Binary Coded Decimal (BCD) conversions

BCD (Binary Coded Decimal)

·         It represents 0 to 9 digits.

·         4-bits binary = 1-bit BCD.

·         Invalid BCD numbers are 1010, 1011, 1100, 1101, 1110 and 1111.

   Decimal Digit BCD

   0          1         2          3          4          5          6          7          8          9         (decimal number)

0000   0001   0010   0011   0100    0101   0110   0111   1000   1001      (BCD code)

  Convert BCD code into Decimal number

(10000110)₂

Step 1: break the given number in 4, 4-bit.

1000   0110

Step 2: convert these 4-bit into their respective decimal numbers.

1000   0110

  8           6

Given BCD is (86)₁₀ in Decimal number.

  Convert Decimal  number into BCD code

(453)₁₀

Step 1: convert each decimal digit into 4-bit of binary number.

   4           5          3

0100    0101    0011

Step 2: join these binary digits.

(010001010011)₂

 BCD Addition

   23      →   00100011        

+15      →    00010101

   38      →   00111000

  BCD Subtraction

86-41=?

41 → 01000001 → 2’s compliment → 10111111 → -41

  86 →   10000110

-41 →   10111111

 45 → 1 01000101

Here  left most 1 is discarded.

Note:

If answer of addition or subtraction of BCD numbers is invalid, then add +6 or -6 respectively to their answers to get valid answer.