Convert values between Binary, Octal, Decimal, and Hexadecimal in real time with instant copy-ready results.
XConvert's number base converter lets you instantly translate numbers between binary, octal, decimal, and hexadecimal systems. Whether you're debugging low-level code, studying computer science, or working with memory addresses, this tool handles the math so you don't have to.
Step 1: Choose Your Input Base. Select the number system of the value you want to convert — Binary (base 2), Octal (base 8), Decimal (base 10), or Hexadecimal (base 16). The tool validates your input in real time, so you'll immediately know if you've entered an invalid digit for the selected base.
Step 2: Enter Your Number. Type or paste the number you want to convert. For binary, use only 0s and 1s. For octal, use digits 0–7. For decimal, use digits 0–9. For hexadecimal, use digits 0–9 and letters A–F (case-insensitive).
Step 3: View All Base Conversions Simultaneously. XConvert converts your input into all four number bases at once. You'll see the binary, octal, decimal, and hexadecimal representations side by side, making it easy to compare and verify values across systems.
Step 4: Copy Your Result. Click on any converted value to copy it to your clipboard. Use it directly in your code, documentation, or calculations without manual transcription errors.
A number base converter is a tool that translates numerical values between different positional numeral systems. In everyday life, we use the decimal system (base 10), which has ten digits (0–9). Computers, however, operate fundamentally in binary (base 2), using only 0s and 1s to represent all data. Other bases like octal (base 8) and hexadecimal (base 16) serve as convenient shorthand for binary values, making it easier for humans to read and write machine-level data.
Each numeral system uses a different set of symbols and a different positional weight. In decimal, the number 255 means (2 × 10²) + (5 × 10¹) + (5 × 10⁰). In binary, the same value is 11111111, meaning (1 × 2⁷) + (1 × 2⁶) + ... + (1 × 2⁰). In hexadecimal, it's simply FF. The underlying quantity is identical — only the representation changes. Converting between bases requires recalculating these positional weights, which is tedious by hand but instant with a converter.
XConvert's number base converter processes all conversions client-side in your browser. It supports arbitrarily large numbers, handles leading zeros correctly, and provides clean output suitable for direct use in programming languages like Python, JavaScript, C, and Java. The tool is particularly useful alongside the hash generator, which outputs hexadecimal digests that you may need to inspect at the binary level.
| Property | Binary (Base 2) | Octal (Base 8) | Decimal (Base 10) | Hexadecimal (Base 16) |
|---|---|---|---|---|
| Digits Used | 0, 1 | 0–7 | 0–9 | 0–9, A–F |
| Common Prefix | 0b |
0o or 0 |
None | 0x |
| Bits per Digit | 1 | 3 | ~3.32 | 4 |
| Primary Use | Hardware/logic design | Unix file permissions | Human-readable math | Memory addresses, colors |
| Example (decimal 255) | 11111111 | 377 | 255 | FF |
| Readability | Low (long strings) | Medium | High | High (compact) |
| Programming Languages | All major languages | C, Python, JS | Universal | All major languages |
| Grouping Convention | 4-bit nibbles | 3-digit groups | 3-digit groups (commas) | 2-digit bytes |
Debugging and Low-Level Programming. Systems programmers and embedded developers frequently need to convert between hexadecimal memory addresses and binary bit patterns. When examining register values, interrupt vectors, or memory dumps, converting hex to binary reveals individual flag bits and field boundaries.
Understanding Unix File Permissions. Unix/Linux file permissions are expressed in octal notation. The permission 755 means the owner has read/write/execute (7 = 111 in binary), while group and others have read/execute (5 = 101). Converting between octal and binary clarifies exactly which permission bits are set.
Web Development and Color Codes. HEX color codes like #FF5733 are hexadecimal values. Understanding that FF equals 255 in decimal (maximum intensity) helps developers reason about color channel values. Use the color converter for full color model translations.
Networking and Subnet Calculations. IP addresses and subnet masks are fundamentally binary values displayed in decimal (IPv4) or hexadecimal (IPv6). Converting a subnet mask like 255.255.255.0 to binary (11111111.11111111.11111111.00000000) reveals the network/host boundary clearly.
Computer Science Education. Students learning about data representation, Boolean algebra, and digital logic need to convert between bases constantly. This tool provides instant verification of manual calculations, helping learners build confidence and catch errors.
Cryptography and Security Analysis. Hash values, encryption keys, and digital signatures are typically displayed in hexadecimal. Converting these to binary can reveal patterns, and converting to decimal is sometimes needed for mathematical operations in cryptographic algorithms. The hash generator produces hex digests that pair well with this converter.
All the number bases supported by this converter are positional numeral systems. This means the value of each digit depends on its position within the number. Understanding this principle is the key to converting between any bases.
The decimal system that we use daily is base 10. Each position represents a power of 10: the ones place (10⁰ = 1), the tens place (10¹ = 10), the hundreds place (10² = 100), and so on. The number 347 means (3 × 100) + (4 × 10) + (7 × 1) = 347.
Binary (base 2) works identically, but each position represents a power of 2. The binary number 1101 means (1 × 8) + (1 × 4) + (0 × 2) + (1 × 1) = 13 in decimal. Binary is the native language of digital electronics because transistors have two states: on (1) and off (0). Every piece of data in a computer — text, images, video, programs — is ultimately stored as binary.
Octal (base 8) groups binary digits into sets of three. Since 2³ = 8, each octal digit represents exactly three binary digits. The binary number 110 101 converts to octal 65 — each group of three bits maps to one octal digit. This made octal popular in early computing when systems used word sizes that were multiples of three bits (12-bit, 24-bit, 36-bit machines).
Hexadecimal (base 16) groups binary digits into sets of four. Since 2⁴ = 16, each hex digit represents exactly four binary digits (one nibble). The binary number 1111 1111 converts to hex FF. Hexadecimal became the dominant shorthand for binary because modern computers use 8-bit bytes, and each byte is neatly represented by exactly two hex digits. This is why memory addresses, MAC addresses, and color codes all use hexadecimal.
Converting between bases follows a systematic process. To convert from any base to decimal, multiply each digit by its positional weight and sum the results. To convert from decimal to another base, repeatedly divide by the target base and collect the remainders. To convert between binary and hex (or octal), simply group or ungroup the binary digits — no arithmetic needed.
For example, converting hex 2A to binary: 2 = 0010 and A = 1010, so 2A = 00101010. Converting binary 10110 to octal: pad to groups of three (010 110), then 010 = 2 and 110 = 6, giving octal 26. These grouping shortcuts are why hex and octal exist — they make binary data human-readable without complex calculations.
Remove prefixes before entering values. If your number includes a language-specific prefix like 0x (hex), 0b (binary), or 0o (octal), remove it before pasting into the converter. XConvert expects raw digits only.
Use hexadecimal for compact binary representation. If you're working with long binary strings, convert to hex first. A 32-bit binary number becomes just 8 hex digits, making it far easier to read, compare, and communicate.
Verify with known values. When learning base conversion, use landmark values to check your work: decimal 255 = hex FF = binary 11111111, decimal 16 = hex 10 = binary 10000, decimal 10 = hex A = binary 1010.
Group binary digits for readability. When reading binary output, mentally group digits into nibbles (4 bits) from right to left. This makes it easier to spot patterns and convert to hex visually.
Remember that letter case doesn't matter in hex. FF, ff, and Ff all represent the same value (255 in decimal). XConvert accepts any case, but convention in most programming contexts uses lowercase (0xff) or uppercase (0xFF) consistently.
Use this tool alongside the hash generator. When analyzing hash outputs, converting individual bytes from hex to binary can help you understand bit distribution and verify hash properties.
Computers use binary because digital circuits are built from transistors that have two reliable states: on and off. Representing these states as 1 and 0 is the simplest and most error-resistant approach. While it's theoretically possible to build circuits with more states (ternary or decimal), the engineering complexity and error rates increase dramatically. Binary keeps hardware simple, fast, and reliable.
XConvert's number base converter supports very large numbers well beyond the standard 64-bit integer range. The tool uses arbitrary-precision arithmetic in JavaScript, so you can convert numbers with hundreds of digits without overflow or precision loss. This makes it suitable for working with cryptographic values and large hash outputs.
Negative numbers in different bases depend on the representation scheme. In everyday math, you simply convert the magnitude and add a minus sign. In computing, negative integers are typically stored using two's complement representation, where the most significant bit indicates the sign. XConvert converts the absolute value — for two's complement interpretation, you'll need to know the bit width of your system.
Hexadecimal is used because it provides a compact, human-readable representation of binary data. Each hex digit maps to exactly 4 binary bits, so a 64-bit memory address becomes just 16 hex characters instead of 64 binary digits. This makes addresses like 0x7FFF5FBFF8A0 far easier to read, compare, and type than their binary equivalents.
Octal (base 8) uses digits 0–7, with each digit representing 3 binary bits. Hexadecimal (base 16) uses digits 0–9 and A–F, with each digit representing 4 binary bits. Hex is more common in modern computing because it aligns with 8-bit bytes (2 hex digits = 1 byte), while octal was more common in older systems with non-byte-aligned word sizes. Today, octal is primarily used for Unix file permissions.
Read binary numbers from right to left, with each position representing a doubling power of 2. The rightmost digit is the 1s place, then 2s, 4s, 8s, 16s, and so on. For example, binary 1011 = (1×8) + (0×4) + (1×2) + (1×1) = 11 in decimal. Grouping into nibbles (4 bits) from the right makes longer numbers manageable.
XConvert's converter handles integer values. Fractional base conversion is more complex because many simple decimal fractions (like 0.1) have infinite repeating representations in binary. For integer conversions — which cover the vast majority of programming and educational use cases — this tool provides exact results.
The 0x prefix is a convention used in programming languages like C, C++, Java, JavaScript, and Python to indicate that the following digits are hexadecimal. Similarly, 0b indicates binary and 0o indicates octal. These prefixes help compilers and interpreters distinguish between 10 (decimal ten), 0x10 (hex sixteen), and 0b10 (binary two).
CSS color codes like #FF5733 are three hexadecimal byte values concatenated together. FF is the red channel (255), 57 is green (87), and 33 is blue (51). Each pair of hex digits represents one byte (0–255) of color intensity. You can use this converter to understand the decimal values behind any hex color, or use the color converter for full color model support.
Unix file permissions use three sets of three bits: read (4), write (2), and execute (1) for owner, group, and others. Since each set of three bits maps perfectly to one octal digit, octal provides the most compact single-digit representation for each permission group. The permission chmod 755 means owner=rwx (7=111), group=r-x (5=101), others=r-x (5=101).