Why do storage and memory follow a pattern of 2 (i.e. 2, 4, 8, 16, 32, 64, 128, and so on)?
In: Technology
Imagine memory and storage to be a collection of identical looking boxes that can only be identified by a number written on it. The content of the boxes are the things (data) that you store.
If you use only single digit numbers, the most number of boxes uniquely identified is 10 – ie from 0 to 9. If you use two digit numbers, then you can identify 100 boxes ie 00 to 99. Because we use decimal (base 10) numbers the number increases as 10, 100, 1000 which is 10^1, 10^2, 10^3 where 1,2 and 3 are the number of digits used.
Computers use binary numbers which has only two digits 0 and 1. This means as the number of digits used to identify boxes increases, the number of different boxes identified increases by 2^1, 2^2, 2^3, 2^4 which is 2, 4, 8, 16 and so on.
Computers use binary numbers because that is easy to implement in electronics where 0 is “off” and 1 is “on”.
Maybe it’s because computers use binary number system and one memory cell is 1 or 0, two cells have 2^2 = 4 variations of filling and so on.
Upd: correct me If i’m wrong, please
If you have one wire you can address two memory cells number 0 (power off) and number 1 (power on).
With two wires you can address 4 memory cells. With four wires you can do 16. If you want 17 memory cells you need to have everywhere 5 wires and use the fifth one for just that one cell. This is not efficient. If you already have the wire in place, why not to utilize all the possible capacity of it?
Because computers operate on binary, because they are digital – they deal in absolutes of a particular electrical line either having power or not having power, and nothing in between.
Take your fingers. Now, if a finger can *only* be up or down, and nothing in between, see what numbers you can get up to. With only two fingers you have both-down, one-up-one-down, one-down-one-up, and both-up. 4 combinations. With 3 fingers there are 8 combinations. With 10 fingers there are 1024 combinations. They’re all powers of 2 because there are only 2 digital states, on and off.
If you have, say, 10 electrical pins addressing a storage device, and they operate in binary, that means you have 1024 possible addresses. If you have 11, that’s 2048.
If you made a 1000-byte storage device, you’d have 24 bytes that you couldn’t access, for no real good reason. And you’d probably need some extra logic or circuitry to refuse access to only those 24-bytes.
Notice, also, that the pattern of your numbering is not even the full answer… you’re already sending and receiving *bytes* (which are 8 binary bits), kilobytes, megabytes, gigabytes, etc. The choice of the number of those is a power of two just like the number of bits in a byte is a power of two.
If you had analogue computers, it would be different. If you had ternary computers (computers that have 3 states for each connection, i.e. off, half and full), then it would be powers of three (or you’d be wasting some bits, or in this case “trits”).
Your computers and other devices convert everything – even analogue signals like those going over your telephone cable, microphone, video camera, etc. – to digital information in order to process it. As such everything ends up as some power-of-two. That slightly-red colour your webcam picks up is converted to the nearest RGB equivalent and sent as three digital bytes to your computer. Everything gets digitised.
To make it more basic than some of the great answers here, a computer only can think of something as on or off. It could count from 0-255 with 255 light switches, but it’s easier to make the first one worth 1, the next one worth 2, the third one worth 4, the next worth 8, then 16, 32, 64, and 128. By flipping those 8 switches on and off you can represent any number from 0-255. (Remember how the first Zelda capped out at 255 rupees? Have you ever noticed IP addresses are 4 numbers between 0 and 255? Same logic applies.)
But computer hardware gets more efficient, so we can keep adding switches. Using the same architecture we can add a 256 switch and a 512 switch. Now I can get any number between 0 and 1023. Every time we add a new switch, it’s the sum of all the switches that came before it +1. Well we kept doing that over and over and over again until we got some pretty big banks of switches compared to what we had 30 years ago.
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