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Why actual Hard Disk Space does not match the size indicated on the Drive November 11, 2009

Posted by General Zod in Tech.
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A long time ago, when I was working IT for a financial company, one of the executives had called me up to his office to chat.  There wasn’t anything strange in this at the time… it was a fairly new and casual corporation, and I frequently found myself in the upstairs offices having carefree conversations about family, cars, aircraft, and investment strategies with several of the executives.

It seems that the executive had purchased a new 200 GB hard disk for one of his home computers the previous evening.  He said that he had been determined to install it himself, and I told him that I had every confidence in his success.  Continuing his tale of the previous evening, he informed me that he did get the drive installed, partitioned, and formatted… but had one question.  The box that the drive had come in indicated that the drive was 200 GB in size, but he was a bit perplexed as to why the drive was only recognizing 186 GB of space.  He had thought to call the manufacturer’s support line to find out what happened to the other 14 GB of space, but decided to ask me about it before doing so.

Too many people are confused by this phenomenon.  So here is the explanation.

The first thing you have to understand is the difference in how a computer does math compared to a human being.

People (at least all the people that I’ve met) use Base-10 math.  We learned to count that way as children (mainly because we were counting on our fingers).

10^N Operations:

10^0 = 1
10^1 = 10
10^2 = 100
10^3 = 1,000
10^9 = 1,000,000,000
etc…

Computers counts in Base-2 math because the “fingers” they count on are bits.  A bit is the smallest increment of data on a computer which can hold a “value” of 0 or 1.  Period.  (If that doesn’t work for you, then think of it in terms of On/Off… or… True/False.)

2^N Operations:

2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^10 = 1,024 (bytes = 1 KB)
2^20 = 1,048,576 (bytes = 1 MB)
2^30 = 1,073,741,824 (bytes = 1 GB)
etc…

So what does this have to do with the price of beans?

People tend to round their numbers up to factors of 10.  It’s human nature.  We all do it… and so do the disk manufacturers.  When they indicate that a drive has 1 GB of disk space on it, what they are really saying is that the drive consists of approximately 1,000,000,000 bytes.  So they don’t actually mean “1 GB” so much as they should be labeling the drive as “1 billion bytes”.

Following this logic, we deduce that the above mentioned 200 GB hard disk has an amount of space equal to the following.

Indicated Disk Space =
200 x 10^9 = 200,000,000,000 bytes.

So how does your computer see this hard disk?  It adds up all of the available bytes of space, and then calculates the “actual” size of the drive using Base-2 math.  The results are as follows.

Reported Disk Space =
200,000,000,000 bytes / 2^30 = 186.26 GB

So technically, the 14 GB of space weren’t really missing.  In truth, it’s the disk manufacturer that is misreporting the true size of the drive by using GB as short-hand for 1 billion even.

Comments»

1. Louis - March 31, 2012

Always wondered about it, thanks for the great explanation!!!

2. Cam - July 21, 2012

Still techinally false advertising they use computers in the process of procduction surely they can use a computer to work the correct space. Good information though


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