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.
Binary to BCD Converter
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:
- Convert binary → decimal (e.g.,
1010→10) - Split decimal digits (e.g.,
1and0) - Map each digit to 4-bit BCD (e.g.,
0001and0000) - 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?
- Enter your binary number (e.g.,
1101). - Convert it to decimal (
13). - Split digits (
1and3). - 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
