Convert Binary to BCD

Easily convert binary numbers to BCD (Binary-Coded Decimal) with this free Binary to BCD Converter. Simply enter your binary value, and get the instant BCD conversion with clear, spaced 4-bit groupings for each decimal digit.

How to Convert Binary to BCD

Converting binary to BCD involves two key steps:

Step 1: Convert the binary number to its decimal equivalent.

Step 2: Encode each decimal digit into its 4-bit BCD form.

Binary to BCD Formula

Since BCD represents each decimal digit separately, the conversion follows:

BCD = (D₁)₄-bit (D₂)₄-bit … (Dₙ)₄-bit

D₁ to Dₙ = Decimal digits of the converted binary number

Each 4-bit segment = Binary representation of a single digit (0-9)

For example:

Binary: 1101 (13 in decimal) → BCD: 0001 0011 (1 and 3 in 4-bit BCD)

Each 4-bit segment = Binary representation of a single digit (0-9)

Binary to BCD Truth Table

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

Note: Values 1010 to 1111 (10-15 in binary) are invalid in standard BCD.

Binary to BCD Algorithm

The simplest method for binary to BCD conversion is:

1. Convert binary → decimal (e.g., 1010 → 10)
2. Split decimal digits (e.g., 1 and 0)
3. Map each digit to 4-bit BCD (e.g., 0001 and 0000)
4. Combine results → 0001 0000

For 5-bit, 8-bit, or larger binary numbers, the process remains the same:

• 5-bit example: 11011 (27) → BCD: 0010 0111
• 8-bit example: 11110000 (240) → BCD: 0010 0100 0000

Binary to BCD Examples

Binary Input	Decimal Value	BCD Output
0101 (5)	5	0101
1010 (10)	10	0001 0000
11011 (27)	27	0010 0111
1111000 (120)	120	0001 0010 0000

FAQs – Binary to BCD Conversion

1. How do I convert Binary to BCD?

1. Enter your binary number (e.g., 1101).
2. Convert it to decimal (13).
3. Split digits (1 and 3).
4. Replace each with 4-bit BCD (0001 0011).

2. Can I convert 8-bit binary to BCD?

Yes! The method works for any binary length.
Example: 10010110 (150) → BCD: 0001 0101 0000

3. Is there a Binary to BCD truth table?

Yes (see above). Each decimal digit (0-9) has a fixed 4-bit BCD code.

4. Why use BCD instead of pure binary?

• Precision: Avoids rounding errors in financial/measurement systems.
• Readability: Easier to decode for displays (e.g., digital clocks).

Try Our Binary to BCD Converter Online

Our tool automates the conversion, providing fast, accurate results for:

• 4-bit, 5-bit, 8-bit, and larger binary numbers
• Error-checking for invalid binary inputs
• Formatted BCD output with clear spacing

Related: Binary to Gray Code