Base Converter
Convert numbers bidirectionally between binary (base 2), octal (base 8), decimal (base 10), hexadecimal (base 16), and any custom radix from base 2 to base 36. Uses JavaScript BigInt to handle arbitrarily large integers without rounding errors, with 8-bit, 16-bit, and 32-bit zero-padding controls.
Real-Time Bidirectional Base Conversion
Custom Radix Conversion (Base 2 ~ Base 36)
Client-Side Computation
All radix conversions and BigInt calculations run locally in your browser's JavaScript engine — nothing is sent to a server.
Radix Systems Overview
Decimal (Base 10)
Standard human base-10 numbering system (0-9).
Hexadecimal (Base 16)
Ubiquitous in memory addresses, bitmasks, and RGB hex colors (0-9, A-F).
Binary (Base 2)
Fundamental low-level digital computing switch representation (0, 1).
Octal (Base 8)
Standard in Unix file permission systems (e.g. chmod 755) (0-7).
Serverless Real-Time Number Base & Radix Converter
Inspect memory offsets, perform bitwise operations, debug hardware registers, and convert between binary, octal, decimal, and hexadecimal with sub-millisecond precision.
BigInt High-Precision Arithmetic
Bypasses JavaScript Number 64-bit precision limits (2^53 - 1) using native BigInt to convert massive numbers without precision loss.
8 / 16 / 32-Bit Binary Padding
Align binary outputs to clean byte boundaries (8-bit, 16-bit, 32-bit) with leading zeros for register and packet debugging.
Arbitrary Base Conversion (Base 2 to 36)
Convert freely between non-standard radices including Base 3, Base 12 (Duodecimal), and Base 36 alphanumeric encodings.
Common Number Bases Comparison Table (2, 8, 10, 16)
Side-by-side representation of integer values across standard number systems.
| Decimal (Base 10) | Binary (Base 2) | Octal (Base 8) | Hexadecimal (Base 16) | Bit / Byte Specification |
|---|---|---|---|---|
| 0 | 0b00000000 | 0o000 | 0x00 | 1 Byte Minimum (Zero) |
| 15 | 0b00001111 | 0o017 | 0x0F | 4-bit Nibble Maximum |
| 255 | 0b11111111 | 0o377 | 0xFF | 8-bit 1 Byte (0-255) Maximum |
| 65535 | 0b1111111111111111 | 0o177777 | 0xFFFF | 16-bit 2 Bytes (64K) Maximum |
Developer Implementation Snippets for Radix Conversion
Convert number bases programmatically across modern programming languages.
// Decimal to Hex
const hex = (255).toString(16); // "ff"
// Hex to Decimal
const dec = parseInt("FF", 16); // 255# Decimal to Hex / Binary
hex_val = hex(255) # "0xff"
bin_val = bin(255) # "0b11111111"
# Hex to Decimal
dec_val = int("FF", 16) # 255// Decimal to Hex
String hex = Integer.toHexString(255); // "ff"
// Hex to Decimal
int dec = Integer.parseInt("FF", 16); // 255// Decimal to Hex
string hex = Convert.ToString(255, 16); // "ff"
// Hex to Decimal
int dec = Convert.ToInt32("FF", 16); // 255Industry Engineering Applications of Number Bases
Where each numbering system is utilized in computer science and systems programming.
Hexadecimal (Base 16) Applications
Used in CSS hex color codes (#FF5733), memory address pointers (0x7FFF), binary hex dumps, and SHA-256 hash digests.
Binary (Base 2) Applications
Essential for bitmasking operations, bitwise permission flags (FLAG_READ = 1 << 0), hardware I/O registers, and IPv4 subnet calculations.
Octal (Base 8) Applications
Standard representation for Linux/Unix file permissions (chmod 755, chmod 644) where 3 bits map to read, write, and execute permissions.
Step-by-Step Base Converter Guide
Step 1: Input Number
Type a number into any field (Decimal, Hexadecimal, Binary, or Octal).
Step 2: Instant Synchronization
All other base fields and binary bit alignments update instantly in real-time.
Step 3: Copy Result & Bit Padding
Copy outputs with one click and apply 8-bit, 16-bit, or 32-bit zero-padding.
Frequently Asked Questions (FAQ)
Q.Are hexadecimal inputs case-sensitive?
No. You can type uppercase (A-F) or lowercase (a-f) characters; the tool parses both seamlessly.
Q.Why does Unix file permissions (chmod) use Octal (Base 8)?
Unix permissions represent 3 binary flags: Read (4), Write (2), and Execute (1). Since , an octal digit (0-7) represents all 8 possible permission combinations for a single user category.
Q.What is the advantage of BigInt support?
Standard JavaScript Numbers suffer rounding errors above . Native BigInt allows converting numbers of thousands of digits with mathematical precision.
Q.What is Binary Bit Padding (8-bit, 16-bit, 32-bit)?
Bit padding pads binary numbers with leading zeros to align them to clean byte boundaries (e.g. 15 becomes 00001111 in 8-bit mode).
Q.Is any data transmitted to external servers?
No. All calculations on Toolbase run locally in your browser memory.