This number base converter transforms numbers between different numeral systems including binary, decimal, octal and hexadecimal. Simply enter a number in any base and the tool instantly shows the equivalent values in all other bases. It supports conversions between any combination of bases from 2 to 36. The tool also displays the calculation steps so you can understand how the conversion works. Everything runs in your browser with no server processing needed.
Enter your values to see the result.
255 (decimal) → Binary: 11111111 | Octal: 377 | Hex: FF
The maximum value representable by a single byte in all common bases.
1010 (binary) → Decimal: 10 | Octal: 12 | Hex: A
A binary number converted to all other common bases simultaneously.
1A4 (hexadecimal) → Binary: 110100100 | Decimal: 420 | Octal: 644
Hexadecimal input converted to binary, decimal and octal representations.
A number base, also known as a radix, is the number of unique digits used to represent numbers in a particular numeral system. The base determines both the available digit symbols and the place value of each position in a number. In our everyday decimal system (base 10), we use ten digits from 0 to 9, and each position represents a power of 10 — ones, tens, hundreds, thousands and so on. Other bases follow the same principle but with different digit counts and place value progressions.
The concept of number bases is fundamental to mathematics and computer science. While humans naturally count in base 10, likely because we have ten fingers, computers operate exclusively in base 2 because electronic circuits have two states. Programmers frequently work with hexadecimal (base 16) because it provides a compact, human-readable representation of binary data. Understanding how to convert between bases is an essential skill for anyone working in software development, networking, digital electronics or any field that intersects with computing.
This number base converter takes a number in any supported base and converts it to all other common bases simultaneously. The conversion process works in two stages. First, the input number is converted from its original base to a decimal (base 10) internal representation. Each digit of the input is multiplied by the base raised to the power of its position index, and all the products are summed to produce the decimal value.
In the second stage, the decimal value is converted to each target base by repeatedly dividing by the target base and collecting the remainders. The remainders, read in reverse order, form the digits of the result in the target base. For bases higher than 10, letters A through Z are used as digit symbols for values 10 through 35. The tool supports all bases from 2 to 36 and displays results for binary, octal, decimal and hexadecimal simultaneously.
Programmers use base conversion constantly in their daily work. When debugging network issues, you need to convert between binary and decimal to understand subnet masks and IP address ranges. When working with color values in CSS or graphic design, you convert between hexadecimal color codes and their decimal RGB component values. When dealing with Unix file permissions, you convert between octal notation like 755 and the individual read, write and execute permission bits.
Students studying computer science use base conversion to understand how data is represented at the hardware level. Converting between binary and hexadecimal helps students understand memory addressing, bit manipulation and data encoding schemes. Electrical engineers use base conversion when designing digital circuits, working with truth tables and verifying the output of combinational logic. Network administrators convert between binary and decimal when calculating subnet ranges and verifying network configurations.
All conversion operations happen locally in your browser using JavaScript arithmetic. Your input numbers are never sent to any server, stored in any database, or processed by any third party. The conversion algorithms execute in microseconds and can handle any number within JavaScript's safe integer range without any noticeable delay. There is no file upload, no network dependency and no data collection involved, making this tool completely private and suitable for converting any values including those from sensitive or classified work contexts.
A number base, also called a radix, defines how many unique digits a numeral system uses to represent values. The most common base is base 10 or decimal, which uses ten digits from 0 to 9 and is the system humans use for everyday counting. Base 2 or binary uses only two digits, 0 and 1, and is the foundation of all digital computing since electronic circuits naturally operate in two states. Base 16 or hexadecimal uses sixteen symbols from 0 to 9 and A to F, and is widely used in programming because each hex digit maps directly to four binary digits making it a compact way to represent binary data.
Binary is the fundamental language of all digital computers because electronic circuits operate using two states: on and off, which correspond to the binary digits 1 and 0. Every piece of data stored in a computer, every instruction executed by a processor, and every pixel displayed on a screen is ultimately represented as a sequence of binary digits. Understanding binary is essential for programmers working on low-level systems, embedded devices, network protocols or performance-critical code where bit manipulation provides significant speed advantages. Binary also forms the basis for understanding how data is stored, transmitted and processed at the hardware level.
Converting between number bases involves two main steps. First, convert the input number from its original base to decimal by multiplying each digit by the base raised to the power of its position and summing the results. Second, convert the decimal value to the target base by repeatedly dividing by the target base and recording the remainders in reverse order. For example, to convert the decimal number 255 to hexadecimal, divide by 16 repeatedly: 255 divided by 16 is 15 remainder 15, which gives FF in hexadecimal. This tool automates both steps for any combination of bases.
Four bases are most commonly encountered in programming and computer science. Binary is used for bitwise operations, network masks and understanding data at the hardware level. Octal was historically used in early computing systems and is still used for Unix file permissions where each digit represents three permission bits. Decimal is used for everyday values and user-facing numbers. Hexadecimal is used extensively for memory addresses, color codes in web design, MAC addresses and anywhere binary data needs to be represented compactly since each hex digit encodes exactly four binary bits.
This tool handles numbers within JavaScript's safe integer range which extends up to approximately 9 quadrillion. For most practical purposes including memory addresses, color codes, network addresses and permission values, this range is more than sufficient. The tool validates your input to ensure it contains only valid digits for the selected base and displays a clear error message if the input is invalid or exceeds the supported range. Both integer values and the conversion between any bases from 2 to 36 are fully supported.
Last updated on 2026-09-26 · Written by UtiliaTools