32 bit {note: 2^32 = 2 to the power of 32}

2^32 = 4,294,967,296 bytes
4,294,967,296 / (1,024 x 1,024) = 4,096 MB = 4GB

64-bit

2^64 = 18,446,744,073,709,551,616
18,446,744,073,709,551,616 / (1,024 x 1,024) = 16EB (exabytes)

I had no idea what an Exabyte was.

KB - Kilobyte
MB - Megabyte (x 1000 KB)
GB - Gigabyte (x 1000 MB)
TB - Terrabyte (x 1000 GB)
PB - Petabyte (x 1000 TB)
EB = Exabyte? (x 1000 PB)