Computers store information as binary digits. We frequently explain it like a light switch. A switch can be “on” or “off”. So that switch can store two values. We represent these as numbers. A zero is “off” and a one is “on.” This is a bit.

If we put two bits together, we can store up to four values (00, 01, 10, 11). If we put three bits together, we can store eight values (000, 001, 010, 011, 100, 101, 110, 111). Every time we add a bit, we double the number of values we can store. Mathematically, we can represent this with exponents. Given n bits, we can store 2ⁿ different values. A collection of eight bits (with a possible 256 values) is a byte.

So far, so good. Here’s where you need to pay attention, though. If you have 2¹⁰ bytes, that’s 1,024 bytes. We call that a kilobyte. It’s pretty close to 1,000, and we frequently round it off to say a kilobyte is “about a thousand bytes.” But nobody talks about kilobytes anymore. They’re not big enough. A megabyte is 2²⁰ bytes, or 1048576. That’s about a million bytes. But it’s not as close to a million as a kilobyte is to a thousand. A megabyte is actually 4.8% larger than a million bytes. And a kilobyte is only about 2.4% larger than a thousand bytes.

As it turns out, the larger the numbers get, the more the numbers deviate. A gigabyte is 2³⁰ bytes. That’s 1073741824 bytes, which is 7.4% larger than a billion bytes.

Who cares? Well, Seagate cares, for one. The hard drive manufacturer sold hard drives as having, for example, 80 gigabytes of storage space. In reality, they only had 80 billion bytes of storage space. That means they were shortchanging their customers by 7% according to the standard definition of “gigabyte.” They were sued in California, and just settled what became a class action lawsuit.

Under the terms of the agreement, if you purchased a Seagate hard drive between March 22, 2001 and January 1, 2006, you are entitled to a cash settlement of 5% of the price you paid for the drive (minus taxes and rebates). If you purchased a drive between January 1, 2006 and September 26, 2007, you are entitled to a software settlement, which includes a $40 hard drive maintenance and backup utility from Seagate.

Details are on the Seagate Hard Drive Settlement web site. The deadline to submit claims is March 10. 2008.