Decimal to Binary

Decimal to Binary Conversion: In number system, we have learned about different types of numbers such as

  • Binary Numbers – Base 2
  • Octal Numbers – Base 8
  • Decimal Numbers – Base 10
  • Hexadecimal Numbers – Base 16

These numbers can be converted from one system to other systems like decimal to binary, decimal to hex, decimal to octal and vice versa. In this article, we are going to discuss the conversion of decimal to binary number system along with the conversion steps and examples.

Decimal to Binary Table

In order to convert from decimal to binary number system, you should remember the decimal to binary table to solve the problems in an easy way with an accurate solution. Here the decimal to binary conversion up to 20 numbers is given below for reference.

Decimal Number

Binary Number

0

0

1

1

2

10

3

11

4

100

5

101

6

110

7

111

8

1000

9

1001

10

1010

11

1011

12

1100

13

1101

14

1110

15

1111

16

10000

17

10001

18

10010

19

10011

20

10100

How to Convert Decimal to Binary Numbers?

To convert decimal to binary numbers, proceed the steps given below:

  • Divide the given decimal number by “2” where it gives the result along with the remainder.
  • If the given decimal number is even, then the result will be whole and it gives the remainder “0”
  • If the given decimal number is odd, then the result is not divided properly and it gives the remainder “1”.
  • By placing all the remainders in order where the Least Significant Bit (LSB) at the top and Most Significant Bit (MSB) at the bottom.

Now, let us convert the given decimal number 294 into a binary number.

Divide by 2

Result

Remainder

Binary Value

294 ÷ 2

147

0

0 (LSB)

147 ÷ 2

73

1

1

73 ÷ 2

36

1

1

36 ÷ 2

18

0

0

18 ÷ 2

9

0

0

9 ÷ 2

4

1

1

4 ÷ 2

2

0

0

2 ÷ 2

1

0

0

1 ÷ 2

0

1

1 (MSB)

Therefore, the binary equivalent for the given decimal number 29410 is 1001001102

29410 =1001001102

Decimal to Binary Examples

Example 1: Convert 16010 to binary Number

Solution:

Given: Decimal Number = 16010

Divide by 2

Result

Remainder

Binary Value

160 ÷ 2

80

0

0 (LSB)

80 ÷ 2

40

0

0

40 ÷ 2

20

0

0

20 ÷ 2

10

0

0

10 ÷ 2

5

0

0

5 ÷ 2

2

1

1

2 ÷ 2

1

0

0

1 ÷ 2

0

1

1 (MSB)

Therefore, 16010 = 101000002

Example 2: Convert 1710 into a binary number

Solution:

Given: Decimal Number = 1710

Divide by 2

Result

Remainder

Binary Value

17 ÷ 2

8

1

1 (LSB)

8 ÷ 2

4

0

0

4 ÷ 2

2

0

0

2 ÷ 2

1

0

0

1 ÷ 2

0

1

1 (MSB)

Therefore, 1710 = 100012

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Practise This Question

Which of the following is an example of perpendicular lines?

1. Corners of your circular room floor

2. One of the angles in both your set squares

3. Angle included between the hour hand and minute hand when it is 12:15 in your wall clock