[basic.numberBase.title]
[basic.numberBase.description]
Decimal - Valid digits: 0-9
Binary - Valid digits: 0, 1
[basic.numberBase.inputs.hint]
Quick Reference Table (0-15)
| [basic.numberBase.bases.decimal] | [basic.numberBase.bases.binary] | [basic.numberBase.bases.octal] | [basic.numberBase.bases.hexadecimal] |
|---|---|---|---|
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 2 | 0010 | 2 | 2 |
| 3 | 0011 | 3 | 3 |
| 4 | 0100 | 4 | 4 |
| 5 | 0101 | 5 | 5 |
| 6 | 0110 | 6 | 6 |
| 7 | 0111 | 7 | 7 |
| 8 | 1000 | 10 | 8 |
| 9 | 1001 | 11 | 9 |
| 10 | 1010 | 12 | A |
| 11 | 1011 | 13 | B |
| 12 | 1100 | 14 | C |
| 13 | 1101 | 15 | D |
| 14 | 1110 | 16 | E |
| 15 | 1111 | 17 | F |
Ergebnisse
Geben Sie Werte ein und klicken Sie auf Berechnen, um das Ergebnis zu sehen.
Theory & Formula
What are Number Bases?
A number base (or radix) is the number of unique digits used to represent numbers in a positional numeral system. Different bases are used in different contexts, especially in computer science.
[basic.numberBase.theory.commonBases]
- [basic.numberBase.bases.binary] (Base 2): [basic.numberBase.theory.binaryDescription]
- [basic.numberBase.bases.octal] (Base 8): [basic.numberBase.theory.octalDescription]
- [basic.numberBase.bases.decimal] (Base 10): [basic.numberBase.theory.decimalDescription]
- [basic.numberBase.bases.hexadecimal] (Base 16): [basic.numberBase.theory.hexDescription]
[basic.numberBase.theory.conversionMethod]
[basic.numberBase.theory.toDecimal]
\(N_{base} = d_n \times base^n + d_{n-1} \times base^{n-1} + \ldots + d_1 \times base^1 + d_0 \times base^0\)[basic.numberBase.theory.fromDecimal]
Divide the decimal number by the target base repeatedly, collecting remainders. Read the remainders from bottom to top.
Example: Convert Binary to Decimal
Convert 1011₂ to decimal:
\(1011_2 = 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\)\(= 8 + 0 + 2 + 1\)\(= 11_{10}\)