8-4-2-1BCD code converted to decimal


  
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8-4-2-1 BCD Code (Binary Coded Decimal) Conversion to Decimal

The 8-4-2-1 BCD code is a method of representing decimal numbers in binary, where each digit of the decimal number is represented by a 4-bit binary number. This system uses the weights 8, 4, 2, and 1 for each bit of a 4-bit binary number.

How the 8-4-2-1 BCD Code works:

Each decimal digit is represented by a 4-bit binary number, and the binary digits (bits) are weighted with 8, 4, 2, and 1 in that order. For example:

  • 8 = 1000
  • 4 = 0100
  • 2 = 0010
  • 1 = 0001

So, in 8-4-2-1 BCD, the binary code for each decimal digit is:

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

Example:

Let’s convert an 8-4-2-1 BCD code to decimal.

Consider the BCD code: 1001 0101 0011

  1. Break it into 4-bit groups (each group represents a decimal digit):

    • 1001 → 9
    • 0101 → 5
    • 0011 → 3

  2. The decimal number is: 953.

Another Example:

Consider the BCD code: 0110 0001 1000

  1. Break it into 4-bit groups:

    • 0110 → 6
    • 0001 → 1
    • 1000 → 8

  2. The decimal number is: 618.

When is the 8-4-2-1 BCD used?

  • Digital electronics: BCD is used in digital circuits and displays (like in 7-segment displays) for easy conversion between human-readable decimal digits and the binary representation used in computers.
  • Computer systems: BCD is used for processing decimal numbers, especially in applications where decimal accuracy is crucial, such as financial systems.
  • Embedded systems: BCD helps with representing numbers in systems where decimal output is required.