BCD code with examples

BCD (Binary Coded Decimal) is a code in which each decimal digit (0–9) is represented separately by its 4-bit binary equivalent. It is also called the 8421 code, since the four bits have weights 8, 4, 2 and 1.

BCD table

The six combinations 1010 to 1111 are invalid in BCD.

Examples

• $(259)_{10}$ = 0010 0101 1001 (BCD)
• $(47)_{10}$ = 0100 0111 (BCD), whereas in pure binary $47 = 101111_2$.
• BCD 1001 0011 = $(93)_{10}$.

BCD addition

Add the digits in binary. If the 4-bit sum is greater than 1001 (9) or a carry is produced, add 0110 (6) to correct it.

Example: $7 + 5$

    0111      (7)
  + 0101      (5)
  ------
    1100      invalid (>9)
  + 0110      add 6
  ------
  1 0010   -> 0001 0010 = 12

Advantages

• Easy conversion between decimal and BCD; ideal for displays (7-segment), calculators, digital clocks and meters.
• Decimal fractions such as 0.1 are exact.

Disadvantages

• Needs more bits than pure binary (e.g. 99 needs 8 bits in BCD, 7 in binary), so storage is wasted.
• Arithmetic is more complex because of correction steps.
• Six of the 16 combinations are unused.