115 LearnersLast updated on July 10th, 2025
Binary to BCD Conversion
Binary and BCD (Binary-Coded Decimal) are two different systems for representing numbers. Binary is a base-2 number system that uses only two digits, 0 and 1, to represent numbers. It is widely used in computers and digital systems. BCD, on the other hand, is a form of representing decimal numbers where each digit is represented by its own group of binary digits. This can simplify some operations and make it easier to display numbers on digital displays. Sometimes we need to convert binary numbers to BCD format for these reasons. In this topic, we will learn how to convert binary to BCD.
What is Binary?
Binary is a number system that is part of the fundamental basis of computer science. It uses only two digits, 0 and 1, to represent all numbers. It is a base-2 system, which simplifies calculations and processing in digital electronics. Each binary digit represents a power of 2, with the rightmost digit representing 2^0.
What is BCD?
BCD, or Binary-Coded Decimal, is a class of binary encodings of decimal numbers where each digit is represented by a fixed number of binary digits, usually four or eight. BCD is used in digital systems where a numerical value needs to be displayed, especially in systems that require precise decimal representation rather than binary approximation.
Binary to BCD Conversion Method
To convert binary numbers to BCD, we use a process called the Double Dabble or Shift-and-Add-3 algorithm. The main steps involve shifting and adjusting the binary input to transform it into BCD format. This involves checking each digit and adjusting it if it is greater than 4, then shifting and repeating the process until the binary number is fully converted.
How to Convert Binary to BCD?
Converting binary to BCD involves a series of steps: 1. Start with the binary number. 2. Initialize BCD digits to zero. 3. For each binary digit, shift BCD number to the left and add binary digit. 4. If any 4-bit BCD digit is greater than 4, add 3 to that digit. 5. Continue until all binary digits are processed. Example: Convert the binary number 1011 (11 in decimal) to BCD. - Write down the binary number: 1011. - Apply the conversion process to get the BCD result: 0001 0001 (11 in decimal).
Binary to BCD Conversion Chart
When working with digital systems, it is often necessary to convert binary numbers to BCD for easier interpretation and display. Below is a chart showing binary to BCD conversions for numbers 0 to 15 for quick reference.
Common Mistakes and How to Avoid Them in Binary to BCD Conversion
When converting binary numbers to BCD, people often make mistakes. Here are some common mistakes to better understand the concepts of conversion.
Mistake 1
Using Incorrect Conversion Method
People sometimes confuse methods and use incorrect steps for conversion, such as misunderstanding the shift-and-add-3 process.
Mistake 2
Not Adjusting BCD Digits Correctly
Mistakes occur when failing to add 3 to BCD digits greater than 4, resulting in incorrect BCD values.
Mistake 3
Misplacing Bits During Shift
Errors can arise from incorrect bit shifting, leading to improper BCD representations.
Mistake 4
Ignoring Leading Zeros
People might ignore necessary leading zeros in BCD format, which can cause display issues.
Mistake 5
Confusion Between Binary and Decimal
It's easy to confuse binary representations with decimal values, leading to incorrect conversions.
Binary to BCD Conversion Examples
Problem 1
Convert the binary 1101 to BCD
1101 in binary is 13 in decimal, and its BCD representation is 0001 0011.
Explanation
Convert binary 1101: - Decimal equivalent is 13. - Convert 13 to BCD: 0001 0011.
Problem 2
Convert binary 1010 to BCD.
Solution: The BCD representation of binary 1010 is 0001 0000.
Explanation
- Decimal equivalent of binary 1010 is 10. - Convert 10 to BCD: 0001 0000.
Problem 3
Binary 1111 to BCD conversion?
The BCD representation of binary 1111 is 0001 0101.
Explanation
- Decimal of binary 1111 is 15. - Convert 15 to BCD: 0001 0101.
Problem 4
Convert binary 1001 to BCD.
The BCD of binary 1001 is 0000 1001.
Explanation
- Decimal of binary 1001 is 9. - Convert 9 to BCD: 0000 1001.
Problem 5
Convert binary 0110 to BCD
0110 in binary is 6 in decimal, and its BCD is 0000 0110.
Explanation
- Decimal equivalent of binary 0110 is 6. - Convert 6 to BCD: 0000 0110.
FAQs on Binary to BCD Conversion
1.How do I convert binary to BCD?
2.What is BCD for binary 0001?
3.Why use BCD instead of binary?
4.What is the BCD of binary 1011?
Important Glossaries for Binary to BCD
Conversion: The process of changing one representation of a number into another form, such as binary to BCD. Binary: A base-2 number system using only the digits 0 and 1. BCD (Binary-Coded Decimal): A method of encoding decimal numbers using binary digits. Shift-and-Add-3: A common algorithm used for converting binary numbers to BCD. Digit: An individual number within a larger numerical representation.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
