Convert Binary-Coded Decimal (BCD) to decimal with nibble-by-nibble 4-bit decoding
Input BCD
Result
Decimal
Step-by-Step Derivation
BCD to Decimal Principle
0 = 0000, 1 = 0001, 2 = 0010, 3 = 0011
4 = 0100, 5 = 0101, 6 = 0110, 7 = 0111
8 = 1000, 9 = 1001
Split into 4-bit nibbles, convert each, concatenate
BCD encodes each decimal digit as a 4-bit nibble. Split BCD into 4-bit groups from right, convert each nibble to digit, and concatenate.
⚠BCD must contain only 0s and 1s, and length should be a multiple of 4. Nibbles 1010-1111 are invalid.
What Is BCD?
Binary-Coded Decimal (BCD) encodes each decimal digit (0-9) as a 4-bit binary nibble. This makes decimal conversion straightforward and preserves precision.
4-bit Nibble
Each decimal digit is exactly 4 bits: 0=0000, 5=0101, 9=1001.
Easy Conversion
BCD to decimal is trivial - just decode each nibble directly.
Precision Preserved
No rounding errors like binary floating point - perfect for finance.
Invalid Codes
1010-1111 are invalid - they don't represent decimal digits 0-9.
💡 Teaching Example: Convert BCD 00010010 to decimal. Step 1: Split into nibbles from right → 0001 0010. Step 2: 0001=1, 0010=2. Step 3: Concatenate → 12. So BCD 00010010 = decimal 12.
Applications
Financial CalculationsDigital DisplaysDigital ClocksLegacy SystemsPrecision Math
Frequently Asked Questions
What is BCD (Binary-Coded Decimal)?▼
BCD encodes each decimal digit (0-9) as a 4-bit binary nibble: 0=0000, 1=0001, ..., 9=1001. Values 1010-1111 are invalid.
How do you convert BCD to decimal?▼
1. Split BCD into 4-bit nibbles (from right). 2. Convert each nibble to decimal (0000-1001 only). 3. Concatenate the decimal digits to form the result.
What is invalid BCD?▼
4-bit values from 1010 (10) to 1111 (15) are invalid in BCD because they don't represent decimal digits 0-9. These are illegal BCD codes.
Why use BCD instead of binary?▼
BCD makes decimal conversion easy, preserves precision (no rounding), and is used in financial applications, displays, digital clocks, and legacy systems.
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