8421 BCD to Decimal Converter

The 8421 BCD to Decimal Converter is a specialized tool designed to transform Binary-Coded Decimal (BCD) numbers into their decimal equivalents. This converter is particularly useful in digital systems, computer science, and electronic applications where BCD representation is commonly used.

What is 8421 BCD?

8421 BCD (Binary-Coded Decimal) is a system of encoding decimal numbers where each decimal digit is represented by a 4-bit binary sequence. The name "8421" refers to the weights assigned to each bit position (8, 4, 2, and 1). In this system, decimal digits from 0 to 9 are represented using four binary digits.

8421 BCD to Decimal Conversion Formula

The formula for 8421 BCD to Decimal conversion can be expressed as:

\[ Decimal = \sum_{i=0}^{n-1} (BCD_i \times 10^i) \]

Where:

• \(BCD_i\) is the decimal value of each 4-bit BCD group
• \(n\) is the number of BCD groups
• \(i\) is the position of each group (0-indexed from right to left)

Calculation Steps

Let's convert the 8421 BCD number "0001 0010" to decimal:

1. Split into 4-bit groups: 0001 | 0010
2. Convert each group to decimal:
   • 0001 → 1
   • 0010 → 2
3. Combine the results: 12

Therefore, 0001 0010 (BCD) = 12 (Decimal)

Example with Visual Representation

Let's visualize the conversion of the BCD number "0101 1001" to decimal: