Decimal to Binary Converter

Binary Result:

Combinations Calculator

Calculate the number of ways to choose r items from n items (order doesn't matter)

Permutations Calculator

Calculate the number of ways to arrange r items from n items (order matters)

Key Differences:

Combinations: Order doesn't matter. Choosing ABC is the same as choosing CBA.

Permutations: Order matters. ABC and CBA are counted as different arrangements.

Example: Choosing 3 team members from 5 people uses combinations (order doesn't matter). Assigning president, vice-president, and secretary from 5 people uses permutations (order matters).

How to Use This Tool

This tool converts a non-negative decimal number into binary format. It also offers calculators for combinations and permutations.

  1. Type your decimal number in the first input field. Only non-negative integers are accepted.
  2. Click the "Convert to Binary" button or press Enter. The result will show immediately.
  3. Observe the step-by-step calculation. Each division by 2 is displayed with its remainder.

Input Fields Explained

The first field accepts a decimal number. If you input a wrong number or a negative value, the tool shows an error message.

The combinations calculator asks for two numbers. One field is for the total items and the other for the items to choose. The permutations calculator uses similar fields for arranging items. Enter only positive numbers in these fields.

Understanding the Output

The binary result appears in a clear, monospaced font. The tool also displays the full calculation process. Read the steps from bottom to top to see how the binary number is formed.

The calculators for combinations and permutations show the computed result along with the formulas. The formula for combinations is C(n,r) = n! / (r! × (n - r)!) and for permutations it is P(n,r) = n! / (n - r)!. The output breaks down the calculations step by step.

Limitations and Special Notes

Only non-negative integers work correctly with the decimal to binary converter. The calculators work best with smaller numbers. For large numbers, the step-by-step display may be lengthy.

Take care to use proper inputs. Wrong values might lead to error messages.

Examples and Use Cases

This tool is helpful for students learning how to convert decimal numbers to binary. It assists teachers by showing the calculation process clearly. Hobbyists and anyone curious about number systems may also find it useful.

For the combinations and permutations calculators, the tool simplifies basic calculations. Use these calculators to quickly learn the differences between the two methods. They are practical for classroom settings and quick reference.