Binary to BCD Conversion in VHDL Programming Language

Introduction to Binary to BCD in VHDL Programming Language

Hello, and welcome to this blog post on how to implement Binary to BCD Conversion in VHDL

a> Programming Language! Whether you’re new to VHDL or looking to enhance your skills, you’re in the right place. In this post, I will guide you through the steps to write and implement a VHDL code that converts binary numbers to Binary-Coded Decimal (BCD). By the end of this post, you will have a clear understanding of how to handle binary-to-BCD conversion and be able to incorporate it into your VHDL designs. Let’s get started!

What is Binary to BCD Conversion in VHDL Programming Language?

Binary to BCD (Binary-Coded Decimal) conversion is the process of transforming a binary number into its BCD equivalent. In BCD, each decimal digit (0-9) is represented by a 4-bit binary value. This format is often used in digital systems that interact with human-readable decimal numbers, such as digital displays (e.g., seven-segment displays), calculators, and similar devices.

In the context of VHDL (VHSIC Hardware Description Language) programming, Binary to BCD conversion is essential when you are designing hardware systems that need to display binary values in a human-readable format. Since binary values can be difficult to interpret for humans, converting them to decimal numbers in BCD makes them easier to present and understand.

BCD	Decimal
0000	0
0001	1
0010	2
0011	3
0100	4
0101	5
0110	6
0111	7
1000	8
1001	9
others	undefined

Key Concepts

1. Binary Representation:

• Binary is the base-2 numbering system, consisting only of the digits 0 and 1.
• For example, the binary number 1101 represents the decimal number 13.

2. BCD Representation:

• In BCD, each decimal digit is represented by its 4-bit binary equivalent.
• For example, the decimal number 13 would be represented as two separate BCD digits: 0001 for ‘1’ and 0011 for ‘3’.
• This makes BCD different from the pure binary system since each decimal digit is encoded separately.

3. Why is Binary to BCD Conversion Needed?

• Human Readability: Many systems need to display numbers in decimal format, such as on LED or LCD displays.
• Interfacing with External Devices: Certain devices and controllers require input or output in BCD format.

Conversion Process

The process of converting a binary number to BCD in VHDL can be implemented using different algorithms. One commonly used method is the Double Dabble Algorithm, which performs the conversion by shifting the binary number and adjusting the result into the correct BCD form.

Here’s a general outline of how Binary to BCD conversion works:

Start with a binary number: Let’s say you have a 4-bit binary number like 1101 (which is 13 in decimal).

Initialize BCD digits: You prepare placeholders for each decimal digit, each represented as a 4-bit BCD value.

• Shifting and Adjustment:
  • For each bit in the binary number, shift it into the BCD placeholders.
  • If the BCD digit becomes greater than 4 after the shift, adjust it by adding 3. This ensures that the BCD digits correctly represent the decimal values.

Final Result: Once the algorithm completes the shifts and adjustments, the BCD digits hold the equivalent decimal value of the original binary number.

Example of Binary to BCD Conversion

Let’s consider converting the binary number 1101 (which is 13 in decimal) into BCD:

• Step 1: Start with binary 1101.
• Step 2: Prepare placeholders for two decimal digits (because 13 has two digits: ‘1’ and ‘3’).
• Step 3: Shift and adjust using the Double Dabble algorithm.
• Step 4: The result is 0001 0011, which represents ‘1’ and ‘3’ in BCD.

VHDL Code Implementation

The conversion process can be implemented in VHDL using sequential logic. Below is an example of how Binary to BCD conversion might be written in VHDL:

library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.NUMERIC_STD.ALL;

entity binary_to_bcd is
    Port (
        binary_in : in STD_LOGIC_VECTOR(7 downto 0); -- 8-bit binary input
        bcd_out   : out STD_LOGIC_VECTOR(11 downto 0) -- 12-bit BCD output
    );
end binary_to_bcd;

architecture Behavioral of binary_to_bcd is
begin
    process(binary_in)
        variable binary : unsigned(7 downto 0);
        variable bcd    : unsigned(11 downto 0);
        variable i      : integer;
    begin
        binary := unsigned(binary_in);
        bcd := (others => '0');
        
        -- Double Dabble algorithm
        for i in 0 to 7 loop
            if bcd(11 downto 8) > "0100" then
                bcd(11 downto 8) := bcd(11 downto 8) + "0011";
            end if;
            if bcd(7 downto 4) > "0100" then
                bcd(7 downto 4) := bcd(7 downto 4) + "0011";
            end if;
            if bcd(3 downto 0) > "0100" then
                bcd(3 downto 0) := bcd(3 downto 0) + "0011";
            end if;
            
            bcd := bcd(10 downto 0) & binary(7); -- shift left
            binary := binary(6 downto 0) & '0';
        end loop;
        
        bcd_out <= std_logic_vector(bcd);
    end process;
end Behavioral;

Explanation of the Code

• Inputs and Outputs: The input (binary_in) is an 8-bit binary number, and the output (bcd_out) is a 12-bit BCD result.
• Double Dabble Algorithm: The process shifts bits from the binary input and checks the BCD digits. If a BCD digit exceeds 4, it adjusts the value by adding 3 to ensure it stays within the valid BCD range.
• Shift Operations: The code handles shifting the binary value into the BCD result.

Why do we need Binary to BCD Conversion in VHDL Programming Language?

Binary to BCD (Binary-Coded Decimal) conversion is crucial in VHDL programming for several key reasons, especially when working with digital systems that need to represent numerical data in a way that is easily understood by humans or interfaced with certain devices. Let’s explore why this conversion is necessary:

1. Human-Readable Decimal Representation

• Human Interaction: In many digital systems, data is often stored and processed in binary form. However, humans are more accustomed to reading numbers in decimal form. Binary numbers can be large and difficult for humans to interpret directly. By converting binary numbers to BCD, it becomes easier to display the data on human-readable devices like seven-segment displays, LCD screens, or other numerical interfaces.
• Digital Displays: Devices such as calculators, clocks, and digital counters often display numbers in decimal format, not binary. BCD allows you to translate a binary number into a format that can be easily displayed to users.

2. Interfacing with External Devices

• Hardware Interfaces: Many external hardware devices, such as displays and controllers, work directly with BCD rather than binary. This is especially true in embedded systems where BCD is used for numerical outputs. For example, when interfacing with a seven-segment display, each decimal digit is represented as a separate 4-bit BCD value. Converting binary values to BCD is essential for ensuring compatibility between binary data processed internally by a system and the BCD data expected by display hardware.
• Legacy Systems: Some legacy systems and protocols require BCD input or output. Converting binary to BCD ensures compatibility with older equipment or communication protocols that use BCD as their numerical format.

3. Decimal Precision and Ease of Use

• Decimal Arithmetic: While binary numbers are efficient for computations in digital logic, BCD is often preferred for decimal-based arithmetic, especially in applications where accuracy in decimal operations is important. This is particularly relevant in systems like digital clocks, banking, and financial systems, where decimal precision is critical, and binary floating-point representations might lead to rounding errors.
• Avoiding Binary Conversion Issues: When working with binary values, especially larger numbers, translating them directly into decimal values can become complicated. BCD simplifies this process by directly encoding each decimal digit, reducing the need for complex conversion algorithms during runtime.

4. Applications in Digital Design

• FPGA and ASIC Designs: In VHDL programming, particularly in FPGA (Field-Programmable Gate Array) and ASIC (Application-Specific Integrated Circuit) design, binary to BCD conversion is used in a variety of applications such as digital counters, timers, and numerical displays. This is especially true when designing systems where numerical output must be displayed or interpreted by users.
• Digital Systems: Systems like fuel gauges, speedometers, or temperature displays in automobiles use BCD to show numerical values in a readable format on digital dashboards.

5. Simplicity in Handling Decimal Operations

• Simplicity of Conversion: The conversion of binary to BCD simplifies the process of converting large binary numbers into readable decimal format. Since each decimal digit is directly encoded into a 4-bit binary number in BCD, it makes it straightforward to split and represent large numbers.
• Avoiding Complex Decimal Calculations: In some applications, working directly with binary numbers can lead to complicated calculations when trying to represent decimal-based values. BCD simplifies these operations, making it easier to handle values with a clear decimal structure.

6. Compatibility with User Interfaces

• Control Panels and User Interfaces: Many user interfaces that allow input or display of numbers expect those numbers to be in decimal format. For example, control panels in elevators, ticketing machines, or point-of-sale (POS) systems might expect BCD inputs or outputs to represent numbers in a user-friendly way.
• Consumer Electronics: Devices like microwaves, washing machines, and other appliances often display numbers like time, temperature, or countdowns in decimal format. Using BCD ensures that these devices can represent the necessary numerical information correctly.

Example of Binary to BCD Conversion in VHDL Programming Language

To demonstrate Binary to BCD conversion in VHDL, we will implement the Double Dabble Algorithm. This is a common technique used to convert a binary number into its BCD representation by performing bit shifts and adjustments on the binary value.

In this example, we will convert an 8-bit binary number to a 12-bit BCD number. The binary number can represent values up to 255, and the BCD representation will have 3 decimal digits (since 255 in decimal is represented as “255” in BCD).

Overview of the Double Dabble Algorithm

The Double Dabble Algorithm shifts the binary input bit by bit into a temporary register that holds the BCD value. As the bits are shifted, the BCD digits are adjusted when their value exceeds 4 to ensure correct representation of decimal digits.

• Initialize the BCD output to zero.
• Iterate through each bit of the binary input:
  • Shift the binary value into the BCD register.
  • If any of the BCD digits are greater than 4, add 3 to adjust them (this corrects any discrepancies from shifting binary digits directly into a decimal system).
• Repeat this process for all bits of the binary input.

Step-by-Step Process

Let’s convert an 8-bit binary number (e.g., 11001101, which is 205 in decimal) to BCD using the Double Dabble Algorithm. The process is as follows:

• Initialize: Start with the binary number 11001101 and a BCD register initialized to zero.
• Shift and Adjust: For each binary bit, shift it into the BCD digits. If any BCD digit is greater than 4, adjust by adding 3.
• Final BCD: After processing all bits, the BCD register will hold the equivalent decimal representation in BCD format.

For 11001101 (binary), the BCD result will be 0010 0000 0101 (which represents “205” in BCD).

VHDL Code Implementation

Here’s the VHDL code that implements this Binary to BCD conversion using the Double Dabble Algorithm:

library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.NUMERIC_STD.ALL;

-- Entity Declaration
entity binary_to_bcd is
    Port (
        binary_in : in STD_LOGIC_VECTOR(7 downto 0); -- 8-bit binary input
        bcd_out   : out STD_LOGIC_VECTOR(11 downto 0) -- 12-bit BCD output (3 decimal digits)
    );
end binary_to_bcd;

-- Architecture Declaration
architecture Behavioral of binary_to_bcd is
begin
    process(binary_in)
        -- Internal variables for binary and BCD manipulation
        variable binary_value : unsigned(7 downto 0);
        variable bcd_value    : unsigned(11 downto 0);  -- 12 bits for 3 BCD digits
        variable i            : integer;
    begin
        -- Initialize binary and BCD variables
        binary_value := unsigned(binary_in);
        bcd_value := (others => '0'); -- Initialize the BCD output to 0

        -- Double Dabble Algorithm
        for i in 0 to 7 loop
            -- If the most significant digit of BCD is greater than 4, add 3
            if bcd_value(11 downto 8) > "0100" then
                bcd_value(11 downto 8) := bcd_value(11 downto 8) + "0011";
            end if;

            -- If the middle BCD digit is greater than 4, add 3
            if bcd_value(7 downto 4) > "0100" then
                bcd_value(7 downto 4) := bcd_value(7 downto 4) + "0011";
            end if;

            -- If the least significant BCD digit is greater than 4, add 3
            if bcd_value(3 downto 0) > "0100" then
                bcd_value(3 downto 0) := bcd_value(3 downto 0) + "0011";
            end if;

            -- Shift the binary value left and add the current binary bit to the BCD
            bcd_value := bcd_value(10 downto 0) & binary_value(7); -- Shift left
            binary_value := binary_value(6 downto 0) & '0';        -- Shift binary left
        end loop;

        -- Assign the final BCD value to the output
        bcd_out <= std_logic_vector(bcd_value);
    end process;
end Behavioral;

Explanation of the Code

1. Entity Declaration:

The entity has one input (binary_in), which is an 8-bit binary number, and one output (bcd_out), which is a 12-bit BCD result representing three decimal digits.

2. Process:

• The process block is triggered whenever there is a change in the binary_in input.
• binary_value holds the unsigned representation of the binary input.
• bcd_value holds the BCD result as an unsigned 12-bit number.

3. Double Dabble Algorithm:

• The algorithm loops 8 times, once for each bit in the binary number.
• For each iteration, it checks whether the current BCD digits exceed 4, and if so, it adds 3 to correct the BCD digit.
• The binary number is then shifted, and its most significant bit is added to the BCD result.
• The loop continues until all binary bits are processed.

4. Final Output:

The final BCD value is assigned to the output bcd_out, which can then be displayed or processed further.

Example Walkthrough

Let’s walk through a conversion example using the binary number 11001101 (205 in decimal):

1. Initialize:

• binary_in = 11001101
• bcd_value = 0000 0000 0000 (initially all zeros)

2. First Iteration:

• Shift binary left, add the most significant bit (1) to BCD.
• bcd_value = 0000 0000 0001

3. Subsequent Iterations:

• Continue shifting and adjusting. After each shift, check if any BCD digit exceeds 4 and adjust accordingly.
• Eventually, after processing all bits, bcd_value becomes 0010 0000 0101 (which is 205 in BCD).

3. Final Output:

The output BCD value 0010 0000 0101 represents the decimal number 205.

Advantages of Binary to BCD Conversion in VHDL Programming Language

Binary to BCD conversion in VHDL offers several advantages, particularly in digital design and hardware systems. Below are the key benefits:

1. Ease of Decimal Representation

• Human-Readable Format: BCD (Binary-Coded Decimal) format makes it easier to represent numbers in a way that humans understand. Since each decimal digit is individually encoded in binary, it is more intuitive for interfacing with numerical displays, such as seven-segment displays or LCDs.
• Simplified Display Control: When driving displays, BCD simplifies the conversion of binary numbers to decimal digits, eliminating the need for complex binary-to-decimal conversion algorithms at the display level.

2. Direct Display Driving in Embedded Systems

• Interfacing with Digital Displays: BCD is commonly used in embedded systems where numbers need to be displayed, such as in clocks, calculators, and digital counters. Converting binary data to BCD allows the system to directly drive seven-segment or LCD displays, which operate on decimal values rather than binary.
• Reduced Complexity in FPGA/ASIC Designs: By using BCD conversion in hardware implementations, it is easier to handle decimal-based outputs in Field Programmable Gate Arrays (FPGA) and Application-Specific Integrated Circuits (ASIC).

3. Error-Free Decimal Representation

• Accurate Representation of Decimal Numbers: In applications where precise decimal representation is required (such as in financial or measurement systems), BCD ensures that numbers are represented accurately without rounding errors that can occur when using binary floating-point numbers.
• Avoids Conversion Artifacts: Binary-to-decimal conversions using floating-point representations can introduce errors. BCD avoids these issues by working directly with decimal digits.

4. Efficient Hardware Implementation

• Simple Conversion Algorithms: The Double Dabble Algorithm, often used for binary to BCD conversion in VHDL, is relatively simple to implement in hardware. It requires basic shift operations and conditional additions, making it efficient for hardware processing.
• Low Resource Utilization: VHDL implementations of binary to BCD conversion can be optimized for FPGA or ASIC designs to minimize resource usage, such as logic gates and flip-flops.

5. Better Precision for Decimal-Centric Applications

• Suited for Decimal-Based Calculations: For applications that work primarily with decimal numbers, such as financial calculations or display units, BCD is a better fit than binary, as it ensures precise handling of decimal digits without approximation errors.
• Used in Time-Critical Applications: Many embedded systems, like digital clocks or real-time counters, need to display accurate decimal numbers in real-time. BCD conversion enables smooth and reliable decimal output.

6. Compatibility with Legacy Systems

• Interfacing with Legacy Equipment: Many older or legacy hardware systems use BCD for numerical representation. Binary to BCD conversion ensures compatibility with such systems, enabling modern VHDL-based designs to work seamlessly with older interfaces.

7. Simplified Arithmetic Operations

• Decimal Arithmetic: When performing arithmetic operations where decimal precision is important (such as in calculators or billing systems), BCD can simplify operations like addition and subtraction. Binary arithmetic, in contrast, requires additional steps to convert and interpret decimal results.

8. Portability Across Different Platforms

• Standardized Approach: BCD conversion is a well-understood and standardized process that can be implemented across various hardware platforms. The use of BCD ensures portability of designs and code in VHDL across different FPGA or ASIC platforms.

Disadvantages of Binary to BCD Conversion in VHDL Programming Language

While Binary to BCD conversion has several benefits, it also comes with certain disadvantages, particularly when considering the context of hardware design and implementation. Here are the main drawbacks:

1. Increased Hardware Complexity

• Additional Logic Required: The process of converting binary to BCD requires extra logic, such as shift registers, adders, and comparators. This increases the complexity of the hardware design, leading to more gate usage and potentially a larger footprint on FPGAs or ASICs.
• Implementation Overhead: While the algorithm (e.g., Double Dabble) is straightforward, it still adds overhead to the design, which could be avoided if binary representations were used directly. This may lead to increased design and verification time.

2. Higher Resource Utilization

• More FPGA Resources: Binary to BCD conversion consumes more resources, such as lookup tables (LUTs), flip-flops, and registers, when implemented in FPGAs. In resource-constrained environments, this can be a significant drawback, limiting the ability to implement other functionalities on the same chip.
• Larger ASIC Designs: In ASICs, the extra logic needed for BCD conversion can lead to larger die sizes, increasing the cost of manufacturing and power consumption.

3. Lower Performance

• Slower Operations: The conversion process, which involves multiple shifts and conditional additions, takes additional clock cycles. For systems requiring high-speed processing, such as real-time applications, this can introduce latency and reduce overall performance.
• Timing Delays: In systems with strict timing constraints, the additional operations required for conversion may cause timing issues, especially if the system is running at high clock frequencies.

4. Inefficient for Purely Binary Systems

• Unnecessary Overhead in Binary-Based Systems: For systems that primarily work with binary data (such as most digital systems), converting binary to BCD adds unnecessary overhead. If decimal display or interaction is not a core requirement, the conversion process becomes redundant and wastes processing power and resources.
• Better Alternatives: In some cases, simply working with binary representations and converting to decimal only at the display level (or in software) might be more efficient, avoiding the need for BCD altogether.

5. Limited Range for Number Representation

• Larger Bit-width for the Same Number: BCD uses more bits than binary to represent the same number. For example, a 4-bit binary number can represent values from 0 to 15, but a 4-bit BCD can only represent the decimal digits 0 to 9. This limits the range of numbers that can be represented in the same bit-width, which may lead to the need for wider registers and buses.
• Wasted Bits: In BCD representation, some binary combinations are invalid (e.g., 1010 to 1111 in a 4-bit BCD digit are not used), leading to inefficient use of available bit space.

6. Increased Power Consumption

• Extra Switching Activity: The additional logic involved in binary to BCD conversion causes more switching activity in the hardware, leading to higher dynamic power consumption. This can be a concern in power-sensitive applications, such as portable or battery-operated devices.
• Larger Circuitry: As the design becomes more complex, it also requires more power to drive the additional logic, contributing to increased overall power consumption of the system.

7. Design and Debugging Complexity

• More Complex Debugging: Since BCD is not as straightforward as binary in terms of direct calculations and bit manipulation, debugging issues related to BCD conversion can be more challenging. The designer must ensure that the conversion algorithm is functioning correctly and that edge cases are handled properly, increasing the complexity of the design verification process.
• Challenging for Beginners: For beginners in VHDL programming or hardware design, understanding and implementing binary to BCD conversion can be more challenging than directly working with binary numbers. The need for shift and add operations might not be intuitive for those new to digital design.

8. Less Efficient Arithmetic Operations

• Complexity in Arithmetic: Performing arithmetic operations directly on BCD numbers is more complex than in binary. While addition in binary is simple and efficient, adding two BCD numbers requires extra logic to adjust for overflow within each decimal digit, further complicating the design.
• Slower Arithmetic: Due to the added complexity in handling BCD arithmetic, operations such as addition, subtraction, and multiplication tend to be slower than their binary counterparts. This impacts the performance of the system, particularly in real-time applications.