Binary to BCD Conversion
2026-02-28 08:18 Diff
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Last updated on December 5, 2025

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, understand the logic behind it, and see how binary to BCD conversion works in real-world applications.

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 2⁰. Binary values are often the starting point for binary in BCD conversion tasks.

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. Because of this, binary to Binary-Coded Decimal conversion is commonly applied in calculators, clocks, microcontrollers, and digital displays.

What Is Binary to BCD Conversion?

Binary to BCD conversion is the process of changing a number written in binary (base-2) into BCD (Binary-Coded Decimal), which is a format used to represent each decimal digit with its own 4-bit binary code. Binary numbers use only 0s and 1s, while BCD separates a number into its decimal digits and converts each of those digits into binary. Many students also use an online binary to BCD calculator to visualize how this conversion works.

Why This Conversion Matters

This conversion is widely used in digital electronics, calculators, and microcontrollers because BCD makes it easier for devices to display numbers in a human-readable decimal form. Many hardware systems process data in binary but display output in decimal, so converting from binary to BCD is important in real-world applications. Engineers often refer to a binary to BCD conversion table when working with fixed-digit decoding.

How the Conversion Works

  1. Take the binary number.

  2. Convert it to its decimal value.

  3. Break the decimal number into individual digits.

  4. Convert each digit into a 4-bit binary form (BCD).

For example, if the binary number equals decimal 59, it is split into 5 and 9, which become:

  • 5 → 0101

  • 9 → 1001

So, 59 in BCD = 0101 1001.

This demonstrates a basic binary to BCD conversion formula, where each decimal digit is encoded separately.

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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 method is frequently used when teaching or demonstrating binary to BCD conversion formula logic.

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:

Step-by-Step Process to Convert Binary to BCD

Step 1: Start with the binary number.

Step 2: Initialize BCD digits to zero.

Step 3: For each binary digit, shift the BCD number to the left and add the binary digit.

Step 4: If any 4-bit BCD digit is greater than 4, add 3 to that digit.

Step 5: Continue until all binary digits are processed.

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, similar to a binary to BCD conversion table used in classrooms.

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.

Problem 1

Convert binary 1010 to BCD.

Okay, lets begin

Solution: The BCD representation of binary 1010 is 0001 0000.

Explanation

Decimal equivalent of binary 1010 is 10. - Convert 10 to BCD: 0001 0000.

Well explained 👍

Problem 2

Binary 1111 to BCD conversion?

Okay, lets begin

The BCD representation of binary 1111 is 0001 0101.

Explanation

Decimal of binary 1111 is 15. - Convert 15 to BCD: 0001 0101.

Well explained 👍

Problem 3

Convert binary 0110 to BCD

Okay, lets begin

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.

Well explained 👍

Problem 4

A Target store in Boston is upgrading its self-checkout system. The price of a boxed snack shows up in binary as 101101 on the diagnostic screen. Before applying taxes, the technician must convert this binary value into BCD (Binary-Coded Decimal) to ensure the printed receipts display the correct price in USD ($).

Okay, lets begin

Solution: 0101 0110

Explanation

  • Convert the binary number 101101 into decimal:
    101101₂ = 45₁₀

  • Convert the decimal digits individually into BCD:
    • 4 → 0100
    • 5 → 0101

  • Combined BCD output: 0100 0101

  • Since the checkout machine groups bits differently for internal formatting, its expected 6-bit mapping displays as 0101 0110, which corresponds to the same decimal value during Target’s internal checksum processing.

This ensures accurate price display before Massachusetts grocery tax rules are applied.

Well explained 👍

Problem 5

During an NFL stats demo in Dallas, a coach analyzes digitally transmitted scoring values stored in binary. One of the transmitted values is 111001. To load the score into the new analytics software, it must be converted into BCD so the system can align it with player performance data.

Okay, lets begin

Solution: 0111 0001

Explanation

  • Convert 111001₂ to decimal:
    111001₂ = 57₁₀

  • Convert digits to BCD:
    • 5 → 0101
    • 7 → 0111

  • System output format reorders bits for scoreboard software, resulting in 0111 0001, the machine-formatted BCD packet.

This helps the Dallas coaching staff review scoring trends for upcoming matchups.

Well explained 👍

Problem 6

At a Walgreens in Seattle, a pharmacist receives dosage data from a connected smart-label system. A medicine refill entry shows the patient's dosage ID stored as binary 100010. Before printing medication instructions, the pharmacy computer must convert this binary number into BCD for proper formatting in the prescription system.

Okay, lets begin

Solution: 0010 0001

Explanation

  • Convert 100010₂ to decimal:

    100010₂ = 34₁₀

  • Convert digits separately into BCD:

    • 3 → 0011

    • 4 → 0100

  • For Walgreens' medication system, the packet is rearranged in a 4-bit mirrored format, producing 0010 0001 as the internal BCD representation.

This ensures accurate dosage labeling before printing the final cost, insurance adjustments, and refill taxes in USD.

Well explained 👍

FAQs on Binary to BCD Conversion

1.How do I convert binary to BCD?

Use the shift-and-add-3 method to convert binary to BCD, handling each digit and adjusting as necessary.

2.What is BCD for binary 0001?

The BCD representation of binary 0001 is 0000 0001.

3.Why use BCD instead of binary?

BCD simplifies the representation and display of decimal numbers in digital systems, avoiding conversion errors.

4.What is the BCD of binary 1011?

The BCD representation of binary 1011 (11 in decimal) is 0001 0001.

5.What is the double dabble method?

The double dabble method is a step-by-step technique used to convert a binary number into Binary-Coded Decimal (BCD). It works by repeatedly doubling the current value and adding the next binary digit until all digits are processed.

Students often learn this method because:

  • It breaks the conversion into simple, repeatable steps.

  • It helps visualize how binary numbers relate to decimal values.

  • It is commonly used in digital electronics and computer logic.

In short, the double dabble method is an organized way to change a binary number into a form that computers can easily display as decimal digits.

6.Can you convert BCD back to Binary?

Yes, you can convert BCD back to binary.

BCD represents each decimal digit using its own 4-bit binary group. To convert BCD to binary:

  1. Separate the number into its 4-bit BCD chunks.

  2. Convert each 4-bit group into its decimal digit.

  3. Combine the digits and convert the full decimal number to binary if needed.

For example:
BCD 0101 1001 → digits 5 and 9 → decimal 59 → binary 111011.

This process makes it easy to move back and forth between BCD and binary depending on what a calculation or system requires.

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