Online BCD to Hex Converter - Free Binary Coded Decimal to Hex

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

Our free online BCD to Hex Converter enables you to instantly convert Binary Coded Decimal (BCD) values to their hexadecimal (base-16) equivalent. Ideal for digital electronics students, hardware designers, embedded systems programmers, and computer architects, this client-side utility translates BCD bitstreams into readable hex representation with step-by-step mathematical decomposition.

What is Binary Coded Decimal (BCD)?

Binary Coded Decimal (BCD) (specifically 8421 BCD) is a format where each decimal digit of a number is represented by its own 4-bit binary group (nybble). For example, the decimal value 95 is represented as:

9 $\rightarrow$ 1001
5 $\rightarrow$ 0101
Combined BCD $\rightarrow$ 1001 0101

In standard binary, 95 is encoded as 01011111. BCD is distinct because it encodes digit-by-digit, making it easy to display values on numerical screens like seven-segment LED displays.

How BCD to Hex Conversion Works

Converting BCD to hexadecimal requires a two-step process:

BCD to Decimal: Split the BCD bitstream into 4-bit groups, decode each group back into its corresponding decimal digit (0–9), and join them to form the decimal number.
Decimal to Hex: Convert the resulting decimal number into its base-16 hexadecimal representation.

The BCD-to-Decimal Digit Map

Only the 4-bit sequences representing 0 to 9 are valid BCD. The remaining sequences (1010 to 1111) are considered invalid BCD states:

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

Step-by-Step Conversion Example

Let's convert the BCD sequence 0011 1001 0111 to Hexadecimal:

Decode 4-bit Groups to Decimal Digits:
- First group 0011 $\rightarrow$ 3
- Second group 1001 $\rightarrow$ 9
- Third group 0111 $\rightarrow$ 7
- Assembled Decimal Value $\rightarrow$ 397
Convert Decimal to Hexadecimal:
- $397 \div 16 = 24 \text{ remainder } 13 \rightarrow \text{D}$
- $24 \div 16 = 1 \text{ remainder } 8 \rightarrow \text{8}$
- $1 \div 16 = 0 \text{ remainder } 1 \rightarrow \text{1}$
- Reading remainders from bottom to top $\rightarrow$ $18\text{D}_{16}$
Result: BCD binary 0011 1001 0111 converts to Hexadecimal 18D.

Key Features of Our Converter

⚡ Instant Live Processing: Watch your BCD bitstream convert to hex in real-time as you type.
🔧 Multiple Parse Options: Supports space-separated groups, dash-separated groups, continuous binary strings, and line-by-line batch inputs.
🔒 Fully Client-Side & Secure: All parsing and encoding are executed in your browser; your data is never uploaded to any server.
🧠 Detailed Step-by-Step Breakdown: Displays the complete grouping, decimal digit mapping, and final base-16 conversion.

Frequently Asked Questions

What happens if my BCD input contains binary values like 1111 or 1010?

Since standard 8421 BCD digits are limited to the decimal range 0–9, binary values greater than 1001 (such as 1010, 1011, 1100, 1101, 1110, 1111) are considered invalid BCD states. The converter will display a validation error identifying the invalid group.

What if my continuous BCD string is not a multiple of 4 bits?

Our smart converter automatically pads your BCD string with leading zeros to form a complete 4-bit group (for example, 111 is padded to 0111 = 7) and shows you the details of the padding step in the conversion breakdown.

Is BCD the same as binary to hex conversion?

No. In binary to hex conversion, the entire bitstream is parsed as a single base-2 integer (e.g., 00010101 is 21, which is 0x15). In BCD to hex conversion, the bitstream is parsed as individual 4-bit decimal digits (e.g., 00010101 is 15 in BCD, which converts to 0xF in hex).

Can I convert multiple BCD strings at once?

Yes. By selecting the "Line-by-Line BCDs" option, you can enter multiple distinct BCD values (one per line) and convert them all simultaneously.

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