Binary to Decimal Converter
Convert between binary (base-2) and decimal (base-10) numbers. Supports signed/unsigned integers, two's complement, and shows step-by-step calculations for educational purposes.
Conversion Options
Positive numbers only
For signed numbers only
Output format only
Educational breakdown
Recommended Settings
Binary to Decimal Best Practices
- •Binary input accepts only 0 and 1 characters (spaces are ignored)
- •Use unsigned mode for positive numbers (0 to 2^n-1)
- •Use signed mode for negative numbers (two's complement)
- •Enable 'Show Steps' for educational step-by-step breakdown
- •Bit width only matters for signed decimal → binary conversion
Common Use Cases
- •Education: Learn how binary number system works
- •Programming: Convert binary flags, masks, and bit patterns
- •Debugging: Analyze binary data from memory dumps or registers
- •Hardware: Design digital circuits and verify logic states
- •Networking: Parse binary protocol headers and packet data
Pro Tips
- •Live conversion updates automatically as you type for instant feedback
- •Swap button reverses direction and uses current output as new input
- •Two's complement is used for signed negative numbers (-128 in 8-bit = 10000000)
- •Binary format options (grouped/continuous) only apply when converting to binary
Most Popular
Most users convert unsigned binary to decimal for general-purpose number conversion
When to Use This Tool
Learn and teach how computers represent numbers in binary. Essential for understanding computer architecture, programming fundamentals, data types, and bitwise operations. Perfect for computer science courses, coding bootcamps, or self-study materials covering number systems, binary arithmetic, and how CPUs process numeric data at the hardware level.
Debug binary data from memory dumps, registers, or network packets. Convert between binary and decimal when working with bit flags, permissions, masks, or hardware interfaces. Essential for systems programming, embedded development, driver coding, reverse engineering, or troubleshooting binary protocols where understanding exact bit patterns is critical.
Design and verify digital circuits, microcontrollers, and FPGA logic. Convert between binary representations and decimal values for signal analysis, state machines, truth tables, or hardware specifications. Useful for electrical engineering students, hardware designers, and anyone working with digital electronics or computer architecture.
How It Works
Choose conversion direction: Binary → Decimal or Decimal → Binary
Select number type: Unsigned (positive only) or Signed (two's complement)
For signed decimal → binary, choose bit width (8, 16, 32, or 64 bits)
Optionally enable 'Show Calculation Steps' for educational breakdown
Enter your binary number (0s and 1s) or decimal number in the input field
The tool automatically converts as you type with live preview
For Binary → Decimal: Each bit position represents a power of 2
Starting from the right: 2^0, 2^1, 2^2, 2^3, etc.
Each '1' bit contributes its power of 2 to the sum
For signed binary, leftmost bit is sign: 0 = positive, 1 = negative (two's complement)
For Decimal → Binary: Number is repeatedly divided by 2
Remainders are collected and read bottom-to-top to form binary
For negative decimals (signed mode): Get absolute value, convert to binary
Then apply two's complement: invert all bits, add 1
Binary output is formatted as grouped (8-bit bytes) or continuous based on settings
All processing happens in browser - your data never leaves your device
100% Private
Files never leave your device. All processing happens locally in your browser.
Lightning Fast
Powered by Client-side JavaScript with custom binary/decimal conversion and two's complement algorithms for optimal performance on modern browsers.
Open Source
Built with verified, open-source libraries. Fully transparent.
Frequently Asked Questions
How does binary to decimal conversion work?
Binary to decimal conversion uses positional notation. Each binary digit (bit) represents a power of 2 based on its position. Starting from the right, positions represent 2^0, 2^1, 2^2, etc. To convert, multiply each bit by its corresponding power of 2 and sum the results. For example, binary 1011 = 1×2^3 + 0×2^2 + 1×2^1 + 1×2^0 = 8+0+2+1 = 11.
What is the difference between signed and unsigned numbers?
Unsigned numbers represent only positive values from 0 to 2^n-1 (e.g., 0-255 for 8 bits). Signed numbers use two's complement to represent both positive and negative values. The leftmost bit is the sign bit: 0 for positive, 1 for negative. An 8-bit signed number ranges from -128 to 127, while unsigned ranges from 0 to 255.
What is two's complement and when is it used?
Two's complement is the standard method computers use to represent negative numbers in binary. To get two's complement: invert all bits (0→1, 1→0), then add 1. This allows arithmetic operations to work uniformly for positive and negative numbers. Enable 'Signed' mode to use two's complement for negative decimal numbers.
Why do I need to specify bit width for signed numbers?
Bit width determines the range of representable values and affects two's complement calculation. Common widths: 8-bit (-128 to 127), 16-bit (-32768 to 32767), 32-bit (-2147483648 to 2147483647). The sign bit occupies the leftmost position, so bit width must be specified to correctly pad and interpret signed binary numbers.
Can I convert decimal numbers with fractional parts?
No, this tool only supports integer conversions. Binary representation of integers is straightforward (powers of 2), but fractional numbers use different formats like IEEE 754 floating-point. For integers only, use this tool. For floating-point or decimal fractions, you would need a specialized floating-point binary converter.
What is the maximum number I can convert?
For binary to decimal: maximum 64 bits (preventing overflow issues). For decimal to binary: depends on bit width setting and signed/unsigned mode. Unsigned 32-bit: 0 to 4,294,967,295. Signed 32-bit: -2,147,483,648 to 2,147,483,647. The tool validates ranges and shows clear error messages if values are out of bounds.
What does 'Show calculation steps' do?
Enabling this option displays a step-by-step breakdown of the conversion process. For binary to decimal, it shows each bit position and power of 2 calculation. For decimal to binary, it shows the division-by-2 method. For signed numbers, it shows two's complement steps. This is educational and helps verify the conversion logic.
Is my data secure using this tool?
Yes! All conversions happen entirely in your browser using JavaScript. Your numbers never leave your device, are never uploaded to any server, or stored remotely. The tool operates 100% client-side for complete privacy. All calculations are performed locally in real-time.