Number Base Converter: Binary, Octal, Decimal & Hex (2026)

Every number you work with as a developer is really the same value wearing a different outfit. 255, 0xFF, and 11111111 are identical—they just use different number bases. Switching between them by hand is slow and error-prone.

Our Number Base Converter converts between binary, octal, decimal, and hexadecimal instantly. Edit any field and the others update in real time.

What Is a Number Base?

A number base (or radix) is how many distinct digits a system uses before it “rolls over” to the next column.

Base	Name	Digits	Example (decimal 42)
2	Binary	0 1	101010
8	Octal	0–7	52
10	Decimal	0–9	42
16	Hexadecimal	0–9 A–F	2A

In base 10, the number 42 means (4 × 10¹) + (2 × 10⁰). In base 2, 101010 means (1×32) + (0×16) + (1×8) + (0×4) + (1×2) + (0×1) = 42. Same value, different representation.

Why Programmers Care About Bases

Binary (Base 2)

Computers store everything as bits—on/off, 1/0. Binary is the native language of hardware, bitmasks, and flags.

Hexadecimal (Base 16)

Hex is compact and maps perfectly to binary: each hex digit equals exactly 4 bits. That makes it ideal for:

• Memory addresses: 0x7ffee3b2
• Color codes: #14B8A6
• Byte values: 0xFF = 255 = one full byte

Octal (Base 8)

Octal groups bits in threes. You’ll still see it in Unix file permissions (chmod 755).

How to Convert by Hand

Decimal → Binary

Repeatedly divide by 2, recording remainders bottom-to-top:

42 ÷ 2 = 21 r 0
21 ÷ 2 = 10 r 1
10 ÷ 2 =  5 r 0
 5 ÷ 2 =  2 r 1
 2 ÷ 2 =  1 r 0
 1 ÷ 2 =  0 r 1
Result (bottom→top): 101010

Binary → Hex

Group bits into fours from the right and convert each group:

1010 1010
  A    A   →  0xAA  (170 in decimal)

It works, but it’s tedious. Paste the value into our Number Base Converter and skip the arithmetic.

Common Pitfalls

• Mixing up prefixes: 0x means hex, 0b means binary, 0o means octal. Our converter expects the raw digits in each field.
• Leading zeros: They don’t change the value (0042 = 42) but can confuse parsers that treat a leading 0 as octal.
• Signed numbers: Negative numbers use two’s complement in real hardware. This tool works with non-negative integers.
• Precision loss: Many converters break on huge numbers. Ours uses arbitrary-precision integers, so large values stay exact.

Cross-Tool Workflow

Number bases rarely live alone in a developer’s toolbox:

• Number Base Converter → Switch between binary, octal, decimal, and hex
• Color Converter → Turn hex color codes into RGB and HSL
• Hash Generator → Produce hexadecimal digests like SHA-256
• Text to Binary → Encode characters into their binary byte values

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Frequently Asked Questions

Q: How do I convert binary to decimal?

A: Multiply each bit by its place value (a power of 2) and sum them. For 1010: (1×8) + (0×4) + (1×2) + (0×1) = 10. Or just paste the binary into our Number Base Converter for instant results.

Q: Why is hexadecimal used instead of decimal in code?

A: Hex maps cleanly to binary—one hex digit is exactly 4 bits—so it’s a compact, readable way to express byte values, memory addresses, and colors. 0xFF is far easier to reason about than 11111111.

Q: What does the 0x prefix mean?

A: 0x signals that the following digits are hexadecimal (base 16). Similarly, 0b means binary and 0o means octal. They’re conventions used by programming languages, not part of the number itself.

Q: Can this converter handle very large numbers?

A: Yes. Our Number Base Converter uses arbitrary-precision (BigInt) math, so numbers far beyond 64 bits convert without rounding errors.

Q: Is octal still used today?

A: Mostly in Unix/Linux file permissions (chmod 644). It’s less common than hex but still appears in systems programming.

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Convert Any Number Base Instantly

Stop dividing by two on scratch paper. Whether you’re debugging a hex dump, reading a bitmask, or learning computer science, our Number Base Converter gives you binary, octal, decimal, and hex side by side—instantly and privately in your browser.

Explore all free developer tools at Hasare.

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Wrangling hex addresses and binary flags? Convert between every common base in one place with our Number Base Converter.