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Decimal to Binary Converter

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Decimal to Binary Converter is a free online tool to convert Decimal to Binary. Converting between Decimal to Binary is a common task in the everyday life of CS students or programmers. So, GeeksforGeeks provides a free user-friendly and efficient online decimal to binary Conversion tool to simplify this process and ensure accuracy. It is a fast, easy-to-use general-purpose calculator that can be used in any field such as Academics etc. Furthermore, it also helps students and working professionals to solve a wide range of day-to-day problems.

How to use the Decimal to Binary Calculator?

You can easily use the decimal-to-binary calculator by following the steps discussed below:

Step 1: Enter the given value in the decimal input field.

Step 2: Click on the convert button to convert the decimal value into the binary value.

Step 3: The value shown as the result is the required value in the binary form.

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 used for programming or coding purposes. This is because binary digits, 0 and 1 are only understood by computers.

How to Convert Decimal to Binary

For converting Decimal numbers into binary numbers, use different methods such as formula, division methods, and so on. Here, use the remainder formula. Steps to convert decimal number to binary number using decimal to the binary formula are as follow:

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

Step 2: Now divide the quotient (Qi) 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 the reverse order (Rn, 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:

17-in-Binary

Hence the Binary Equivalent of 17 is 10001.

Decimal to Binary Conversion Table

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

Decimal Number

Binary Number

Hexadecimal Number

0 0

0

1 1

1

2 10

2

3 11

3

4 100

4

5 101

5

6 110

6

7 111

7

8 1000

8

9 1001

9

10 1010

A

11 1011

A

12 1100

C

13 1101

D

14 1110

E

15 1111

F

16 10000

10

17 10001

11

18 10010

12

19 10011

13

20 10100

14

21 10101

15

22 10110

16

23 10111

17

24 11000

18

25 11001

19

26

11010

1A

27 11011

1B

28 11100

1C

29 11101

1D

30 11110

1E

31 11111

1F

32 100000

20

64 1000000

40

128 10000000

80

256 100000000

100

Decimal to Binary Examples

Some examples of converting decimal numbers to binary are:

Decimal 10 to Binary

  • Divide 10 by 2 to get quotient 5 and remainder 0.
  • Divide 5 by 2 to get quotient 2 and remainder 1.
  • Divide 2 by 2 to get quotient 1 and remainder 0.
  • Divide 1 by 2 to get quotient 0 and remainder 1.

Reading the remainders in reverse order: 1010. Therefore, the binary equivalent of decimal 10 is 1010.

Decimal 25 to Binary

  • Divide 25 by 2 to get quotient 12 and remainder 1.
  • Divide 12 by 2 to get quotient 6 and remainder 0.
  • Divide 6 by 2 to get quotient 3 and remainder 0.
  • Divide 3 by 2 to get quotient 1 and remainder 1.
  • Divide 1 by 2 to get quotient 0 and 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 to get quotient 23 and remainder 1.
  • Divide 23 by 2 to get quotient 11 and remainder 1.
  • Divide 11 by 2 to get quotient 5 and remainder 1.
  • Divide 5 by 2 to get quotient 2 and remainder 1.
  • Divide 2 by 2 to get quotient 1 and remainder 0.
  • Divide 1 by 2 to get quotient 0 and 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

Qustion 1: What is equivalent value of (278)10 in Binary?

Solution:

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

278-in-Binary

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

Qustion 2: Convert (25)10 in Binary

Solution:

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

25-in-Binary

Hence, the Binary Equivalent of 25 is 11001

Qustion 3: What is the value of 75 in Binary?

Solution:

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

75-in-Binary

Hence, the Binary Equivalent of 75 is 1001011

Practice Problems on Decimal to Binary Conversion

Q1: Convert 248 in Binary.

Q2: Convert 575 in Binary.

Q3: What is Binary equivalent of 49.

Q4: Convert (56)10 to (….)2.

Q5: What is the Binary Form of 95.

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FAQs on Decimal to Binary Conversion

Using decimal to binary formula, convert 3 decimal into a binary number. 

Using decimal to binary formula, 

Step 1: Divide the number by 3, find the remainder.

3 ÷ 2 gives Q1 = 1, R1 = 1

Step 2: Divide Q1 by 2, find the remainder.

1 ÷ 2 gives Q2 = 0, R2 = 1

Step 3: Write down the remainder in the following manner: the last remainder is written first, followed by the rest in the reverse order (Rn, R(n – 1) …. R1), this is the binary conversion of the given decimal number: 11

Answer: Hence, 3 as binary is (11)2

Using decimal to binary formula, convert 5 decimal into a binary number. 

Using decimal to binary formula, 

Step 1: Divide the number by 5, find the remainder.

5 ÷ 2 gives Q1 = 1, R1 = 1

Step 2: Divide Q1 by 2, find the remainder.

2 ÷ 2 gives Q2 = 1, R2 = 0

Step 3: Divide Q2 by 2, find the remainder.

1 ÷ 2 gives  Q3 = 0, R3 = 1

Step 4: Write down the remainder in the following manner: the last remainder is written first, followed by the rest in the reverse order (Rn, R(n – 1) …. R1), this is the binary conversion of the given decimal number: 101

Answer: Hence, 5 as binary is (101)2

Using decimal to binary formula, convert 8 decimal into a binary number. 

Using decimal to binary formula, 

Step 1: Divide the number by 8, find the remainder.

8 ÷ 2 gives Q1 = 2, R1 = 0

Step 2: Divide  Q1 by 2, find the remainder.

4 ÷ 2 gives Q2 = 1, R2 = 0

Step 3: Divide  Q2 by 2, find the remainder.

2 ÷ 2 gives Q3 = 0, R3 = 0

Step 4: Divide  Q3 by 2, find the remainder.

1 ÷ 2 gives Q4 = 0, R4 = 1

Step 5: Write down the remainder in the following manner: the last remainder is written first, followed by the rest in the reverse order (Rn, R(n – 1) …. R1), this is the binary conversion of the given decimal number: 1000

Answer: Hence, 8 as binary is (1000)2

How to convert decimal numbers to binary numbers?

  1. Divide the decimal number by 2.
  2. Note down the remainder (either 0 or 1) and the quotient.
  3. Repeat the division process with the quotient obtained in the previous step until the quotient becomes 0.
  4. Write the remainders obtained from the divisions in reverse order. These remainders form the binary equivalent of the decimal number.

How to convert decimal fraction to binary?

To convert a decimal fraction to binary, follow these steps:

  1. Multiply the decimal fraction by 2.
  2. Note the integer part of the result as the binary digit.
  3. Take the fractional part of the result and repeat step 1.
  4. Continue this process until you obtain the desired precision or until the fractional part becomes 0.

The binary digits obtained in step 2 form the binary equivalent of the decimal fraction.

How to convert point decimal to binary?

Converting a decimal number with both integer and fractional parts (point decimal) to binary involves separating the integer and fractional parts and converting each part individually.

  1. Convert the integer part of the decimal number to binary using the rules mentioned earlier for converting decimal numbers to binary.
  2. Convert the fractional part of the decimal number to binary using the steps outlined for converting decimal fractions to binary.
  3. Combine the binary representations of the integer and fractional parts, placing the binary point (or decimal point) appropriately to form the binary equivalent of the point decimal number.

What are the rules to convert a decimal number into a binary number?

The rules to convert a decimal number to binary are as follows:

  1. Start by dividing the decimal number by 2.
  2. Note the remainder and quotient.
  3. Repeat the division process with the quotient obtained in the previous step until the quotient becomes 0.
  4. Write down the remainders obtained in reverse order. These remainders form the binary equivalent of the decimal number.


Last Updated : 04 Mar, 2024
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