Decimal to Binary conversion is a topic in the Number System that is often asked in exams. It involves changing a number from the decimal system (which uses numbers from 0 to 9) to the binary system (which uses only 0 and 1). To convert a decimal number into binary, we divide the number by 2 again and again until the result becomes 0. At each step, we note the remainder. Finally, we write all the remainders in reverse order — from the last one to the first — to get the binary number.

In this method, each division gives us a part of the binary code. This process helps us understand how computers and digital systems store and use numbers. In this article, you will learn what decimal and binary numbers are, how to convert between them using simple steps, and also go through solved examples and frequently asked questions for better understanding.

Read about Binary Numbers here.

Decimal to Binary Conversion

Each place value in the decimal (base ten) numeral system has ten possible values (0,1,2,3,4,5,6,7,8, or 9) in the decimal (base ten) numeral system. The binary (base two) number system, on the other hand, has two possible values for each place value, which are represented as 0 or 1. Because electronic computers use the binary system as their internal language, serious computer programmers should know how to convert from decimal to binary. To understand how to convert decimal numbers to binary numbers, let us first understand what are decimal and binary numbers.

Decimal Number System Definition

The decimal number system is also called the base-10 number system because it uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. It is the most common number system we use in daily life—for counting, measuring, money, and many other things. In this system, each digit has a place value based on powers of 10.

For example, in the number 452, the digit 2 is in the units place (10⁰), 5 is in the tens place (10¹), and 4 is in the hundreds place (10²). As we move to the left, the place value of each digit becomes 10 times bigger. This pattern continues with thousands (10³), ten-thousands (10⁴), and so on.

The decimal system is very easy to understand and use, which is why it’s the standard number system for most of the world.

Binary Number System Definition

The binary numbers system or the base 2 system constitutes only two digits that are 0 and 1. Computers manipulate and store all of their data, including numbers, words, films, pictures, and music, using the binary number system. Because the number “2” does not exist in this system, 1 + 1 = 10. George Boole, a British mathematician, produced seminal work in 1854 describing an algebraic system of logic based on the Binary System, which became known as Boolean algebra. His logical calculus would play a key role in the development of digital electrical circuitry.

Also, Check out the Latest Railway Exams with Maths as a Part of its Syllabus

How to Convert 3 to Binary in Simple Steps

We want to change the number 3 from decimal (base 10) to binary (base2).

Step 1:
Divide 3 by 2.
3 ÷ 2 = 1 with a remainder of 1

Step 2:
Now divide the quotient (1) by 2.
1 ÷ 2 = 0 with a remainder of 1

Step 3:
Now write the remainders from bottom to top (reverse order).
So, we get: 11

Therefore, 3 in binary is 11.

How to Convert Decimal to Binary Numbers?

Converting a decimal number to binary is popularly done by dividing the digit by 2 and writing out the remainder aside.

By repeatedly dividing a number by two and recording the result, decimal values can be transformed into binary.

Steps to be followed

Conversion of Integral Decimal Numbers 

• Divide the number by 2.
• Get the integer quotient for the next iteration.
• Get the remainder for the binary digit.
• Repeat the above steps until the quotient is equal to 0.

Next is the conversion of the fraction part.

Learn about Properties of Rational Numbers here.

Conversion of Fractional Decimal Numbers 

Fractional numbers can be transformed to binary form by successive multiplication by 2. That is in every step, the digit before the decimal point is transferred to a binary record and the same process is replicated among the remaining fraction.

The last step is decided when the fraction part is zero or it is terminated when the desired precision is achieved.

Take a look at an example to see how this works.

The remainders are to be read from bottom to top to obtain the binary equivalent.

4310=1010112. Also, read about Relations and Functions here

How to Convert 2 to Binary

The number 2 in decimal (normal number system) is written as 10 in binary. Binary numbers use only 0 and 1.

Steps to Convert 2 to Binary:

Step 1:
Divide 2 by 2:

• 2 ÷ 2 = 1 with a remainder of 0

Step 2:
Now divide the result (1) by 2:

• 1 ÷ 2 = 0 with a remainder of 1

Step 3:
Write the remainders in reverse order (from bottom to top):

• So we get 10

Therefore, 2 in binary is 10

How to Convert 3 to Binary

The number 3 in decimal becomes 11 in binary.

Steps to Convert 3 to Binary:

Step 1:
Divide 3 by 2:

• 3 ÷ 2 = 1 with a remainder of 1

Step 2:
Now divide the result (1) by 2:

• 1 ÷ 2 = 0 with a remainder of 1

Step 3:
Write the remainders from bottom to top:

• So we get 11

Therefore, 3 in binary is 11

Decimal to Binary Conversion Table

Decimal to Binary Conversion Examples

Let’s see some examples of Decimal to Binary Conversion that come in exams.

Solved Example 1: Convert the decimal number 25 into a binary number.

Solution:

Follow the steps below to convert 25 into a binary system.

1. Divide the number 25 by 2.
2. Get the integer quotient for the next iteration.
3. Get the remainder for the binary digit.
4. Repeat the above steps until the quotient is equal to 0.

Solved Example 2: Convert the decimal number 0.35 into a binary number.

Solution:

Multiply by 2 and record the carry in the integral position for fractional decimal figures. When the carries are read down, the equivalent binary fraction is produced, as seen in the sample below.

Thus the fractional binary number is .01011, i.e., 0.01011.

Solved Example 3: Convert the decimal number 18 into a binary number

Solution:

We use the division-by-2 method:

Now, write the remainders from bottom to top: 10010

Therefore, the binary form of 18 is: 10010

Hope this article on the Decimal to Binary was informative. Get some practice of the same on our free Testbook App. Download Now!