Binary-Coded Decimal (BCD) Encoding

Binary-Coded Decimal (BCD) represents each decimal digit individually as a 4-bit binary value, rather than converting the entire number to binary. While less space-efficient than pure binary, BCD avoids rounding errors inherent in binary representation and simplifies decimal display.

How BCD works:

Each decimal digit (0-9) is encoded in 4 bits:

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

Values 1010 through 1111 (10-15) are invalid in BCD.

Example — encoding 4729 in BCD:

• 4 = 0100
• 7 = 0111
• 2 = 0010
• 9 = 1001

BCD: 0100 0111 0010 1001

Compare with pure binary: 4729₁₀ = 1001001111001₂ (13 bits vs. 16 bits for BCD). BCD uses more space but preserves the decimal structure.

Packed vs. unpacked BCD:

• Packed BCD: Two decimal digits per byte (as shown above). More space-efficient.
• Unpacked BCD: One decimal digit per byte, with the upper 4 bits set to zero (or sometimes to 0011 for ASCII digits). Easier to process but uses twice the space.

Where BCD is used today:

• Financial systems: BCD avoids the floating-point errors that make 0.1 + 0.2 != 0.3 in binary. COBOL, which powers most banking systems, uses BCD internally.
• Real-time clocks: Most hardware RTCs (like the DS1307) store time in BCD. Reading "12:30:45" from the chip gives you bytes 0x12, 0x30, 0x45 in BCD.
• Digital displays: Seven-segment LED/LCD displays naturally map to BCD — each digit drives one display element.
• SQL DECIMAL type: Many databases use BCD-like encoding for exact decimal arithmetic.