Number Base Converter
Free online number base converter. Instantly convert binary to decimal, decimal to binary, hex to decimal and 15 more base combinations. Perfect for programming, engineering and computer science.
About this tool
Convert binary to decimal, decimal to binary, hex to decimal and any other base pair from 2 to 20 instantly. Maximum precision, zero delays.
Technical Notes
Key technical details about the bases supported by this converter:
- Binary (Base 2)Uses only 0 and 1 — the foundation of all digital computing and hardware logic.
- Octal & HexadecimalCompact representations used in memory addressing, file permissions, and color codes.
- Decimal (Base 10)The standard human-readable system used as the primary interface for all conversions.
- Advanced BasesSupport for bases 11–20, including vigesimal (base 20) used by ancient civilizations.
Common Applications
Number base conversion is a fundamental skill in computer science and engineering. Common real-world uses include:
- Software DebuggingDebug binary and hexadecimal representations in embedded systems and low-level programming.
- Educational PracticePractice numeral system conversions for computer science and digital electronics coursework.
- Systems ProgrammingConvert memory addresses between octal, decimal and hexadecimal in assembly programming.
- Historical ResearchExplore historical numeral systems such as vigesimal for academic and mathematical research.
How to use
Enter Number
Type or paste the number you want to convert in the 'Number' field.
Select Bases
Choose the source base (From) and the target base (To) from the dropdown menus.
Copy Result
The converted number will appear instantly in the result area for you to copy.
Supported Numeral Systems
Learn about the 19 number bases supported by this converter and their functions:
Uses only digits 0 and 1. The fundamental base of all digital computing, integrated circuits, and Boolean logic.
Uses digits 0, 1, and 2. Applied in three-state computing architectures and information theory.
Uses digits 0 through 3. Commonly used in genetic data representation (DNA: A, C, G, T) and signal transmission.
Uses digits 0 through 4. Historical numeral system based on counting five fingers on one hand.
Uses digits 0 through 5. Used in number theory studies and ancient counting systems.
Uses digits 0 through 6. Applied in theoretical mathematical analysis and calendar counting.
Uses digits 0 through 7. Popular in computing for grouping sets of 3 bits (e.g. Unix file permissions 755).
Uses digits 0 through 8. Applied in specific mathematical algorithms and numerical analysis.
Uses digits 0 through 9. The standard numeral system adopted by humanity for daily counting and commerce.
Uses digits 0 through 9 and the letter A. Used in theoretical mathematics and validation algorithms.
Uses digits 0 through 9 and A, B. Valued for having many divisors (2, 3, 4, 6), used in clocks and dozens.
Uses digits 0 through 9 and A, B, C. Employed in number theory research and cryptography.
Uses digits 0 through 9 and A through D. Intermediate system for positional notation studies.
Uses digits 0 through 9 and A through E. Applied in computational logic and auxiliary numeral systems.
Uses digits 0 through 9 and A through F. Essential in computing for memory addresses, web colors (#HEX), and bytes (8 bits = 2 hex digits).
Uses digits 0 through 9 and A through G. Used in advanced number theory and algebra studies.
Uses digits 0 through 9 and A through H. Applied in abstract algebra and experimental numeral systems.
Uses digits 0 through 9 and A through I. Theoretical positional system in cryptography and mathematics.
Uses digits 0 through 9 and A through J. Historical system used by Mayans and Aztecs, based on 20 fingers and toes.
Learn the Calculation Behind Each Conversion
This converter shows the result of the calculation automatically. To see the step-by-step and understand the method behind each conversion, select one of the four guides below:
Add up the powers of 2 for each bit, or use the doubling method to reach the base-10 value without writing down any powers.
Divide by 2 repeatedly and read the remainders from the bottom up to assemble the sequence of bits.
Multiply each digit by its power of 16, or apply successive multiplication to avoid calculating powers altogether.
The shortest conversion of all: swap each digit for its block of 4 bits, with no arithmetic involved.
Questions & Answers
Binary ↔ Hexadecimal. Hexadecimal is a compact representation of binary: each hex digit maps exactly to 4 binary digits (nibble). For example, 0xFF = 11111111 in binary = 255 in decimal.
Enter the binary number in the input field, select Base 2 as the source, and Base 10 as the target. The result appears instantly — no button press needed.
Hexadecimal is used for memory addresses, color codes (#RRGGBB), error and status codes (e.g. 0x80070005), network MAC addresses, and raw byte values in debugging tools and hex editors.
Yes. This tool supports safe integers up to 2⁵³ - 1 (about 9 quadrillion in decimal). For most practical uses in programming and education, this limit is never reached.