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). This tool is especially useful for computer science students, programmers, and anyone who frequently deals with number system conversions.

Also, Check other Converters

• Binary to Decimal
• Decimal to Hexadecimal

Decimal to Binary Conversion

Before learning how to convert decimal to binary in a number system, let's first understand what a decimal number system is and what is a binary number system.

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.

How to Convert Decimal to Binary

To convert decimal numbers into binary, there are several methods, including formulas and division techniques. In this explanation, we'll use the remainder method. 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.

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

The common numbers in the Decimal number system and their corresponding binary number, along with the hexadecimal form, are as follows:

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.

Decimal 47 to Binary

Divide 47 by 2:
Quotient = 23, Remainder = 1.

1. Divide 23 by 2:
   Quotient = 11, Remainder = 1.
2. Divide 11 by 2:
   Quotient = 5, Remainder = 1.
3. Divide 5 by 2:
   Quotient = 2, Remainder = 1.
4. Divide 2 by 2:
   Quotient = 1, Remainder = 0.
5. Divide 1 by 2:
   Quotient = 0, Remainder = 1.

Reading the remainders in reverse order: 101111.
Therefore, the binary equivalent of decimal 47 is 101111.

Conclusion

In Conclusion, Decimal to Binary Calculator is a free online tool prepared by GeekforGeeks that converts the given value of the decimal number into the value of the binary number (0,1). It is a fast and easy-to-use tool that helps students solve various problems.

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)₁₀ to 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?