# Decimal to Binary

In the conversion of decimal to binary, we have to change a base 10 number into a base 2 number with the help of some simple techniques. For instance; in case ‘1210’ is a decimal number, then its equal binary number will ‘11002’. Let us learn decimal to binary in detail.

## Definition

We have learned about various types of numbers in the number system in mathematics, thus, some of them are as follows:

• Binary Numbers: ‘Base 2’
• Octal Numbers: ‘Base 8’
• Decimal Numbers: ‘Base 10’

Moreover, we can convert these numbers from one system to another system. For instance, decimal to binary, decimal to hex, decimal to octal, and vice versa.

### Decimal to Binary Conversion

A decimal number consumes base 10 and a binary number consumes base 2. Further, in the conversion of decimal to binary, the base of the number changes too, i.e. from base 10 to base 2. In addition, all the decimal numbers have their equivalent binary numbers as well. Majorly, these binary numbers are applicable in the computer software applications, where we use it for programming purposes or for coding also. Thus, it is because the computers recognize the binary language that has digits: ‘0’ and ‘1’.

Therefore, after giving the input to the computer system in the decimal form it starts converting them into the binary digits. Thus, it conducts the necessary operations and provides the output into the decimal form again. Consequently, we have to learn how the decimal numbers can be symbolized in the binary form. However, before learning the steps for converting, we have to see the table to find out the equivalent binary number from a decimal number.

### Decimal to Binary Table

For converting it from decimal to binary number system, we must remember the decimal to the binary table. In other words, it will help in solving the problems in an easy and effortless way with an accurate answer.

The decimal to binary conversion for up to 20 numbers is provided 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 the Decimal Numbers into Binary Numbers?

To convert the decimal numbers into the binary numbers, we have to follow the steps available below:

• Firstly, we have to divide the provided decimal number with ‘2’ where it will give the result along with the remainder.
• In case the given decimal number is even, then it will give the remainder ‘0’.
• In case the given decimal number is odd, then the result will not be divided accurately and it will give the remainder ‘1’.
• Lastly, by placing all the remainders in an order where the Least Significant Bit i.e. ‘LSB’ at the highest and the Most Significant Bit i.e. ‘MSB’ at the lowest.

## Solved Examples for You

Example 1: Convert 16010 into a 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)

So, 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)

Consequently, 1710 = 100012.

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