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Binary vs. Decimal Capacity Measurements

Computer measurements are expressed in both binary and decimal terms, often using the same notation. Due to a mathematical coincidence, the fact that 2^10 (1024) is almost the same number as 10^3 (1000), there are two similar but different ways to express a megabyte or a gigabyte. This phenomenon, and the general problems it causes, are discussed in detail in this fundamentals section. I also discuss there how and why I have begun using alternative measurement notations for binary numbers.

The problems with binary and decimal are probably more noticed in the area of hard disk capacity than anywhere else. Hard disk manufacturers always use decimal figures for their products' capacity: a 72 GB hard disk has about 72,000,000,000 bytes of storage. However, hard disk makers also use binary numbers where they are normally used--for example, buffer capacities are expressed in binary kilobytes or megabytes--but the same notation ("kB" or "MB") is used as for decimal figures. Hard disks are large, and larger numbers cause the discrepancy between decimal and binary terms to be exaggerated. For example, a 72 GB hard disk, expressed in binary terms, is "only" 67 GB. Since most software uses binary terms, this difference in numbers is the source of frequent confusion regarding "where the rest of the gigabytes went". In fact, they didn't go anywhere. It's just a different way of expressing the same thing.

This is also the source of much confusion surrounding 2.1 GB hard disks (or 2.1 GB hard disk volumes) and the 2 GB DOS limit on partition size. Since DOS uses binary gigabytes, and 2.1 GB hard disks are expressed in decimal terms, a 2.1 GB hard disk can in fact be entirely placed within a single DOS partition. 2.1 decimal gigabytes is actually 1.96 binary gigabytes. Another example is the BIOS limit on regular IDE/ATA hard disks, which is either 504 MB or 528 MB, depending on which "MB" you are talking about.

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