The following prefixes are commonly used for the measurements discussed in this course. For a full list of all 20 prefixes recognised by the National Institute of Standards and Technology (NIST), look at their web page, The Twenty SI Prefixes.
| Exponent | Decimal Value | ||||
|---|---|---|---|---|---|
| Name | Prefix | Decimal | Binary | Decimal | Binary |
| Quadrillion | Peta | 15 | 50 | 1,000,000,000,000,000 | 1,125,899,906,842,624 |
| Trillion | Tera | 12 | 40 | 1,000,000,000,000 | 1,099,511,627,776 |
| Billion | Giga | 9 | 30 | 1,000,000,000 | 1,073,741,824 |
| Million | Mega | 6 | 20 | 1,000,000 | 1,048,576 |
| Thousand | Kilo | 3 | 10 | 1,000 | 1,024 |
| Thousandth | Milli | -3 | 0.001 | ||
| Millionth | Micro | -6 | 0.000,001 | ||
| Billionth | Nano | -9 | 0.000,000,001 | ||
| Trillionth | Pico | -12 | 0.000,000,000,001 | ||
| Quadrillionth | Femto | -15 | 0.000,000,000,000,001 | ||
Computer memories are typically built with capacities that are powers of two because it makes address decoding more efficient than using decimal values. Because 210 (1,024) is approximately equal to 103 (1,000), the prefixes orginally adopted for the various powers of ten have also been adopted for the approximately-equivalent powers of two. That is why there are two "Exponent" columns and, correspondingly, two "Decimal Value" columns.
But note that disk memories do not follow this convention. A 1 gigabyte disk would contain just 1,000,000,000 bytes, not 1,073,741,824 bytes. Cynics would claim that disk manufacturers are overstating their drives' capacities compared to main memory manufacturers. But it's also true that there is nothing in the organizational structure of disks that would suggest using powers of two, the way there is for main memory.
Because of the confusion over whether a particular prefix refers to a power of two or not, the International Electrotechnical Commission (IEC) adopted a distinct set of prefix names for the power of two quantities. For example, a "gibi" ("gigabinary") is used for 230 and "giga" is reserved for 109. However, these binary prefixes are not widely used yet, and the power of ten prefixes continue to be used widely in both decimal and binary contexts. The NIST gives a full list of the binary prefixes and tells how to pronounce them.
You do not need to memorize the exact decimal values of the binary powers of two.
Fractional binary numbers do not typically use the scientific prefixes the way the integer values do, and thus are not listed here.
In this course the most common use of fractional decimal numbers will be when discussing units of time. Thus, one nanosecond is one billionth of a second, which is 1 * 10-9 second. Remember the reciprocal relationship between numbers with positive and negative exponents: A clock with a frequency of one Gigahertz has a period of one nanosecond. A clock with a 2 nanosecond period has a frequency of 0.5 Gigahertz, which is 500 Megahertz.
Also see the Powers of Two web page.