Appendix A.2: Binary Coded Decimal (BCD)#

Binary Coded Decimal, also known as BCD or 8421 format is another widely used numbering system whereby each decimal digit from 0-9 is individually represented as a 4-bit binary number between ``0000and1001`.

The main advantage of binary coded decimal is that it allows easy conversion between decimal and binary form.

Where is BCD used

  • Calculators

  • Decimal display drivers

  • Digital Clock

  • PC BIOS to store date and time

Binary Coded Decimal shows the codes for the 10 values that are used in BCD coded representations.

Table 19 Binary Coded Decimal#

Decimal

BCD Coding

0

0000

1

0001

2

0010

3

0011

4

0100

5

0101

6

0110

7

0111

8

1000

9

1001

Examples#

\(5_{10} ≡ 0101_\textrm{BCD}\)

\(22_{10} ≡ 0010\, 0010_\textrm{BCD}\)

\(86_{10} ≡ 1000\, 0110_\textrm{BCD}\)

\(2020_{10} ≡ 0010\, 0000\, 0010\, 0000_\textrm{BCD}\)

Pros and Cons of Binary Coded Decimal#

Pros#

  • Simple to convert between BCD and decimal values.

  • SLess data loss in floating point calculations.

Cons#

  • Requires more complex circuitry.

  • Wasteful as only uses 10 out of 16 possible 8-bit representations.

  • Requires more storage than other encoding systems.

    • \(15_{10} = 1111_2 = 0001\, 0101_\textrm{BCD}\)

    • \(255_{10} = 1111\, 1111_2 = 0010\, 0101\, 0101_\textrm{BCD}\)

    • \(8579_{10} = 0010\, 0001\, 1000\, 0011_2 = 1000\, 0101\, 0111\, 1001_\textrm{BCD}\)