Understanding Binary-Coded Decimal (BCD)
Binary-Coded Decimal (BCD) is a system where each individual decimal digit (0-9) is represented by its own 4-bit binary code. Unlike pure binary, which encodes an entire decimal number into a single binary value, BCD encodes each digit separately. For example, the decimal number 23 is represented in BCD as 0010 0011 (where 0010 is 2 and 0011 is 3), not as its pure binary equivalent which would be 10111.
Key Principles of BCD Encoding
The core principle of BCD is to maintain the distinct identity of each decimal digit. This approach simplifies the conversion between decimal and binary, which is beneficial for human interaction or for specific arithmetic operations in digital circuits. Each 4-bit segment of a BCD number can only represent values from 0 (0000) to 9 (1001); binary combinations for 10 through 15 (1010-1111) are considered invalid in the standard BCD representation.
Practical Example: Representing a Number in BCD
To illustrate, consider the decimal number 157. In a pure binary system, this number would be represented as 10011101. However, in BCD, each digit is converted individually: the digit 1 becomes 0001, the digit 5 becomes 0101, and the digit 7 becomes 0111. Therefore, the decimal number 157 in BCD is represented as 0001 0101 0111. This direct mapping makes BCD easy to use for displaying numbers on screens, like those found in digital clocks or calculators.
Importance and Applications of BCD
BCD is primarily utilized in digital systems where accurate decimal representation and arithmetic are crucial, such as financial calculators, digital voltmeters, real-time clocks, and some legacy computer systems. Its main advantage lies in simplifying decimal display and input/output operations, eliminating the complex conversion logic that would otherwise be needed if pure binary were used to interact with decimal numbers. A notable disadvantage is its lower storage efficiency compared to pure binary for large numbers.