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’
• Hexadecimal Numbers: ‘Base 16’

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 = 10100000_2.

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.