Binary ToolsFree Interactive Tool

Binary to BCD Converter

Convert binary integers into 8421 Binary-Coded Decimal (BCD) 4-bit nibbles. Designed for software developers, electrical engineers, students, and computer architecture researchers requiring deterministic client-side accuracy.

Engine: Client-Side Verified (0ms Latency)

Binary String

Enter binary sequence (e.g. 10110 for 22).

Calculated Output

Primary Representation

Calculating...

Step-by-Step Mathematical Proof

Active Derivation

Ready. Enter input above to generate derivation.

Concept

What Is Binary to BCD Converter?

Binary to BCD conversion translates natural binary numbers into 8421 Binary-Coded Decimal format, where each individual decimal digit is encoded into a separate 4-bit nibble (0000 to 1001).

Methodology

How Does It Work?

Convert the binary number to its decimal value, then replace each decimal digit with its 4-bit binary representation. In hardware, this is accomplished via the Double-Dabble (Shift-and-Add-3) algorithm.

Formula & Rules

Mathematical Algorithm

D = \sum d_k 10^k \xrightarrow{} \text{BCD} = [\text{nibble}_k \dots \text{nibble}_0] \quad (0000_2 \le \text{nibble} \le 1001_2)

Worked Problem

Step-by-Step Example

Convert binary 10110_2 (decimal 22) to BCD: Decimal digits are 2 and 2. 2 -> 0010_2 2 -> 0010_2 BCD: 0010 0010.

Important Rules & Edge Cases

Each decimal digit requires exactly 4 bits.
Values 1010 through 1111 (10 to 15) are strictly invalid in 8421 BCD.

Practical Applications in Engineering

Driving 7-segment LED and LCD numeric display controllers.
Financial transaction processing and accounting microchips.
Real-time clock (RTC) chips (e.g., DS1307).

Common Mistakes to Avoid

Caution: Confusing BCD with standard binary (e.g. thinking decimal 22 in BCD is 10110 instead of 0010 0010).
Caution: Allowing nibbles greater than 1001 (9).

FAQ