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Binary to Decimal Converter

Type any binary number and instantly see its decimal, hexadecimal, and octal equivalents.

Last updated: May 29, 2026

Client-Side Processing
Input Data Stays on Device
Instant Local Execution
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What is Binary to Decimal Converter?

Binary is the base-2 number system, using only the digits 0 and 1. It is the native language of digital computers — every number, character, and instruction stored in a computer is ultimately represented in binary.

Decimal is the familiar base-10 system we use in everyday life (digits 0–9).

Converting binary to decimal means calculating the positional value of each bit. Each bit position represents a power of 2, from right to left: 2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, and so on.

For example: 1010 in binary = (1×8) + (0×4) + (1×2) + (0×1) = 10 in decimal.

This converter also shows the equivalent hexadecimal (base 16) and octal (base 8) values, since these bases are closely related to binary.

How to Use Binary to Decimal Converter

1

Type or paste a binary number into the input field (digits 0 and 1 only)

2

The decimal, hexadecimal, and octal equivalents appear instantly

3

Click any "Copy" button to copy a specific result

4

Click "Load Sample" to see an example conversion

Common Use Cases

  • Converting binary memory addresses or register values to decimal for easier comparison.
  • Translating binary ASCII codes to decimal to find the character they represent.
  • Verifying binary-to-decimal conversion in programming assignments.
  • Checking subnet mask calculations by converting binary subnet masks to decimal octets.
  • Understanding CPU instruction encoding in computer architecture courses.
  • Debugging embedded systems output where values appear as binary strings.

Example Input and Output

The binary number 11001010 is converted to decimal 202, hex CA, and octal 312.

Binary input
11001010
Decimal equivalent
202 (decimal) = CA (hex) = 312 (octal)

Privacy

All number conversions run in your browser using JavaScript BigInt. No data is sent to any server.

Hex and binary relationship

To quickly convert binary to hex, group your binary number into chunks of 4 bits from the right, then convert each nibble: 0000=0, 0001=1, 0010=2, 0011=3, 0100=4, 0101=5, 0110=6, 0111=7, 1000=8, 1001=9, 1010=A, 1011=B, 1100=C, 1101=D, 1110=E, 1111=F.

Frequently Asked Questions

How do I convert binary to decimal manually?

Write out the binary number and assign each bit a positional value — starting from the right: 1, 2, 4, 8, 16, 32, 64, 128, … Multiply each bit (0 or 1) by its positional value and sum the results. Example: 1101 = (1×8) + (1×4) + (0×2) + (1×1) = 8 + 4 + 0 + 1 = 13.

Can I enter binary numbers with the 0b prefix?

Yes. The tool accepts both plain binary (1010) and the 0b-prefixed format (0b1010) used in JavaScript, Python, and C.

How large a binary number can this converter handle?

This tool uses JavaScript BigInt, which handles arbitrarily large integers with no precision loss. You can convert binary numbers with hundreds of bits without overflow.

Why is hexadecimal related to binary?

Every 4 binary bits (a "nibble") maps to exactly one hex digit: 0000=0, 0001=1, …, 1111=F. This makes it easy to convert between binary and hex mentally. For example, 11001010 binary splits into 1100 (=C hex) and 1010 (=A hex) = CA hex.

Is this the same as using the Number Base Converter?

Yes — the Number Base Converter handles binary to decimal (and many other base combinations) with additional features like bit grouping and signed integers. This page provides a simpler, focused binary-to-decimal experience.

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