Base 2 Numeral System
This glossary is far from complete. We are constantly adding math terms.
For instructions on adding new terms, please refer to Math Glossary Main Page
| Base 2 System of Numeration
Also known as binary system of numeration in which only two symbols namely [math]0[/math] and [math]1[/math] are used to express all numbers. The system of numeration most commonly used is is decimal system or base ten in which ten symbols [math]0, 1, 2, 3, 4, 5, 6, 7, 8, 9[/math] are used.The number these symbols represent are well known. |
Examples
To convert any number "[math]n[/math]" (decimal system) to binary system we write [math]n[/math] as sum of powers of [math]2[/math] as
- [math]n=d\cdot2^0+d\cdot2^1+d\cdot2^2+d\cdot2^3+\ldots\;\![/math]
- where [math]d\,\,[/math] can take values [math]0\,\,[/math] or [math]1\,\,[/math].
| Decimal | Binary | Explanation |
|---|---|---|
| [math]0\,[/math] | [math]0\,[/math] | [math]0\cdot2^0[/math] |
| [math]1\,[/math] | [math]1\,[/math] | [math]1\cdot2^0[/math] |
| [math]2\,[/math] | [math]10\,[/math] | [math]1\cdot2^{1}+0\cdot2^0[/math] |
| [math]3\,[/math] | [math]11\,[/math] | [math]1\cdot2^{1}+1\cdot2^0[/math] |
| [math]4\,[/math] | [math]100\,[/math] | [math]1\cdot2^{2}+0\cdot2^{1}+0\cdot2^0[/math] |
| [math]5\,[/math] | [math]101\,[/math] | [math]1\cdot2^{2}+0\cdot2^{1}+1\cdot2^0[/math] |
Start writing the coefficients of powers of 2 from left to right in ascending order.
[math]\begin{align}
7_{10} & = 1+2+4 \\
& = 2^0+2^{1}+2^{2} \\
& = 1\cdot2^0+1\cdot2^{1}+1\cdot2^{2} \\
& = 111_{2}
\end{align}[/math]
[math]\begin{align}
26_{10} & = 0+2+0+8+16 \\
& = 0+2^1+0+2^{3}+2^{4} \\
& = 0\cdot2^0+1\cdot2^{1}+0\cdot2^{2}+1\cdot2^{3}+1\cdot2^{4} \\
& = 11010_{2}
\end{align}[/math]
See also
|
