Overview
Need to inspect packed decimal fields or decode legacy financial streams? Binary-Coded Decimal (BCD) encodes every base-10 digit into an independent 4-bit nibble. Unlike IEEE 754 binary floating-point, BCD eliminates fractional rounding errors in accounting and hardware controllers. Convert decimal values to 8421, Aiken, Excess-3, and Gray BCD directly in your browser.
Supported Formats
- Encodes decimal digits 0 through 9 into 4-bit binary nibbles across 5 distinct weighting schemes.
- Decodes unpacked and packed BCD binary streams back to base-10 numbers.
- Supports 8421 (Natural BCD), 2421 (Aiken), 5421 (Bi-quinary), Excess-3 (Stibitz), and Gray BCD.
- Flags illegal 4-bit states (such as 1010 to 1111 in standard 8421) to catch corrupted byte streams.
Encoding Architecture and Standards
In Natural BCD (8421), each decimal digit maps to its 4-bit binary representation: - 0: 0000 - 1: 0001 - 5: 0101 - 9: 1001
Because 4 bits yield 16 possible states (0000 to 1111) but decimal digits only require 10 states, the bit patterns 1010 through 1111 are invalid in 8421 BCD.
In Packed BCD, two decimal digits share a single 8-bit byte. For example, the decimal integer 79 is packed into 0x79 (binary 0111 1001). This format was standardized across mainframe architectures, including IBM System/360 and x86 decimal instructions (DAA and DAS), as well as real-time clock chips like the DS1307.
Usage Steps
- Enter a decimal integer for encoding or a binary bitstream for decoding.
- Select your target weighting variant from the BCD format dropdown.
- Toggle Packed mode if your binary data stores two digits per 8-bit byte.
- Inspect the resulting byte layout or copy the parsed decimal number.
Weighted Variants and Arithmetic Properties
Different BCD variants solve specific hardware design challenges:
1. 2421 (Aiken Code): Uses weights 2, 4, 2, and 1. It is self-complementing, meaning the 9s complement of a digit equals its bitwise NOT inversion. This simplifies hardware subtraction. 2. Excess-3 (Stibitz Code): Adds 3 (binary 0011) to each digit before encoding. Also self-complementing, it allows carry bits in binary adders to trigger decimal carries directly. 3. Gray BCD: Restricts transitions between consecutive decimal digits to exactly 1 bit flip, preventing transient glitches in optical shaft encoders.
Storage Overhead and Decimal Precision
BCD trades storage efficiency for arithmetic precision. Representing values up to 9999 requires 16 bits in packed BCD (4 nibbles), whereas 16 bits of pure binary store values up to 65535. However, financial platforms avoid binary floating-point representation because fractions like 0.10 cannot be stored cleanly in base-2, causing cumulative rounding errors in high-volume transaction ledgers.
Frequently asked questions
Why do real-time clock (RTC) chips use BCD?
RTC registers output seconds, minutes, hours, and years directly in packed BCD nibbles so microcontrollers can display clock values without executing division or modulo instructions.
What happens when an invalid BCD nibble like 1101 is parsed?
In 8421 BCD, 1101 (decimal 13) is an illegal state. The tool flags this as an unassigned pattern, alerting developers to corrupted memory dumps.
Summary
BCD remains an essential format in embedded electronics, telecommunications, and financial mainframes. For generic base conversions, explore our Base64 converter or the Hex encoder and decoder.