Binary Coded Decimal

Binary Coded Decimal (BCD)

Overview

Binary Coded Decimal (BCD) is a method of encoding decimal numbers where each decimal digit is represented by its own 4-bit binary code. While BCD uses more bits than pure binary, it simplifies conversion to and from decimal and is widely used in digital systems where decimal display is important, such as calculators and digital meters.

Detailed Explanation

Basic Encoding

Decimal | BCD    | Binary
--------|--------|--------
0       | 0000   | 0000
1       | 0001   | 0001
2       | 0010   | 0010
3       | 0011   | 0011
4       | 0100   | 0100
5       | 0101   | 0101
6       | 0110   | 0110
7       | 0111   | 0111
8       | 1000   | 1000
9       | 1001   | 1001
10      | 0001 0000 | 1010

Characteristics

1. Each decimal digit: 4 bits
2. Valid codes: 0000 to 1001
3. Invalid codes: 1010 to 1111
4. Storage efficiency: ~17% overhead
   (e.g., 0-99 needs 8 bits in BCD vs 7 in binary)

BCD Addition

Step 1: Add normally
Step 2: If sum > 9, add 6 (0110)

Example:
  5 (0101)
+ 4 (0100)
-------
  9 (1001) OK

  8 (1000)
+ 4 (0100)
-------
 12 (1100) Invalid!
+    (0110) Correction
-------
 18 (0001 1000) Final BCD

Applications

1. Digital Displays
   7-segment displays
   LCD readouts

2. Financial Systems
   Exact decimal representation
   No rounding errors

3. Data Entry Systems
   Keypad inputs
   User interfaces

Practice Problems

  1. Convert to BCD:

    • 28
    • 395
    • 1000

  2. Perform BCD addition:

    • 45 + 38
    • 67 + 86
    • 93 + 8

References

  • Digital Design Principles by Wakerly
  • Digital Electronics by Floyd
  • BCD Tutorial

← Back to Minor - Digital Electronics