Simplify Decimal to Binary Conversion

Convert In Seconds

Turn base 10 into base 2 fast. This decimal to binary converter shows each step and a final check. This page includes Combinations and Permutations calculators with clear notes on differences. Use this guide to make quick, accurate work.

Why Use This Tool?

This page keeps math clear and quick. You type a number and get the binary answer. You see how the method works. Extra calculators help with counting tasks in one place.

• Instant result for decimal to binary
• Step by step division shows every remainder
• An exponents of two sum confirms the value
• Accepts whole numbers zero or greater
• Press Enter to run a calculation
• Clear tips show when order matters

How It Works

The converter reads your input and checks it. If the field is empty it asks for a number. If the value fails to parse it shows an error message. If the value is below zero it asks for a positive number.

If the value is zero it returns 0 with a short note. For any other value it converts your number to base 2 and prints the digits. Then it lists divide by 2 steps with quotients and remainders. It prints a sum of exponents of two that equals your number. The binary string has no leading zeros.

How to Use This Tool

Follow these steps.

Decimal to Binary

• Enter a whole number in the decimal field
• Click Convert to Binary or press Enter
• Read the Binary Result below the label
• Check the divide by 2 steps under the result
• Review the exponents of two check line

Input rules

• Use whole numbers only
• The tool reads only the integer part of a decimal
• Zero counts as a valid input
• Use numbers zero or greater

Output explained

• Binary Result shows bits from left to right
• The steps show each divide by 2 with quotient and remainder
• The last line adds exponents of two where the bit is 1
• That sum equals your original number

Example

• 42 becomes 101010 in binary

Combinations Calculator

• Enter the total items as n
• Enter the items to choose as r
• Click Calculate Combinations or press Enter in either field
• Read the count and the formula lines
• Scroll the list if it appears

Input fields explained

• n is the number of available items
• r is the number you choose
• Use whole numbers zero or greater
• r must be less than or equal to n

Output explained

• The tool shows the number of combinations
• It also shows the formula used for the count
• For small cases it lists every combination
• Items use labels from 1 up to n
• The list appears only if n is at most 10 and r is at most 5 and the total count is at most 100

Examples

• n equals 5 and r equals 3 gives 10 combinations
• n equals 4 and r equals 2 gives 6 combinations and shows the full list

Permutations Calculator

• Enter the total items as n
• Enter the items to arrange as r
• Click Calculate Permutations or press Enter in either field
• Read the count and the formula lines
• Scroll the list if it appears

Input fields explained

• n is the number of available items
• r is the number you arrange
• Use whole numbers zero or greater
• r must be less than or equal to n

Output explained

• The tool shows the number of permutations
• It shows the formula used for the count
• For small cases it lists every arrangement
• Items use labels from 1 up to n
• The list appears only if n is at most 8 and r is at most 4 and the total count is at most 100

Examples

• n equals 5 and r equals 3 gives 60 permutations
• n equals 4 and r equals 2 gives 12 permutations and shows the full list

Friendly and Fast

Here are common use cases. Pick the one that fits your task today.

• Convert decimal to binary for coding or class
• Check bit masks and flags in a program
• Review how repeated division creates a binary number
• Quick checks for homework and quizzes
• Use combinations for team picks where order does not matter
• Use permutations for seat order or rankings where order matters

Limits and notes

• The converters use whole numbers only
• The integer part is used for any decimal input
• Large n or r values can exceed standard number limits
• Factorials grow fast and very large counts may show Infinity
• Lists of items appear only for small inputs as noted above
• Press Enter in any input to run that calculator

Key Differences

• Combinations ignore order
• Permutations use order
• ABC and CBA count as one combination
• ABC and CBA count as two permutations

Use this decimal to binary tool to learn and check your work. Keep inputs clear and simple, and the results stay easy to read.