Number Base Converter
Convert numbers between binary, octal, decimal, and hexadecimal instantly. Supports large numbers with BigInt precision. Free online tool.
How to Use
- Select the input base (Binary, Octal, Decimal, or Hexadecimal).
- Enter your number in the input field.
- View the converted values in all four bases instantly.
- Click Copy on any result to copy it to your clipboard.
Number Systems Explained
Decimal (base 10) is the number system humans use daily. Each position represents a power of 10: ones, tens, hundreds, and so on. The number 255 means 2×100 + 5×10 + 5×1.
Binary (base 2) uses only 0 and 1. Each position represents a power of 2. The binary number 11111111 equals 128+64+32+16+8+4+2+1 = 255 in decimal. Binary is the foundation of all computing because transistors have two states: on (1) and off (0).
Hexadecimal (base 16) extends beyond 0-9 with letters A-F (representing 10-15). The hex number FF equals 15×16 + 15 = 255 in decimal. Hex is widely used in programming for colors (#FFFFFF), memory addresses (0x7FFF), and byte representations.
Octal (base 8) uses digits 0-7. The octal number 377 equals 3×64 + 7×8 + 7 = 255 in decimal. Octal is used in Unix file permissions and some legacy computing contexts.
Common Conversions
- 255 decimal = FF hex = 11111111 binary = 377 octal
- 128 decimal = 80 hex = 10000000 binary = 200 octal
- 65535 decimal = FFFF hex = 1111111111111111 binary
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Calculate Unix file permissions with the chmod Calculator. Generate hashes in hexadecimal with the Hash Generator. Encode binary data as Base64 with the Base64 Encoder. Convert colors between hex and RGB with the Color Picker. Calculate subnets and IP ranges with the Subnet Calculator. Convert images to Base64 data URIs with the Image to Base64 Converter.
Frequently Asked Questions
- What are number bases?
- A number base (or radix) is the number of unique digits used to represent numbers. Decimal (base 10) uses 0-9, binary (base 2) uses 0-1, octal (base 8) uses 0-7, and hexadecimal (base 16) uses 0-9 and A-F.
- Why do programmers use hexadecimal?
- Hexadecimal is compact — one hex digit represents exactly 4 binary bits, so a byte (8 bits) is always exactly 2 hex digits. This makes hex ideal for memory addresses, color codes (like #FF5733), and byte-level data inspection.
- What is binary used for?
- Binary (base 2) is the native language of computers. All data in a computer is ultimately stored as binary — sequences of 0s and 1s. Developers work with binary when dealing with bitwise operations, network masks, file permissions, and hardware registers.
- What is octal used for?
- Octal (base 8) is primarily used in Unix/Linux file permissions. Each octal digit maps to three permission bits (read, write, execute). For example, chmod 755 represents rwxr-xr-x in binary.
- Does this tool support large numbers?
- Yes. The converter uses BigInt for arbitrary-precision arithmetic, so it can handle numbers of any size without losing precision.
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