What counts as a valid BCD nibble?

A valid BCD nibble is exactly 4 binary digits representing a value from 0 to 9 (binary 0000 through 1001). Nibbles from 1010 to 1111 don't correspond to any decimal digit and are rejected as invalid BCD.

How does the tool reconstruct the number?

Each nibble is decoded to its single decimal digit (0-9), the digits are concatenated in order to form the full decimal number, and that number is then converted to binary.

Why is "0001 0101" converted to binary "1111"?

The nibble 0001 decodes to digit 1 and 0101 decodes to digit 5, giving the decimal number 15. Binary 1111 is exactly 15, so that's the output.

What happens if I enter an invalid nibble like 1010?

The tool rejects it with an explicit error identifying the invalid nibble and its position, since 1010 through 1111 (10-15) have no meaning in Binary-Coded Decimal.

BCD to Binary Converter - Decode 4-Bit Nibbles to Binary

Overview

Introduction

Binary-Coded Decimal stores each decimal digit as its own 4-bit nibble, which is convenient for digit-by-digit display but isn't a number a computer can do binary arithmetic on directly.

This tool reverses that encoding: it decodes a sequence of BCD nibbles back into the plain binary value they represent.

What Is BCD to Binary Converter?

A decoder for Binary-Coded Decimal input: give it space-separated 4-bit nibbles and it reconstructs the decimal number they encode, then converts that number to binary.

It's the inverse of the Binary to BCD Converter, so round-tripping a value through both tools should return your original input.

How BCD to Binary Converter Works

Each whitespace-separated token is validated as exactly 4 binary digits and checked to ensure its value doesn't exceed 9 (nibbles 1010-1111 are rejected as invalid BCD).

The decoded digits are concatenated into a decimal digit string, parsed as a BigInt, and converted to binary with `toString(2)`.

When To Use BCD to Binary Converter

Use it when you have data captured from a BCD-based system (old calculators, digital clocks, some embedded sensors) and need the equivalent plain binary value.

It's also a useful check when learning BCD, to confirm you've decoded a nibble sequence correctly by hand.

Often used alongside Binary to BCD Converter.

Features

Advantages

Strictly validates every nibble, catching invalid BCD values (10-15) rather than silently misinterpreting them.
Uses BigInt internally, so it handles arbitrarily long digit sequences without precision loss.
Clear, position-specific error messages when a nibble is malformed or out of range.

Limitations

Expects nibbles separated by whitespace; it doesn't attempt to auto-detect nibble boundaries in a contiguous unspaced string.
Only supports unsigned BCD; there's no support for signed BCD representations (like ten's-complement BCD).

Examples

Two BCD nibbles to binary

Input

0001 0101

Output

Nibble 0001 decodes to digit 1 and 0101 to digit 5, giving decimal 15, which is binary 1111.

Three BCD nibbles to binary

Input

0010 0000

Output

Nibble 0010 decodes to digit 2 and 0000 to digit 0, giving decimal 20, which is binary 10100.

Best Practices & Notes

Best Practices

Separate each nibble with a space so the tool can unambiguously identify nibble boundaries.
Use the Binary to BCD Converter afterward on your result to confirm it round-trips back to the same nibbles.

Developer Notes

Implemented with `parseInt(token, 2)` for per-nibble decoding and validation, then JavaScript BigInt for the final decimal-to-binary conversion so arbitrarily long digit sequences don't lose precision.

BCD to Binary Converter Use Cases

Decoding BCD data captured from legacy hardware or protocols into usable binary
Validating that a sequence of nibbles is actually well-formed BCD
Teaching or verifying manual BCD-to-binary decoding

Common Mistakes

Entering a nibble like 1100 (12) expecting it to be accepted; only 0000-1001 (0-9) are valid BCD digits.
Omitting spaces between nibbles, which prevents the tool from telling where one 4-bit group ends and the next begins.

Tips

If you're unsure whether your nibbles are valid BCD, this tool's validation error will tell you exactly which one and why.
Chain the output into another binary tool (like the Binary Parity Calculator) to continue working with the decoded value.

BCD to Binary Converter