Calculate packed 16-bit BCD from four decimal digits or decode a binary or hex BCD value back into the original digits for 4-digit numbers.

BCD Calculator

Enter all four digits (D1–D4) to encode into BCD, or enter a BCD value to decode back into digits.

BCD (Binary-Coded Decimal) Formula

The following formula gives the numeric value of a packed BCD word for a 4-digit decimal number (D1 D2 D3 D4), where each digit occupies 4 bits (one nibble). Variables:

Packed BCD (16-bit) = (D1 * 2^12) + (D2 * 2^8) + (D3 * 2^4) + D4
  • Packed BCD (16-bit) is the packed BCD code word (often shown as a 16-bit binary string or as a 4-digit hex value like 0x1011).
  • D1, D2, D3, D4 are the decimal digits in the thousands, hundreds, tens, and ones place respectively (each must be an integer from 0–9).

To calculate a BCD representation, convert each decimal digit to its 4-bit binary form (8421 code) and concatenate the groups. For example, digit 7 becomes 0111. Note that BCD is an encoding of decimal digits; it is not the same thing as re-computing the original decimal number from place values.

What is BCD (Binary-Coded Decimal)?

Binary-Coded Decimal (BCD) is a class of binary encodings of decimal numbers where each decimal digit is represented separately in binary. The most common form uses 4 bits per decimal digit (often called “packed BCD” when two digits are stored per byte). Some systems store one digit per byte (sometimes called “unpacked BCD”), leaving the upper 4 bits as zero. In standard 8421 BCD, only the binary patterns for decimal digits 0 through 9 are valid.

How to Calculate BCD (Binary-Coded Decimal)?

The following steps outline how to calculate the BCD (Binary-Coded Decimal) for a 4-digit decimal number:

  1. Identify the digits D1, D2, D3, and D4 (thousands, hundreds, tens, ones), each from 0–9.
  2. Convert each digit to 4-bit binary (8421 BCD). For example: 0 → 0000, 1 → 0001, …, 9 → 1001.
  3. Concatenate the 4-bit groups in order: D1 then D2 then D3 then D4.
  4. (Optional) Express the packed 16-bit result in hexadecimal (4 hex digits).

Example Problem:

Use the following variables as an example problem to test your knowledge:

D1 = 1

D2 = 0

D3 = 1

D4 = 1

Convert each digit to 4-bit BCD and concatenate:

D1 = 1 → 0001, D2 = 0 → 0000, D3 = 1 → 0001, D4 = 1 → 0001

BCD (binary) = 0001 0000 0001 0001

BCD (hex) = 0x1011