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Understanding Hard Disk Drive Sizes

 

Many people ask why their hard drive is not as big as it should be when they check  in Windows. The simple answer is that the hard drive manufacturers quote the size of a gigabyte as less than that quoted by Windows. Usually the prefix "giga" means 109, or 1,000,000,000; so a gigawatt of energy is 1,000,000,000 watts (that's a lot of light bulbs). This is the method that hard disk drive (HDD) manufacturers quote to give you the size of their hard drives.

As most people are aware, computers are digital devices and therefore all data is in binary format. This is base 2, as opposed to base 10 that we are used to.  Basically, this counts with 0 and 1 only so counting to 10 in binary goes: 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010. In base 10 each digit in a number from right to left represents an increase by 10, with base 2 it represents an increase by 2. So multiplying the right most binary digit by 1, then the next by 2, the next by 4, the next by 8, etc. will convert it to decimal. So the binary number 1010 in decimal is (0x1)+(1x2)+(0x4)+(1x8) this all gives you an answer of 10. Wikipedia gives a good explanation of binary here.

The binary number 100000000 is equivalent to 256 in decimal, 1000000000 is 512 and 10000000000 is 1024. You may recognise these numbers as common memory sizes. This is because computers are digital and use the binary system, so just as 1000 is a nice round number in decimal to us, 256, 512 and 1024 are nice round numbers for computers. This has lead the industry to calling kilobyte as 1024 bytes, a megabyte as 1024 kilobytes, and a gigabyte as 1024 megabytes. This makes a gigabyte 1,073,741,824 bytes. Now if we compare that to the 1,000,000,000 bytes that the HDD manufacturers use, you can see that there is over a 7% difference! Therefore Windows will report the hard disk as being approximately 7% smaller than the hard drive manufacturer's quoted size. This will get worse when the terabyte hard drives are available, the size difference will be almost 10%. 1 terabyte will be quoted by HDD manufacturers as 1,000,000,000,000 bytes whereas Windows will quote it as 1,099,511,627,776 bytes.

OK, so who is right? How many bytes are there in a gigabyte? The real answer is both definitions are right. The International System of Units (SI), says that 1,000,000,000 is correct; whereas the International Electrotechnical Commission (IEC) says that 1,073,741,824 is correct. In computing the latter is the most recognised, but as both are correct you can't accuse the hard drive manufacturers of fixing the figures!

Another factor that can mean you have slightly less space on your HDD than quoted is because the file system that your computer puts on the hard drive takes up space which is not available for use for storing data. If you imagine your hard drive is a field of a given size, and you want to keep sheep in it. Before you can keep those sheep in it, you need to build a fence around the outside to prevent you from losing the sheep and not being able to find them later. This fence actually takes up space in your field, effectively reducing the storage space slightly. Hard drives are the same, they need to be formatted to put a file system on so data can be found again. The way the file system works is like an index in a book, the computer can use it to look up where specific data is when it needs it. This takes up space, and is therefore not reported as useable space by Windows. The actual amount of space this takes up is negligible compared to the difference in quoted sizes of gigabytes, so can effectively be ignored.


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Useful Resources

Wikipedia Binary Information
Wikipedia Gigabyte Definition
Binary-Decimal Conversion