Why is the size of RAM always in powers of 2?

Individual sticks of memory always are powers of 2 because of how multiplexers/demultiplexers work.

Basically there is a bit of circuit where every word of memory connects to a bus. The Mux decides which one of the words is loaded on the bus. A series of wires controls which gate is open.

If there is 1 wire there are two possibilities

0, 1

If there are 2 wires there are four possibilities

00, 01, 10, 11

If there are n wires there are n^2 possibilities.

Not using all the possible words for the number of wires. Example 3 words when using 2 wires would cause there to be inputs that break the state machine the instruction stack is interacting with and make developing for the chip very complicated.

So the number of words that can be pulled is restricted by the capacity of the Mux, which is driven by wires that are either off or on. This causes the powers of 2.

http://en.wikipedia.org/wiki/Memory_controller

http://en.wikipedia.org/wiki/Multiplexer

This is more a question of address space. If I have 1 bit, I can address 2 things (0, 1). If I have 2 bits, I can address 4 things (00, 01, 10, 11). With 2 bits, you can also address 3 things, but then you are wasting precious bits, so it makes sense to try to fill up the address space available. Basically everything inside a computer is based in binary and is therefore held to some relationship with powers of 2. The way these addresses work in hardware is basically to go into a massive decoder that lights up the right bit and makes that bit available. If you don't use all your bits, you are basically wasting available logic circuitry. In most DRAM (which is what you think of usually talking about RAM), the capacitor is not the expensive part, the control circuits are, so if you waste control circuits, you are not making the best performance/cost proposition.

Total physical ram of the machine, ram modules or ram allocated by the software?

The first is not always power of two - a machine with 6GB of ram works just fine, the third - it is more convenient to allocate power of 2 sized blocks of ram because this makes the allocation algorithms faster.

The second - not sure but I suppose it is more convenient - while there may not be reasons while you cannot have 1023 Mbit block it makes no sense because everything else is based on the power of 2 in computers anyway.

Because when you add a wire to address bytes, you multiply by 2 the number of addressable bytes.