Decimal to Binary Converter

Decimal to Binary converter is a free online tool to convert decimal data to its binary equivalent. Try the below converter now!

What is Decimal?

The decimal number system is a base-10 system that uses ten digits: 0 through 9. Each digit in a decimal number represents a power of 10. Decimal is the standard syste for counting, calculations, and most daily activities.

Example: 25 (decimal)

Each decimal digit is multiplied by powers of 10, starting from the rightmost position.

25₁₀ = 2×10¹+5×10⁰ = 20+5 = 25

What is Binary?

The binary number system is a base-2 system that uses only two digits: 0 and 1. Most of all modern computers internally use the digital systems because it corresponds directly to the digital logic levels of “on” (1) and “off” (0).

Example: 11001 (binary)

Each binary digit (bit) represents a power of 2, starting from the rightmost position.

11001₂ = 1 * 2⁴ + 1 * 2³ + 0 * 2² + 0 * 2¹ + 1 * 2⁰ = 25₁₀

Decimal to Binary Conversion

To convert a decimal number to binary, we use a method called repeated division by 2. In this process, the decimal number is divided by 2, and the remainder (either 0 or 1) is recorded. This process is repeated until the quotient becomes zero. The binary number is obtained by reading the remainders in reverse order (from the last remainder to the first).

Steps to Convert Decimal to Binary

Divide the decimal number by 2.
Record the remainder (either 0 or 1).
Divide the quotient by 2 again and record the remainder.
Repeat the process until the quotient becomes 0.
Read the binary number by writing the remainders in reverse order.

Example Conversions

Let’s go through a few examples to better understand how to convert decimal numbers to binary.

Example 1: Convert 25 (decimal) to binary.

Divide 25 by 2: quotient = 12, remainder = 1
Divide 12 by 2: quotient = 6, remainder = 0
Divide 6 by 2: quotient = 3, remainder = 0
Divide 3 by 2: quotient = 1, remainder = 1
Divide 1 by 2: quotient = 0, remainder = 1

Now, reading the remainders from bottom to top: 11001

So, 25 (decimal) is equal to 11001 (binary).

Example 2: Convert 10 (decimal) to binary.

Divide 10 by 2: quotient = 5, remainder = 0
Divide 5 by 2: quotient = 2, remainder = 1
Divide 2 by 2: quotient = 1, remainder = 0
Divide 1 by 2: quotient = 0, remainder = 1

Now, reading the remainders from bottom to top: 1010

So, 10 (decimal) is equal to 1010 (binary).

Example 3: Convert 45 (decimal) to binary.

Divide 45 by 2: quotient = 22, remainder = 1
Divide 22 by 2: quotient = 11, remainder = 0
Divide 11 by 2: quotient = 5, remainder = 1
Divide 5 by 2: quotient = 2, remainder = 1
Divide 2 by 2: quotient = 1, remainder = 0
Divide 1 by 2: quotient = 0, remainder = 1

Now, reading the remainders from bottom to top: 101101

So, 45 (decimal) is equal to 101101 (binary).

Decimal to Binary Conversion Table

Here’s a quick reference table showing common decimal numbers converted to their binary equivalents:

Decimal	Binary
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010
15	1111
20	10100
25	11001

Online Decimal to Binary Converter

Using an online converter is the quickest way to convert decimal numbers to binary. These tools are especially useful for large numbers or when multiple conversions are required