# Fri, 28 Aug 2009Snow Leopard's new maths

## All about exponential counting and numbers in Mac OS X 10.6

I did OK in maths. Took a year of calculus in college. Got a B and two A’s, if I recall correctly. (It’s all about getting a good professor.) But maths is not my favourite subject, and if you were to ask me to do a quadratic equation today, I’d give you the lemon face.

This is my roundabout way of saying that some of the maths Apple uses in Mac OS X has changed in Snow Leopard. Particularly, the method Mac OS X uses to describe a file's size. It has to do with how you define a kilobyte, megabyte, and gigabyte.

Believe it or not, these words have had two meanings for a long time. The first meaning relates to computer science. Everything in computer science is about exponential counting. Like this:

Do those numbers look familiar? There’s a reason the iPhone comes in 16GB and 32GB models, and the original Mac came with 128K of RAM and the model after that had 512K.

Now think about this amount: 1024MB of RAM. That’s what we could call 1GB. Because to think in exponential terms, one gigabyte should be made up of 1024 megabytes.

But here’s the catch—and the source of the second meaning for those terms. Most non-computer types don’t think in terms of 1024s. They think in terms of nice, round numbers. And 1000 is a nice, round number.

So you’ve got two groups, each using the same word to mean different things mathematically. Madness! Which is why when you go to your Mac, select your hard-drive icon, and choose Get Info, you’ll see that your “250GB hard drive” claims to have a capacity of 238GB. Which is it?

There are, believe it or not, now two sets of entirely different terms for these two ways of thinking. For example, a gigabyte, or GB, is now defined as 1,000 bytes cubed, or 1,000,000,000 bytes.

A gibibyte, or GiB, is equal to 1024 bytes cubed, or 1,073,741,824 bytes. (The same rules apply for megabyte and mebibyte, which are defined as 1000 bytes squared and 1,024 bytes squared, respectively.)

Wake up, you in back! Because here’s where Snow Leopard comes in. In previous versions of Mac OS X, Apple used the 1024^3 definition of GB. Rather than keep that maths and start calling it GiB, Apple has started using the 1000^3 definition.

That's why one of the QuickTime movies we use in our Speedmark tests, weighing in at 252,916,507 bytes, appeared as 241.2MB in Leopard but as 252.9MB in Snow Leopard.

The file hasn’t gotten bigger. It’s the same number of bytes. It’s just a different kind of megabyte being used to measure it now. (And in terms of us regular human beings who haven’t cracked a calculus book since the spring of 1993, it makes more sense—a long number that starts in 252,916 should be 252.9 MB. Dividing by nice, round numbers is easy!

For those of you who can divide by 1024 in your heads, my apologies. You can still calculate things in mebibytes and gibibytes if you want. But you won’t have the Get Info window to kick around anymore.

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William said on Fri, 28 Aug 2009

Does anybody know why have they changed it? I'm just curious

Tim Scales said on Fri, 28 Aug 2009

This is apparently Macworld UK, can you please not use the hideous word "math" instead of "maths".

David said on Fri, 28 Aug 2009

I think it makes a lot of sense to do it this way. Well done Apple!

Fred said on Fri, 28 Aug 2009

Your explanation is a bit strange to me. Most branches of science are based on decimal numbers so a giga. anything is 10^9, at least ever since the Americans hijacked billion to to mean 1000 million rather than a. million million. It is only computer scientists that use this peculiar 1024 equls 1000 which comed from calculating in binary. IMHO Apple are right to break away from this

Funny said on Fri, 28 Aug 2009

I love the way everyone gets so fiercely destructive about any articles that have ANY connection in ANY way to do with America, 'this is england, why dont you write in english' as if running a website was so easy you should also proof every single article you publish, probably written by americans and make sure there are no minute references to america, so we can pretend they were written by brits, do some work and stop complaining, and if you think you can do so much better start your own mac site, gimps....

Beyonce my wildest dreams said on Fri, 28 Aug 2009

@Tim Scales: WTF? Without input from Macworld.com, there would be NO Macworld mag or website in the UK.

Peter C said on Fri, 28 Aug 2009

It now says maths William.

Fred said on Fri, 28 Aug 2009

If you don't mind your children writing nite and lite, color and theater then fine, don't complain about American spellings creeping into this UK site. But for most of us that is not an acceptable option.

@Fred said on Fri, 28 Aug 2009

Then don't let them on the Internet. Especially if they're going to grow up like you and make pedantic comments on forums. What's wrong with American spelling anyway? racist ;-)

@Fred said on Fri, 28 Aug 2009

Then p**s off elsewhere. Go back to the Daily Mail forums or something. Most of us just want the information and to chat about it - we don't mind if it comes from the UK or US. The Interweb is global, or hadn't you noticed.

Fred said on Fri, 28 Aug 2009

I see all the bigoted flamers don't have the courage to sign their vitriol. Since when were the citizens of the USA defined as a race?? Ignoramus. As for the Daily Mail, the Daily Mail and arguments about spelling don't quite go together. The issue is not about one culture being better than anther, but about losing cultural identity because the small are crushed by the big, or are you so insensitive that this doesn't matter to you?

Christiaan said on Fri, 28 Aug 2009

I'm with you Fred.

P said on Sat, 29 Aug 2009

The "1000 method" of counting GB was made up by marketing men to make hard disk drives look bigger in the marketing material. Look at the big number the digits at the front are bigger lets just use that to sell more product.

Chris Mills said on Mon, 31 Aug 2009

I'm with Fred and Tim Scales too. I don't read the Daily Mail (I'd much rather read the Guardian), but I believe in the preservation of English in its British form.

Chris Mills said on Mon, 31 Aug 2009

and P, the SI definition of 1kB is 10^3 bytes, 1 MB 10^6 bytes 1 GB 10^9 bytes and 1 TB 10^12 bytes.

So it wasn't made up by marketing men, it is the SI

@funny said on Tue, 01 Sep 2009

Reading your illiterate rant I see why you aren't bothered. It isn't to do with America per se, it is to do with basic English literacy. Which you lack.

Eddie said on Tue, 01 Sep 2009

I've often commented on this forum that, while it purports to be MacWorld UK, they simply lift stories off the Macworld US site and stick it on here apparently without even reading it. It doesn't cost much to do it right, does it?
And I usually get the knuckle draggers complaining as well.

Peter said on Tue, 01 Sep 2009

**sigh**

Anyways, this means that Apple products are now incompatible with THE INTERNET! Seeing as most websites refer to files with the "old megabytes" (as you call it) this is going to cause more confusion than it removes. I hope you can turn it off somewhere **fiddles around in system files**

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