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### What is a Terabyte?

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Date: 03/24/2002 at 20:58:06
From: Taina Rivera
Subject: What is a terabyte?

What is a terabyte?  I know a gigabyte is one billon bytes.
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Date: 03/24/2002 at 22:36:43
From: Doctor Twe
Subject: Re: What is a terabyte?

Hi Taina - thanks for writing to Dr. Math.

That's a good question, and it doesn't have a simple answer.

When measuring memory in a computer system, we use powers of 2 to
define the "metric prefixes" like kilo-, mega-, giga-, etc. We say:

1 kilobyte (kB) = 2^10 = 1,024 bytes
1 megabyte (MB) = 2^20 = 1,024 kB = 1,048,576 bytes
1 gigabyte (GB) = 2^30 = 1,024 MB = 1,073,741,824 bytes
1 terabyte (TB) = 2^40 = 1,024 TB = 1,099,511,627,776 bytes
:

Each prefix is 2^10 = 1,024 times the previous value. (In decimal and
in the metric system, each prefix is 10^3 = 1,000 times the previous
one.) This works well with system memory because memory addressing
capacity is closely related to the number of bits in the address.
Every additional bit doubles the capacity, and every 10 bits
multiplies it by 1,024.

Hard drive capacity is not as tightly related to the number of bits,
however. The physical arrangement of the data on the disks means that
the total capacity is often not a nice round number in binary. In
order to make their hard drives sound larger, some manufacturers use
the "decimal" values of the prefixes instead. A hard drive with 40 GB
capacity (as defined above) actually stores 42,949,672,960 bytes. To
make it _seem_ bigger than its competitor's 40 GB drive, a company
might market its drive as 42.9 GB - which makes it sound as if it's
7.25% larger.

Thus a teraabyte might mean:

1,000,000,000,000 bytes (usually with hard drives)
1,099,511,627,776 bytes (usually with system memory)

or even "improper combinations" like:

1,024,000,000,000 bytes (1 billion kB)
1,048,576,000,000 bytes (1 million MB)
1,073,741,824,000 bytes (1 thousand GB)

To clarify the confusion and multiple definitions, in 1998 the
International Electrotechnical Commission (IEC) proposed a different
set of prefixes for the binary multiples. Instead of "kilobytes" we'd
use "kibibytes," instead of "megabytes" we'd use "mebibytes," and so
on. Unfortunately, because of the widespread use of kilobytes,
megabytes, etc. in the industry and in popular culture, the IEC's
proposals have not caught on and are not in common use.

"Prefixes for binary multiples" Web page at:

http://physics.nist.gov/cuu/Units/binary.html

I hope this helps! If you have any more questions, write back!

- Doctor TWE, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Calculators, Computers
Middle School Terms/Units of Measurement

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