Why does computer memory capacity increase in multiples of 2?

[rob4eiwt]

I've noticed both ram and flash card memory capacities only double. For example memory cards only come in 1 gb, 2gb, 4gb, 8gb, 16gb, etc and not something in between.

Is this just arbitrary manufacturer choice or is there something about memory architecture that causes this to happen?

 

[Ken g6]

It comes down to wires. You can add twice as many chips, choose between two wire paths instead of having just one, and double your memory capacity. If you add an amount of memory that doesn't double like that, you have at least one alternate path that goes nowhere, so that wastes wires.

Computers are binary, so they count like that too, which helps.

 

[rob4eiwt]

It comes down to wires. You can add twice as many chips, choose between two wire paths instead of having just one, and double your memory capacity. If you add an amount of memory that doesn't double like that, you have at least one alternate path that goes nowhere, so that wastes wires.

Computers are binary, so they count like that too, which helps.

Can you post a picture to illustrate what you mean by wasted wires?

I'm not seeing why a 2gb card or 4gb card is efficient but a 3gb card is inefficient.

 

[Ken g6]

Actually, there are two situations where wires matter. First, I found this image online:

This is a diagram of a type of memory. It's actually an ancient type of memory called "core memory", but imagine the little circles are capacitors (for DRAM) or "cells" for SRAM, and it's the same idea. Memory is laid out in a grid, and each bit to be read is selected in one column and one row.

Now, if you assigned each cell a number, how many bits would it take to be able to identify them all? Well, there are 4x4=16 cells, so it would take ceiling(log2(16)) = 4 bits. So to access this memory you need a controller that converts each of those 16 numbers represented by the 4 bits to a pair of wires used to select the appropriate cell. It's sort of like this diagram I found online:

Except there should be four wires going into the "I2C Bus control" component. (This is a different circuit, where three wires is correct, but imagine there were four.) Then those 8 output wires would go to the 8 wires on the memory.

Now, imagine you want 32 bits of memory, instead of 16. So you use two memory circuits:

And your memory controller has 12 wires coming out. How many wires does the controller need to have coming in to work with this amount of memory? Five.

Now a couple of scenarios with amounts of memory that are not powers of two. Suppose you wanted not 16 bits, not 32, but 24. That takes 10 wires out of the memory controller. But how many coming in? Five again. 2/3 of the time the high bit will be 0, but you still need a controller that can account for it. Also, should your process for making these produce blocks of 4x4 bits, you'll have 8 bits hanging out there with no connections, wasted.

For a second scenario, suppose we want 48 bits of memory. There are two ways to do that with these building blocks. I'm running out of image space, so imagine a "#" is two wires crossing two other wires...

Method 1:
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Method 2:
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The first way takes 4+(4*3) = 16 wires. The second way takes 8+8 = 16 wires. But note that if you stuck in an extra 16 bits, for a total of 64...

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That still takes 16 wires. Also, as above, this is the only way to fully utilize the memory controller (which now needs 6 wires in for 48 or 64 cells.)

Oh, and you could do:

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For only 14 wires, but only if your process lets you split a 4x4 block like that. In general, the square-er the grid, the better.

Make sense?

 

[gevorg]

LOL!





<===== Highly Technical subforum

 

[rob4eiwt]

For only 14 wires, but only if your process lets you split a 4x4 block like that. In general, the square-er the grid, the better.

Make sense?

Yes that makes sense. Great explanation. Thanks for taking the time to write it up.

A follow up question is why not be maximally efficient and increase each generation of capacity 4x instead of 2x? Since manufacturers currently double memory each generation, then every other generation the memory cell grid will be rectangular instead of square: 4 cells (2x2 square), 8 cells (4x2 rectangle), 16 cells (4x4 square). So why not go from 4 cells to 16 cells?

 

[Ken g6]

I think they can double the number of square chips on a rectangular DIMM first. Then when they double again they go to higher-capacity chips.