Binary numeral system: Difference between revisions
imported>Aleksander Stos mNo edit summary |
imported>Pat Palmer m (Binary numeral system moved to Binary number system: In twenty years of computer science work, I have never heard it called "numeral" instead of "number", although someone in Wikipedia did it that way. So I am changing it to number because I think that is more what people expect.) |
Revision as of 09:05, 28 April 2007
The binary numbering system (also referred to as base-2, or radix-2), represents numbers using only the digits 0 and 1. This is in contrast with the more familiar decimal system (a.k.a. base-10, radix-10) which uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. In the decimal system, each digit position represents a power of ten. The number represents the value consisting of one set of tens (), and no sets of ones (). Equivalently in the binary numbering system each digit position represents a power of two. The same number, represents the value consisting of one set of twos () and no sets of ones () which is represented by the number 2 in the decimal system. When the numbering system used for a number is in question, one can write the radix as a subscript to the number as done in the following table.
Decimal | |
---|---|
Binary |
Because the number of digits in the binary representation of a value can grow quickly, binary values are often represented in the hexadecimal numbering system (base-16), which uses the digits 0 through 9, followed by the letters A through F to represent the values ten, eleven, twelve, thirteen, fourteen, and fifteen.
Decimal | Binary | Hexadecimal |
---|---|---|
0 | 0 | 0 |
1 | 1 | 1 |
2 | 10 | 2 |
3 | 11 | 3 |
4 | 100 | 4 |
5 | 101 | 5 |
6 | 110 | 6 |
7 | 111 | 7 |
8 | 1000 | 8 |
9 | 1001 | 9 |
10 | 1010 | A |
11 | 1011 | B |
12 | 1100 | C |
13 | 1101 | D |
14 | 1110 | E |
15 | 1111 | F |
16 | 10000 | 10 |