Binary and Decimal Converter

Binary to Decimal

Enter Binary Number:

Decimal to Binary

Enter Decimal Number:

How It Works (Formulas)

Binary to Decimal: Calculate the sum of (digit × 2^position). Position starts from 0 on the right.

Decimal to Binary: Repeatedly divide the decimal number by 2 and write down the remainders in reverse order.

Binary to Decimal Examples

Binary	Decimal
110	6
101	5
1001	9
1011	11
10101	21
11110	30
11111	31

Decimal to Binary (0-10)

Decimal	Binary
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010

Binary and Decimal converter: Binary to Decimal and Decimal to Binary

If you are looking decimal number to binary, binary number to decimal, binary and decimal, decimal to binary, binary to decimal. Convert binary to decimal and decimal to binary with this free online Binary and Decimal converter . While humans rely on the base-10 decimal system for daily life, computers process information using the base-2 binary system.

Key Features of this Binary and Decimal converter

Key features this Binary and Decimal converter is below:

Dual-Box Functionality: Convert binary to decimal and decimal to binary on the same page without reloading.
Input Validation: The tool identifies incorrect entries (like using a 2 in a binary field) to prevent calculation errors.
Clean & Responsive Design: Optimized for mobile, tablet, and desktop users.
Reset Capability: Quickly clear your data to start a new conversion with a single click.

How to Use this Binary and Decimal converter

1. Binary Number to Decimal Conversion

Locate the Binary to Decimal box.
Type the binary code (consisting only of 0s and 1s) into the input field (e.g., 101101).
Click the green Convert button.
The decimal equivalent will appear in the result area.

2. Decimal Number to Binary Conversion

Locate the Decimal to Binary box.
Enter any whole number (e.g., 45) into the input field.
Click the green Convert button.
The tool will display the exact binary representation of that number.

How It Works: The Science of Conversion

Have you ever wondered what happens “under the hood” when you click convert? Here is the logic:

From Binary to Decimal

The tool uses positional notation. Each digit in a binary number represents a power of 2.

Example: For binary 101
Calculation: $(1 \times 2^{2}) + (0 \times 2^{1}) + (1 \times 2^{0}) = 4 + 0 + 1 = 5$

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The tool automates this addition process for you.

From Decimal to Binary

To convert a decimal number to binary, the tool uses the Remainder Method.

The decimal number is divided by 2.
The remainder (0 or 1) is recorded.
The quotient is divided by 2 again.
This repeats until the quotient reaches 0. The remainders, read in reverse, form the binary number.