Decimal to Binary Converter

What this converter does

This decimal to binary converter turns a decimal number into binary with clear steps.

It can also convert to octal or hexadecimal when you need those.

You can enter whole numbers, fractions, and negative values.

The tool traces the method for each part of the number.

Fractional parts now convert correctly and show every step.

Use it for class, coding, or a quick check.

How It Works

Here is how to use the tool from start to finish.

1. Enter a decimal number in the input.
2. Choose Binary, Octal, or Hexadecimal in the list.
3. Set fractional precision digits if you need more detail.
4. Click Convert or press Enter on your keyboard.
5. Read the result, then check the steps below it.

Use a dot for the decimal point in your number.

Enter digits only without spaces or commas.

Why Use Our Tool?

You see the logic, step by step, with no guesswork.

The interface stays simple, so you stay focused.

It handles fractions and negative values with care.

It supports binary, octal, and hexadecimal in one place.

• Learn base conversion for school or exams.
• Verify homework and lab results fast.
• Explain number bases in a class or a tutorial.
• Check bit math for code, masks, and flags.
• Switch between bases for quick debugging.

Step-by-Step Guide

Input fields explained

• Decimal number: Type any decimal value, for example 13.625 or -15.75.
• Convert to: Pick the target base, choose Binary, Octal, or Hexadecimal.
• Fractional precision digits: Set how many digits to show after the point.
• Precision range: Use 0 to 20 digits, the default value is 8.
• Start conversion: Click Convert or press Enter to run it.

What the output shows

• Result line: You see your number written in the base you chose.
• Base mark: Look for ₂ for binary, ₈ for octal, or ₁₆ for hex.
• Negative values: A minus sign appears if your input is below zero.
• Conversion steps: The integer part shows divide by base steps with remainders.
• Reading the integer part: Read the remainders from bottom to top.
• Fractional steps: The fractional part shows multiply by base steps and digits.
• Repeating pattern: The steps note a repeat when a cycle appears.
• Truncation note: The steps say truncated at a set digit count when it stops.

Quick examples

• 13.625 to binary: 1101.101
• -15.75 to binary: -1111.11
• 26 to hexadecimal: 1A
• 83 to octal: 123

Final Thoughts

Notes and limits

• Many decimal fractions repeat in binary, the tool marks a repeat when it finds one.
• The output stops at your chosen precision, set more digits to see further detail.
• The method uses repeated division for integers and repeated multiplication for fractions.
• Use a dot for the decimal point, enter digits only.
• Hex uses letters A to F for values ten to fifteen.
• You can press Enter to convert, it saves time.

Try a few values in this decimal to binary converter, then follow the steps it shows.