Calculating bits of RAM

Question

Consider I have 30-bit RAM to calculate its size: 2^30 = 1073741824 / 10^9 = 1GB

What if I had for example 512 MB RAM is there formula to convert it to n-bit ? this is might be noob question but I'm not good with math :/

Number of Bytes*8? ;) put attention to the prefix for k M G T or ki... Gi... — Hastur, Jun 26 '16 at 21:29
No I want to convert it to n-bit just like the example in first line — user, Jun 26 '16 at 21:31
Your first-line calculation is wrong: the result is ~1 Gigabit (1Gb) or ~128 Megabytes (128MB). — AFH, Jun 26 '16 at 22:16
@AFH I think the OP meant that one gigabyte of RAM can be addressed by a 30-bit pointer, assuming that each RAM location is a byte. — Ben N, Jun 27 '16 at 00:28

Ben N · Accepted Answer · 2016-06-27T14:41:34.233

17

You're looking for a logarithm, a base-two logarithm specifically. Logarithms do the opposite of exponentiation, so if b^x = y, then x = log_b y. 2⁴ = 16, so log₂ 16 = 4.

First, you'll need to figure out how many bytes you have. If your number is in kilobytes, multiply by 2¹⁰. For megabytes, 2²⁰, for gigabytes 2³⁰, et cetera. As you can see, I'm using the powers-of-1024 definitions of these units rather the powers-of-1000 definitions, so one kilobyte here is 1024 bytes. The unambiguous name for 1024 bytes is kibibyte. Anyway, 512 MB is equal to 512 • 2²⁰ = 536870912 bytes.

Now you'll need a scientific calculator. I like Wolfram Alpha, which lets you do base-two logarithms with the log2 function. log2(536870912) produces 29, which makes sense, considering that 512 MB is half of 1 GB, so it takes one less power of two. You can use pretty much any operator imaginable in a Wolfram Alpha expression, so log2(512 * 10^20) works too.

If you get a number with a decimal part, round up. For example, you'd need three bits to address five bytes of RAM, though log2(5) is roughly 2.32.

edited Jun 27 '16 at 14:41

answered Jun 26 '16 at 21:38

Ben N

40,965

6

FYI, Google also evaluates log2(536870912) just fine. – Bob Jun 27 '16 at 03:56
4

Feels like log(536870912) / log(2) could be mentioned in case log2() is unavailable. – u1686_grawity Jun 27 '16 at 07:24
Although it is covered in the linked Wikipedia article, it would improve this answer to add a few words about why you're looking for a logarithm. That way, it can be understood not as this strange mathematical concept, but simply as the inverse operation to exponentiation, which the asker already has a grasp on. – Cody Gray - on strike Jun 27 '16 at 12:03
you can use powershell [math]::Log(536870912, 2). Or echo "l(536870912)/l(2)" | bc -l or python -c 'import math; print math.log(536870912, 2)' – phuclv Nov 20 '18 at 07:55

score 4 · Answer 2 · answered Jun 26 '16 at 23:57

Additionally to what Ben said, I recommend first doing the logarithm of your number without units

log₂512 = 9

And then take units into consideration: sum 10 for kibibytes, 20 for mebibytes, 30 for gibibytes, ...

9 + 20 = 29

And that's it. No need to calculate huge numbers. That's because logarithms have the following properties:

logₙ(a × b) = logₙ(a) +  logₙ(b)
logₙ(aᵇ) = b × logₙ(a)

Therefore,

log₂(512 × 2²⁰) = log₂(512) + 20

However, if you already know log₂(1 GiB) = 30,

log₂(512 MiB) = log₂(1 GiB / 2) = log₂(1 GiB) - log₂(2) = 30 - 1 = 29

Calculating bits of RAM

2 Answers2