Decimal to BCD Conversion (8421, 5421, 2421 Codes) – Digital Electronics

Introduction

In Digital Electronics, Binary Coded Decimal (BCD) is a way to represent decimal numbers (0–9) in binary form.

Instead of converting the whole decimal number into a binary equivalent, each decimal digit is represented separately by a 4-bit binary code.

There are different types of BCD codes depending on the weights assigned to each binary digit:

• 8421 Code (Natural BCD, Weighted Code)

• 5421 Code (Weighted Code)

• 2421 Code (Self-Complementing Weighted Code)

Let’s understand each one in detail.

1. 8421 BCD Code (Natural Binary Coded Decimal)

This is the most common BCD code.

• Each digit has positional weights: 8, 4, 2, 1

• Decimal numbers 0–9 are represented as 0000–1001

Decimal	8421 BCD
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001

Example: Convert Decimal 59 into 8421 BCD

• 5 → 0101

• 9 → 1001
  So, 59 = 0101 1001 (BCD)

2. 5421 BCD Code

In this system, the weights are: 5, 4, 2, 1

• Each decimal digit 0–9 is represented by a unique combination of these weights.

Decimal	5421 BCD
0	0000
1	0001
2	0010
3	0011
4	0100
5	1000
6	1001
7	1010
8	1011
9	1100

Example: Convert Decimal 59 into 5421 BCD

• 5 → 1000

• 9 → 1100
  So, 59 = 1000 1100 (BCD in 5421 code)

3. 2421 BCD Code

This is a self-complementing code, meaning:

• The code for a digit and its 9’s complement add up to 1111.

• Weights: 2, 4, 2, 1

Decimal	2421 BCD
0	0000
1	0001
2	0010
3	0011
4	0100
5	1011
6	1100
7	1101
8	1110
9	1111

Example: Convert Decimal 59 into 2421 BCD

• 5 → 1011

• 9 → 1111
  So, 59 = 1011 1111 (BCD in 2421 code)

• 8421 BCD → Most practical, widely used in calculators, clocks, and digital systems.

• 5421 BCD → Alternative weighted code, less common.

• 2421 BCD → Self-complementing code, useful for error checking and arithmetic simplifications.

Mastering these codes is essential for Digital Electronics, Computer Science, and Competitive Exams (GATE, ESE, etc.).

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