Binary-coded decimal (BCD)

Definition

Binary-coded decimal (BCD) is a method of representing decimal numbers in binary form where each digit of a decimal number is represented by its own fixed binary sequence. BCD is useful for applications that require precise decimal representation and easy conversion between binary and decimal formats, especially in digital systems like calculators and digital clocks.

5 Must Know Facts For Your Next Test

1. BCD uses a four-bit binary representation for each decimal digit, meaning the digits 0 through 9 are represented as 0000 to 1001 in binary.
2. Unlike pure binary representation, BCD can lead to increased storage requirements since it is less efficient for larger numbers.
3. BCD is particularly beneficial in applications such as calculators where precise decimal representation is necessary for accurate computations.
4. There are several variants of BCD, including packed BCD, where two decimal digits are stored in one byte, and unpacked BCD, where each digit takes up a full byte.
5. BCD arithmetic can be more complex than binary arithmetic because it requires additional logic to handle carrying between digits when performing addition or subtraction.

Review Questions

• How does binary-coded decimal (BCD) differ from standard binary representation when encoding numerical values?
  • Binary-coded decimal (BCD) encodes each individual decimal digit as a separate four-bit binary value, while standard binary representation converts the entire number into a single binary sequence. For example, the decimal number 45 is represented in BCD as 0100 0101 (where '4' is 0100 and '5' is 0101), whereas in standard binary, it would be 101101. This method allows for easier conversion back to decimal but can lead to inefficiencies in storage.
• Discuss the advantages and disadvantages of using BCD in digital systems compared to pure binary encoding.
  • The main advantage of using BCD is its ability to represent decimal numbers accurately, making it ideal for applications like calculators and digital displays that require precise decimal output. However, the downside is that BCD can be less efficient than pure binary encoding because it uses more bits to represent the same value. As a result, it may lead to increased memory usage and more complex arithmetic operations compared to systems that use standard binary encoding.
• Evaluate the significance of BCD in practical applications like calculators and digital clocks, considering its impact on user experience.
  • BCD plays a crucial role in practical applications like calculators and digital clocks by allowing them to display numbers exactly as users expect in decimal format. This makes it easier for users to read and interpret results without needing to convert from binary. The ability to perform accurate arithmetic operations on decimal values without losing precision enhances the overall user experience, particularly in devices designed for everyday use where clarity and accuracy are essential.

Related terms

Decimal: The base-10 number system, consisting of digits 0 through 9, used for standard numerical representation.

Binary: The base-2 number system that uses only two digits, 0 and 1, to represent values in digital computing.

Gray Code: A binary numeral system where two successive values differ in only one bit, often used to prevent errors in digital circuits.