Decimal to BCD Converter
Convert standard base-10 decimal numbers 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.
Enter any non-negative base 10 integer.
Calculated Output
Step-by-Step Mathematical Proof
Active DerivationWhat Is Decimal to BCD Converter?
Decimal to BCD conversion transforms standard decimal integers into Binary-Coded Decimal (8421 BCD). Rather than converting the entire number into a single binary integer, BCD independently translates each decimal digit (0 through 9) into its own 4-bit binary sequence (0000 to 1001).
How Does It Work?
Split the decimal number into its individual digits. Replace each decimal digit with its corresponding 4-bit binary representation: 0=0000, 1=0001, 2=0010, 3=0011, 4=0100, 5=0101, 6=0110, 7=0111, 8=1000, 9=1001.
Mathematical Algorithm
Step-by-Step Example
Important Rules & Edge Cases
- Each decimal digit must be padded to exactly 4 bits.
- Only decimal digits 0 through 9 are allowed.
- Nibbles from 1010 to 1111 (10 to 15) are strictly illegal in BCD.
Practical Applications in Engineering
- Digital electronic clocks, timers, and multimeters using 7-segment LED/LCD display drivers.
- Financial software engines to avoid binary floating-point roundoff issues.
- Point-of-sale (POS) terminal displays and cash register firmware.
Common Mistakes to Avoid
- Caution: Converting the whole number into pure binary instead of encoding digit by digit (e.g. converting 12 into 1100 instead of 0001 0010).
- Caution: Forgetting leading zeros on individual nibbles (e.g. writing 1 as 1 instead of 0001).
Frequently Asked Questions
What is the difference between pure binary and BCD?
In pure binary, the entire number is converted into base 2 as a single positional value (e.g. 15 is 1111). In BCD, each decimal digit is converted into its own 4-bit nibble (e.g. 15 is 0001 0101).
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Convert decimal integers (base 10) into pure binary bit patterns with repeated division by 2 steps.