Hex Decimal Binary Converter

Number System Conversion Diagram

Hex Decimal Binary Converter Calculator

How to Use This Calculator

1. Type your number—decimal by default, or use 0x for hex, 0b for binary, or 0o for octal.
2. If you don't know the format, just enter the number; the calculator tries to figure it out from your input.
3. Check that the input is displayed how you expect before hitting Calculate.
4. Click Calculate to show the translated values.

📹 Video Walkthrough — How to Use This Calculator

Number Base Conversion Formulas

Complete Guide to Number Base Conversion

Understanding Number Systems

You'll see different number systems because hardware, software, and people each have their own conventions. Binary is direct for logic and hardware, hex is a compact view of binary, decimal is for humans. Each base simply changes digit count and the weight each digit carries. The conversion work is about translating—not inventing—values between these formats.

For any kind of embedded engineering, including linear actuator controls or sensor data work, you'll hit base conversions when programming, reading specs, and debugging protocol traffic.

Binary System (Base 2)

Binary is the direct language of logic chips and embedded hardware. Each bit means a power of 2, which is why all your register operations, logic, and pin states boil down to binary. In actuator control and basic MCU work, binary is everywhere: digital I/O, flag registers, memory pointers—whether you write it as 0s and 1s or mask out the bits with hex values.

• Digital I/O pin states (HIGH/LOW)
• PWM signal generation for motor control
• Status registers and flag operations
• Memory addressing in microcontrollers

Hexadecimal System (Base 16)

Hex is shorthand for binary. Every hex digit is four bits, which slices up long binary data into easier-to-read chunks. You'll see hex everywhere in embedded datasheets, register descriptions, and memory maps. It's also the default for many hardware debuggers and bus analyzers.

• Memory addresses in embedded systems
• Color codes in display applications
• Register values in microcontroller datasheets
• Communication protocol data packets

Practical Conversion Examples

Example 1: Converting Decimal 170 to Other Bases

Example 2: Converting Binary 11010110 to Other Bases

Engineering Applications

Microcontroller Programming

When coding microcontroller systems, you'll always mix notations: setting up GPIO with binary masks, shifting hex values around registers, converting ADC readings from hex to decimal for real-world calculations, or parsing protocol packets that are logged in hex. It’s routine work for any embedded, automation, or actuator project.

• Port Configuration: Setting GPIO pins using binary masks (e.g., 0b11010000)
• PWM Values: Converting percentage duty cycles to 8-bit or 16-bit values
• Sensor Readings: Converting ADC values from hex to decimal for calculations
• Communication Protocols: Interpreting I2C/SPI data packets in hex format

Actuator Control Systems

In any actuator project, you'll run into base conversions just managing feedback signals, setting up motor control, and talking to sensors and limit switches—all real bits and hex values under the hood.

• Position Feedback: Converting encoder values from binary to position units
• Motor Drive Signals: Calculating PWM values for speed and direction control
• Limit Switch Processing: Reading digital inputs and converting to system states
• Network Communication: Formatting data for CAN bus, Modbus, or Ethernet protocols

Design Considerations and Best Practices

Choosing the Right Number System

No single number system fits every use. Binary is direct for bit-work and hardware, but too dense for complex values. Hex is best when you need to represent longer binary values in a readable format, like register configs or memory dumps. Decimal is for things people read, and octal comes up for legacy systems—for example, file permissions in Unix.

• Use Binary for: Bit manipulation, flag operations, and direct hardware control
• Use Hexadecimal for: Memory addresses, register values, and compact binary representation
• Use Decimal for: User interfaces, calculations, and human-readable values
• Use Octal for: Legacy systems and certain permission systems

Common Pitfalls and Solutions

Base conversions cause bugs when interpretation doesn't match code or documentation. Some sticking points:

• Leading Zeros: Not all programming languages treat 010 as decimal ten; double check format rules.
• Signed vs Unsigned: Know if your system uses two's complement for negative numbers—bit patterns mean different things depending on interpretation.
• Overflow Conditions: Watch for values rolling over target base (e.g., 8-bit maxes out at 255).
• Endianness: For multi-byte numbers, check the byte order—big-endian vs little-endian matters for communication protocols and memory dumps.

Advanced Conversion Techniques

Fast Binary-Hex Conversion

Converting between binary and hex is quick—group the binary bits in fours (add leading zeros where needed), then write out the hex value for each group. It’s direct, no calculation needed, just a lookup table.

• Group binary digits into sets of 4 (pad with leading zeros if necessary)
• Convert each group directly: 0000=0, 0001=1, ..., 1111=F
• Combine hex digits for the final result

Binary-Octal Conversion

Same idea as binary/hex, except groups of three bits. This comes up mostly with older hardware or some protocol details.

• Group binary digits into sets of 3 from right to left
• Convert each group: 000=0, 001=1, ..., 111=7
• Combine octal digits for the result

Integration with Modern Development Tools

Most IDEs, debuggers, and logic analyzers handle base conversions for you and allow viewing values in different notations. This takes care of the rote calculation but doesn’t replace the need for understanding how your microcontroller or actuator actually represents and processes those data types.

If you know your way around base conversion, you'll have an easier time debugging, tuning, or extending any actuator or embedded project. Reading datasheets, checking register settings, and analyzing communication protocols all rely on this foundation.

Frequently Asked Questions

About the Author

Robbie Dickson

Chief Engineer & Founder, FIRGELLI Automations

Robbie Dickson brings over two decades of engineering expertise to FIRGELLI Automations. With a distinguished career at Rolls-Royce, BMW, and Ford, he has deep expertise in mechanical systems, actuator technology, and precision engineering.