What is the BCD equivalent of a decimal number?

The BCD (Binary Coded Decimal) equivalent of a decimal number is a digital representation where each decimal digit is converted independently into its 4-bit binary form. Unlike pure binary conversion, BCD does not convert the entire decimal number into a single binary string. Instead, it treats each digit of the decimal number as a separate entity and represents it with a fixed 4-bit binary code.

This method makes it straightforward for digital systems to display decimal numbers, as the conversion process is simplified.

Understanding Binary Coded Decimal (BCD)

BCD is a system that bridges the gap between the human-friendly decimal system and the machine-friendly binary system. It encodes each decimal digit (0-9) into a 4-bit binary sequence.

Here is how common decimal digits are represented in BCD:

It's important to note that BCD only uses the first ten 4-bit combinations (0000 to 1001). The remaining six combinations (1010 to 1111) are considered invalid in a standard BCD representation and are not used.

How to Convert a Decimal Number to BCD

Converting a decimal number to its BCD equivalent involves a simple, digit-by-digit process:

1. Separate the Decimal Digits: Break the decimal number into its individual digits.
2. Convert Each Digit: For each decimal digit, find its corresponding 4-bit BCD representation from the table above.
3. Concatenate the BCD Codes: Combine the 4-bit BCD codes for each digit in the same order as they appeared in the original decimal number.

Example: Converting Decimal 179 to BCD

Let's convert the decimal number 179 to its BCD equivalent.

• Step 1: Separate the Decimal Digits
  The digits are 1, 7, and 9.

• Step 2: Convert Each Digit to BCD

  • Decimal 1 = 0001 (in BCD)
  • Decimal 7 = 0111 (in BCD)
  • Decimal 9 = 1001 (in BCD)

• Step 3: Concatenate the BCD Codes
  Combine these BCD codes in order: 0001 0111 1001

Therefore, the BCD equivalent of decimal 179 is 0001 0111 1001.

Advantages of BCD

BCD offers several benefits in specific applications:

• Ease of Conversion for Displays: It simplifies the design of digital displays (like those found in calculators and digital clocks) because each 4-bit BCD group directly corresponds to a single decimal digit to be displayed.
• Reduced Rounding Errors: In financial or sensitive calculations, BCD can represent decimal fractions exactly, avoiding the rounding errors that can occur when converting decimal fractions to pure binary. This ensures precision in monetary values.
• Human Readability: When debugging or analyzing digital data, BCD makes it easier for humans to interpret the stored numbers directly as decimal values.

Disadvantages of BCD

Despite its advantages, BCD also has drawbacks:

• Inefficient Storage: BCD is generally less space-efficient than pure binary. For instance, a two-digit decimal number up to 99 requires 7 bits in pure binary (1100011 for 99), but 8 bits in BCD (1001 1001 for 99). This means more memory is needed to store the same range of numbers.
• Complex Arithmetic Circuits: Performing arithmetic operations (addition, subtraction, multiplication, division) in BCD often requires more complex logic circuits compared to pure binary arithmetic, which can slow down calculations or increase hardware cost.

Practical Applications of BCD

BCD is commonly used in various digital systems where decimal input/output and precise decimal arithmetic are crucial:

• Digital Clocks and Watches: To easily display time in decimal format.
• Calculators: For accurate decimal calculations and display.
• Point-of-Sale (POS) Systems: Ensuring exact financial calculations without floating-point inaccuracies.
• Electronic Meters: Such as electric or water meters, where readings are displayed in decimal.
• Embedded Systems: Especially those interacting directly with human users through numeric keypads and displays.