Online Hex to BCD Converter - Free Binary Coded Decimal

Hex to BCD Converter - Convert Hexadecimal to Binary Coded Decimal Online

Our free online Hex to BCD Converter allows you to instantly convert hexadecimal numbers (base-16) to Binary Coded Decimal (BCD) format. Designed for microcontroller programmers, digital designers, systems engineers, and computer architecture students, this client-side utility provides instant decoding for arbitrary-length hex strings.

What is Binary Coded Decimal (BCD)?

Binary Coded Decimal (BCD) is a class of binary encodings where each decimal digit of a number is represented by a fixed number of bits, usually four. For example, the decimal number 37 is represented as:

3 $\rightarrow$ 0011
7 $\rightarrow$ 0111
Combined BCD $\rightarrow$ 0011 0111

Unlike standard binary representation where the entire number is converted, BCD treats each decimal digit independently. This makes BCD highly suitable for display systems (such as seven-segment LED displays) because the hardware decoder for each digit can operate independently without complex division circuitry.

How Hex to BCD Conversion Works

To convert a hexadecimal number to BCD, we perform the following steps:

Hex to Decimal: Convert the hexadecimal value into its equivalent decimal base-10 value.
Decimal to BCD: Convert each decimal digit independently into its corresponding 4-bit binary sequence.

The Decimal-to-BCD Digit Map

Each decimal digit maps directly to its 4-bit binary representation:

Decimal Digit	4-bit BCD Binary
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001

Step-by-Step Conversion Example

Let's convert the hexadecimal value 0x3E7 to BCD:

Convert Hex to Decimal:
- $3E7_{16} = (3 \times 16^2) + (14 \times 16^1) + (7 \times 16^0) = 768 + 224 + 7 = 999_{10}$
Encode Decimal Digits to BCD:
- First digit 9 $\rightarrow$ 1001
- Second digit 9 $\rightarrow$ 1001
- Third digit 9 $\rightarrow$ 1001
Result: Hexadecimal 3E7 converts to BCD binary 1001 1001 1001.

Key Benefits of Our Converter

⚡ Instant, Live Conversion: Watch the BCD binary code compute dynamically.
🧩 BCD Separators: Choose between space-separated, continuous, or dash-separated BCD representations for optimal readability.
🔥 Large Inputs Supported: Seamlessly handles extremely large hexadecimal strings using JavaScript's native BigInt parsing.
📝 Comprehensive FAQs & Breakdowns: Learn the low-level logic, tables, and mathematics behind BCD.

Frequently Asked Questions

Why is BCD used instead of standard binary?

BCD is primarily used when numbers need to be displayed on screens, clocks, or digital calculators. Translating standard binary to decimal digits in hardware requires slow and expensive division operations. BCD enables direct, digit-by-digit mapping to displays instantly.

Is BCD the same as binary?

No. In binary, a whole number is converted directly to base-2 (e.g. 10 is 1010). In BCD, each decimal digit is converted individually (e.g. 10 is encoded as 0001 0000).

Does the converter support large hex values?

Yes, our tool supports arbitrarily large hexadecimal inputs. All calculations are performed instantly client-side using BigInt.

Are BCD binary codes limited to 4 bits?

Standard BCD (often called 8421 BCD) always uses exactly 4 bits per decimal digit. Binary codes 1010 through 1111 are considered invalid BCD states.

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Hex to BCD Converter