Convert numbers simultaneously between Binary (Base 2), Octal (Base 8), Decimal (Base 10), Hexadecimal (Base 16), and custom bases (2 to 36).
Type any value in the input boxes above to convert.
A web developer styling a CSS color theme converts RGB values (255, 105, 180) into hex code #FF69B4. A computer architecture student inspecting memory register dumps translates hexadecimal address 0x7FFF into binary bits 0111 1111 1111 1111. A Unix system administrator setting file permissions converts octal 755 into read-write-execute bitmasks rwxr-xr-x.
A number base (also called a radix) specifies the number of unique digit symbols used to represent values in a positional numeral system. Everyday human arithmetic uses the decimal system (base 10) with ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Digital hardware operates on transistor voltage states represented by the binary system (base 2) using two digits: 0 and 1. To compress long binary strings into human-readable code, computer scientists use octal (base 8) and hexadecimal (base 16). Hexadecimal uses digits 0-9 plus letters A-F (where A=10, B=11, C=12, D=13, E=14, F=15). This tool converts numbers across binary, octal, decimal, hexadecimal, and custom bases up to base 36. The following sections explain division-remainder algorithms, positional notation expansions, and computer system applications.
When you type a value into any input field, the engine parses the input string into a 64-bit BigInt decimal value, then re-encodes that integer into all target bases.
1. Base B to Decimal (Positional Notation Expansion):
A number string d_k ... d₁ d₀ in base B evaluates to decimal via:
Decimal = ∑ (d_i × Bⁱ) for i = 0 to k.
Example: 1A3₁₆ = (1 × 16²) + (10 × 16¹) + (3 × 16⁰) = 256 + 160 + 3 = 419₁₀.
2. Decimal to Base B (Division-Remainder Algorithm):
Repeatedly divide the decimal number by base B, record integer remainders, and write remainders in reverse order:
Example: Convert 255₁₀ to Binary (base 2):
255 ÷ 2 = 127, rem = 1
127 ÷ 2 = 63, rem = 1
63 ÷ 2 = 31, rem = 1
...
Result in reverse order: 11111111₂.
3. Hexadecimal 4-Bit Alignment:
Each hex character maps to a 4-bit binary nibble (e.g. F = 1111, A = 1010). Thus FA₁₆ = 11111010₂.
Software engineering and debugging. Programmers read binary memory dumps, network packet payloads, and assembly language instructions formatted in hexadecimal.
Web development and CSS styling. Front-end developers convert 8-bit RGB color channels (0 to 255) into 6-character hexadecimal color strings (e.g., rgb(255, 255, 255) → #FFFFFF).
Linux system administration. Unix file permission modes (e.g. chmod 777 or chmod 644) are specified in octal notation representing user, group, and world permissions.
Network engineering and IPv4/IPv6 addressing. Network engineers convert IP subnets and MAC addresses between dotted-decimal (192.168.1.1), binary bitmasks, and hexadecimal IPv6 notation.
Type into any box (Binary, Octal, Decimal, Hex, or Custom). All other fields update instantly in real time.
Use the Custom Base dropdown to test non-standard bases like Base 3 (ternary), Base 12 (duodecimal), or Base 36 (alphanumeric hash codes).
For prime factor decomposition of decimal values, use our Prime Factorization Calculator. For logarithmic conversions, use our Logarithm Calculator.
The conversion engine executes client-side in JavaScript using BigInt parsing and toString(radix) methods. Conversions evaluate in sub-millisecond time.
| Feature | This Tool | Hand Division | Scientific Calculator |
|---|---|---|---|
| Bases Supported | Bases 2 to 36 | Manual calculation | BIN, OCT, DEC, HEX |
| Simultaneous Display | All bases simultaneously | One target base | One mode at a time |
| Division Steps | Division-remainder chain | Manual paper steps | Not listed |
| Bitwise Formatting | 8-bit, 16-bit, 32-bit paddings | Manual padding | Hardware mode |
| Privacy | Client-side browser | Paper | Local device |
| Cost | Free | Free | Free |
Bases higher than 10 require extra symbol characters beyond 0-9. Base 36 uses digits 0-9 (10 symbols) plus English letters A-Z (26 symbols), totaling 36 unique characters.
A nibble is a 4-bit binary aggregation (half a byte). Since 2⁴ = 16, one hexadecimal digit represents exactly one nibble.
Yes. Fractional components are converted by repeatedly multiplying by 2 and extracting integer bits.
Prime Number Checker — Tests primality of any integer using trial division.
GCD Calculator — Computes greatest common divisors using the Euclidean algorithm.
LCM Calculator — Computes least common multiples for 2+ numbers.