Number Base Converter

What is Number Base Conversion?

Number base conversion translates a value from one positional numeral system to another — for example, from decimal (base 10) to hexadecimal (base 16) or binary (base 2). Every programmer, network engineer, and embedded developer encounters this regularly when reading memory addresses, CSS color codes, Unix file permissions, subnet masks, or raw binary data.

ToolSnap's number base converter supports binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Enter a value in any base and instantly see the equivalent in all other bases. All conversion happens in your browser — nothing is sent to a server.

The Four Common Bases

• Binary (base 2) — Uses digits 0 and 1. Each position is a power of 2. Fundamental to hardware, bitwise operations, and network masks.
• Octal (base 8) — Uses digits 0–7. Each position is a power of 8. Still used for Unix file permissions (e.g. chmod 755).
• Decimal (base 10) — Uses digits 0–9. The everyday number system humans use.
• Hexadecimal (base 16) — Uses digits 0–9 and letters A–F. Each position is a power of 16. Compact way to represent bytes and memory addresses.

How Base Conversion Works

In any positional system, each digit represents a coefficient multiplied by a power of the base. Decimal 354 means 3×10² + 5×10¹ + 4×10⁰. Binary 1011 means 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 11 in decimal. Hexadecimal 2F means 2×16¹ + 15×16⁰ = 47 in decimal.

To convert from any base to decimal, multiply each digit by its place value and sum the results. To convert from decimal to another base, repeatedly divide by the target base and read the remainders in reverse order.

Real-World Uses

• CSS colors — #FF6B35 is three pairs of hex bytes for red, green, and blue (0–255 each).
• Memory addresses — Debuggers display addresses like 0x7FFF5FBFFA10 because hex is more compact than binary.
• Unix permissions — chmod 755 means owner rwx (7), group rx (5), others rx (5) in octal.
• Subnet masks — A /24 network mask is 24 ones followed by 8 zeros in binary: 255.255.255.0.
• Bit flags — Feature toggles and permission masks combine individual bits: Read (4) + Write (2) + Execute (1) = 7.

Frequently Asked Questions

Why do programmers prefer hexadecimal?

One hex digit represents exactly four bits (a nibble), and two hex digits represent one byte. This makes hex a compact, readable representation of binary data. Reading FA is easier than 11111010.

Can I enter letters in hex values?

Yes. Hexadecimal uses A–F (or a–f) for values 10–15. The tool accepts both uppercase and lowercase letters.

What happens if I enter an invalid digit for a base?

Each base only allows specific digits. Binary accepts 0 and 1 only; octal accepts 0–7; decimal accepts 0–9; hex accepts 0–9 and A–F. Invalid characters produce a clear error rather than a wrong result.