Decimal to Binary Converter

The Decimal to Binary Converter is a free, online tool designed to quickly and accurately convert decimal numbers (base 10) to binary numbers (base 2).

Steps to Convert Decimal to Binary

The steps to convert a decimal number to binary using this method are as follows:

Step 1: Divide the given decimal number by 2, and find the remainder (R_i).

Step 2: Now divide the quotient (Q_i) that is obtained in the above step by 2, and find the remainder.

Step 3: Repeat the above steps 1 and 2 until 0 is obtained as a quotient.

Step 4: Write down the remainder in the following manner: the last remainder is written first, followed by the rest in reverse order (R_n, R_{(n - 1)} .... R₁). Thus binary conversion of the given decimal number will be obtained.

Decimal Number System

The number system that has a base value of 10 is called Decimal Number System. Decimal Numbers are consist of the following digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Binary Number System

A binary Number System is a base-2 number system that uses two states 0 and 1 to represent a number. For example: 01, 111, etc.

All the decimal numbers have their corresponding binary numbers. These binary numbers are used in computer applications and for programming or coding purposes. This is because binary digits, 0 and 1 are only understood by computers.

Let's understand the above steps with the help of an example.

Example: Convert 17 to Binary Form.

Solution:

Following the above steps we will divide 17 by 2 successively. The division process is shown the image added below:

Hence the Binary Equivalent of 17 is 10001.

Decimal to Binary Conversion Table

Decimal to Binary Solved Examples

Some examples of converting decimal numbers to binary are:

Decimal 10 to Binary

Divide 10 by 2:
Quotient = 5, Remainder = 0.

1. Divide 5 by 2:
   Quotient = 2, Remainder = 1.
2. Divide 2 by 2:
   Quotient = 1, Remainder = 0.
3. Divide 1 by 2:
   Quotient = 0, Remainder = 1.

Now, write the remainders in reverse order:
Binary of 10 = 1010.

Decimal 25 to Binary

Divide 25 by 2:
Quotient = 12, Remainder = 1.

1. Divide 12 by 2:
   Quotient = 6, Remainder = 0.
2. Divide 6 by 2:
   Quotient = 3, Remainder = 0.
3. Divide 3 by 2:
   Quotient = 1, Remainder = 1.
4. Divide 1 by 2:
   Quotient = 0, Remainder = 1.

Reading the remainders in reverse order: 11001.
Therefore, the binary equivalent of decimal 25 is 11001.

Solved Questions on Decimal to Binary Conversion

Question (278)₁₀ in Binary?

Solution:

We have 278 in Decimal. To Convert in Binary we will divide 278 successively by 2.

Hence, (278) in decimal is equivalent to (100010110) in binary.

Question(25)₁₀ in Binary

Solution:

We have 25 in decimal. To convert 25 in binary we will divide 25 by 2 successively

Hence, the Binary Equivalent of 25 is 11001

Question (75)₁₀to binary?

Solution:

We have 75 in decimal. To convert 75 in binary we will divide 25 by 2 successively

Hence, the Binary Equivalent of 75 is 1001011

Practice Problems on Decimal to Binary Conversion

Question 1: Convert 248 in Binary.

Question 2: Convert 575 in Binary.

Question 3: What is the decimal equivalent of 49?

Question 4: Convert (56)₁₀ to (....)₂.

Question 5: What is the Binary Form of 95?

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