Binary Coded Decimal (BCD) Explained

What is BCD?

Binary Coded Decimal (BCD) encodes each decimal digit separately as a 4-bit binary pattern. Unlike pure binary where the entire number shares one base-2 representation, BCD maps digit-by-digit: 29 decimal becomes 0010 1001 (2 and 9 separately), not 11101.

8421 BCD Encoding

The standard 8421 code assigns weights 8, 4, 2, 1 to four bits:

Decimal Digit	BCD (8421)
0	0000
5	0101
9	1001

Invalid BCD nibbles: 1010–1111 (no valid decimal digit).

Example: Encode 47

4 → 0100, 7 → 0111. BCD: 0100 0111 (often written 01000111 packed).

Example: Decode 0100 1001

Nibbles 0100=4, 1001=9 → decimal 49.

Packed vs Unpacked BCD

• Unpacked: One decimal digit per byte (upper nibble often zero)
• Packed: Two decimal digits per byte (common in legacy financial systems)

Why Use BCD?

• Display drivers: Seven-segment displays show decimal digits directly
• Financial accuracy: Avoids binary floating-point rounding on currency
• Legacy hardware: Older calculators and mainframes used BCD arithmetic

Pure binary is more storage-efficient; BCD trades space for decimal fidelity.

Convert with Numverto

Use the BCD Converter for instant encode/decode with nibble breakdown. Pair with the Number System Converter for full base conversion.

BCD vs Binary Comparison

Value	Pure Binary	BCD
29	11101	0010 1001
99	1100011	1001 1001

Frequently Asked Questions

Is BCD still used?

Yes in embedded displays, some financial firmware, and academic courses on digital design.

What happens with invalid BCD input?

Patterns like 1011 are not valid 8421 BCD — tools should flag them. Our BCD Converter validates nibbles.

How does BCD relate to ASCII?

ASCII codes for digits ‘0’–‘9’ (48–57) are not BCD — BCD is a numeric encoding, not character encoding. See ASCII Explained.

Can BCD represent fractions?

Standard BCD handles integers. Fixed-point BCD exists for currency but is specialised.

What is excess-3 BCD?

A variant where 3 is added to each digit before encoding — used in some legacy systems, not 8421 standard.