Binary and Decimal Byte Equivalents

Binary and Decimal Byte “Equivalents”

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It is an interesting coincidence that every tenth power of two is approximately equal to every third power of ten. This has resulted in two different definitions of these numbering systems. The terms Kilobyte, Megabyte, Gigabyte, etcetera can mean either of two different things depending on the context in which it is used. Obviously this can, and often does, result in confusion, especially in respect to hard disk size measurements, where both measurements are often used.

Name	Abbr.	Binary Power	Binary Value	Decimal Power	Decimal Value
Kilobyte	KB	210	1,024	103	1,000
Megabyte	MB	220	1,048,576	106	1,000,000
Gigabyte	GB	230	1,073,741,824	109	1,000,000,000
TeraByte	TB	240	1,099,511,627,776	1012	1,000,000,000,000

We define one megabyte as 10⁶ or one million bytes (1,000,000)
and one gigabyte as 10⁹ or one billion bytes (1,000,000,000)       

This is the industry standard, and all major disk drive manufacturers employ this definition.

Capacity Calculations

Different applications like FDISK, CHKDSK, Windows, BIOS, etc., use different methods and numbering systems to calculate hard drive capacities. The two most common numeric representations of the hard drive capacity are presented in the base 10 (decimal) and base 2 (binary) numbering systems. The basic formula to calculate the capacity of a drive is:

Cylinders * Heads * Sectors * 512 (bytes per sector)

This formula calculates a number representing the total number of bytes (characters) that can be stored on the hard drive. This is a decimal number, to convert this number to the decimal equivalent of the binary Megabytes (MB) or Gigabytes (GB), this value must be divided by the decimal value of a binary MB or GB. The decimal equivalent of 1 MB (2²⁰) is 1,048,576 and 1 GB (2³⁰) is 1,073,741,824. Example for a 3.5 GB hard drive:

6,800 * 16 * 63 * 512 = 3,509,452,800 bytes or 3.5 GB using 10⁶ or decimal values

The equivalent in binary MB is 3,509,452,800 / 1,048,576 = 3,346 MB

The equivalent in binary GB is 3,509,452,800 / 1,073,741,824 = 3.268 GB

Capacity Limitations

Achieving full capacity of today’s Gigabyte giants at 8.4 GB and above, can be quite problematic. There are limitations at these capacity points due to a combination of Hardware, BIOS, and Operating System constraints. These barriers may require the use if installation procedures utilizing specialized software, upgrades to hardware or the BIOS to successfully install a drive exceeding these barriers.

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