BCD (Binary Coded Decimal) — What It Is and How to Convert

Introduction

Binary Coded Decimal (BCD) is a special encoding system where each decimal digit is represented individually as a 4-bit binary pattern. Unlike pure binary conversion (where the entire number converts to one binary value), BCD treats each digit of the decimal number separately. This concept appears frequently in BCA, BTech, and diploma courses under digital electronics and computer architecture.

What is BCD?

In BCD (specifically 8421 BCD, the most common type), each decimal digit from 0 to 9 maps to its 4-bit binary equivalent:

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

Patterns 1010 through 1111 (10–15) are invalid in BCD because they don’t correspond to any single decimal digit.

BCD vs Pure Binary

This is the most important distinction students must understand:

Decimal 25 in pure binary: 11001 (single binary number) Decimal 25 in BCD: 0010 0101 (each digit encoded separately)

BCD uses more bits but maintains a direct, readable mapping to decimal digits.

How to Convert Decimal to BCD

Steps:

1. Take each decimal digit individually
2. Convert each digit to its 4-bit binary equivalent
3. Concatenate all 4-bit groups

Example 1: Convert 47 to BCD

• 4 → 0100
• 7 → 0111

BCD Result: 0100 0111

Example 2: Convert 839 to BCD

• 8 → 1000
• 3 → 0011
• 9 → 1001

BCD Result: 1000 0011 1001

Example 3: Convert 2056 to BCD

• 2 → 0010
• 0 → 0000
• 5 → 0101
• 6 → 0110

BCD Result: 0010 0000 0101 0110

How to Convert BCD to Decimal

Steps:

1. Separate the BCD number into groups of 4 bits (from the right)
2. Convert each 4-bit group to its decimal digit
3. Combine the digits

Example: Convert BCD 1001 0100 0011 to Decimal

• 1001 → 9
• 0100 → 4
• 0011 → 3

Decimal Result: 943

Packed vs Unpacked BCD

Type	Storage	Example (digit 5)
Packed BCD	Two digits per byte	0101 xxxx (shares byte)
Unpacked BCD	One digit per byte	0000 0101 (upper nibble zeros)

Packed BCD is more storage-efficient. Unpacked BCD is simpler to process in software.

Advantages of BCD

• Exact decimal representation — No rounding errors for decimal values
• Easy display conversion — Each nibble maps directly to one display digit
• Simple hardware — Seven-segment decoders work directly with BCD
• Financial accuracy — Banking and accounting avoid floating-point errors

Disadvantages of BCD

• Wastes storage — Uses more bits than pure binary (6 invalid patterns per nibble)
• Slower arithmetic — BCD addition requires correction when sum exceeds 9
• Limited range — 8 bits of BCD stores 0–99; 8 bits of binary stores 0–255

BCD Addition and the “Add-6” Correction

When adding BCD numbers, if a nibble sum exceeds 9 or produces a carry, add 6 (0110) to correct:

Example: 7 + 8 in BCD

  0111  (7)
+ 1000  (8)
──────
  1111  (15 — invalid BCD!)
+ 0110  (add 6 correction)
──────
 10101  → 0001 0101 = 15 in BCD ✓

Applications

• Digital clocks and timers (seven-segment displays)
• Financial calculators and point-of-sale systems
• Microcontroller interfacing with numeric displays
• Legacy mainframe COBOL programs
• Exam questions in digital electronics courses

Try It Online

Use the free BCD Converter on Numverto to convert between decimal and BCD instantly. The tool shows the nibble breakdown for each digit and validates BCD inputs automatically.

Frequently Asked Questions

What does “8421” mean in 8421 BCD?

The name “8421” refers to the positional weights of the four bits: 8, 4, 2, 1. These weights are the same as standard binary place values. Other BCD variants exist (like Excess-3) but 8421 is the most common.

Is BCD the same as binary?

No. Binary encodes the entire number as one value. BCD encodes each decimal digit separately as 4 bits. For example, decimal 12 is 1100 in binary but 0001 0010 in BCD.

Why is 1010 invalid in BCD?

BCD represents decimal digits 0–9 only. The 4-bit patterns 1010 through 1111 (10–15 in binary) don’t correspond to any single decimal digit, so they are invalid in BCD encoding.

Where is BCD used in real life?

BCD is used in digital clocks, calculators, ATM displays, financial systems requiring exact decimal accuracy, and seven-segment display drivers in embedded hardware.

How many BCD digits fit in one byte?

Two BCD digits fit in one byte (packed BCD). Each digit uses 4 bits (one nibble), and one byte has 8 bits. So one byte can store values from 00 to 99 in packed BCD format.