# [Maths Class Notes] on Decimal to Binary Pdf for Exam

It is important to convert a value from one number system to another number system. With this, we would be in a position to tell when the two different values will represent a similar amount. In the conversion of Decimal to Binary, we convert base 10 numbers to base 2 numbers using a simple procedure. For example, if the decimal number is (11)₁₀ then its equivalent binary number would be (1011)₂. In this article, we will discuss the conversion of Decimal to Binary Number Systems through Decimal to Binary number conversion examples.

### Decimal to Binary Conversion Example

Here we will discuss the Decimal to Binary Conversion example:-

As we know, the Decimal Number System has base 10 and Binary Number System has base 2. While converting decimal numbers to binary numbers, the base of decimal numbers i.e. 10 will be changed into the base of the Conversion Binary Number System i.e. 2. All the decimal numbers retain their equivalent binary number. For example, if we want to convert (294)₁₀, then we will divide this number by 2. We will be left with some remainder and quotient value after dividing the given number by 2. The number will be divided by 2 till the quotient value reaches zero. As the quotient value reaches 2, place the remaining value in the series of Least Significant Bit (LSB) at the top and the Most Significant bit (MSB) at the bottom,

The binary numbers are most commonly used by computers for coding and programming purposes because the binary numbers system retains 2 digits 0 and 1 and computers only understand the language of the Binary Number System. (the )

## Decimal to Binary Conversion Method

### How to Convert a Decimal Number System to a Binary Number System?

To convert Decimal to Binary numbers, the following steps should be followed:-

Take any decimal number and divide it by “2″. After dividing, you will get some results along with the remainder.

If the decimal number chosen by you is even, then the result will be in a whole number and it will give the remainder 0.

If the decimal number chosen by you is odd, then the number will not be divided fully and you will get the remainder “1”.

Continue dividing the number till you get the quotient  0

Now place all the remainders in the series of Least Significant Bit (LSB) at the top and the Most Significant bit (MSB) at the bottom.

Based on the above steps, let us discuss the Decimal to Binary Conversion through example.

### Let us Convert the Decimal Number 244 into a Binary Number.

 Division of Decimal Number by 2 Quotient Remainder Binary 244/2 122 0 0 (LSB) 122/2 61 0 0 61/2 30 1 1 30/2 15 0 0 15/2 7 1 1 7/2 3 1 1 3/2 1 1 1 1/2 0 1 1 (MSB)

Hence, 244₁₀ =11110100₂

### Decimal to Binary Conversion Solved Example

Some of the Decimal to Binary Conversion solved examples are:-

1. How to convert 145 into the Binary Number System?

Solution:

 Division of Decimal Number by 2 Quotient Remainder Binary 145/2 72 1 1 (LSB) 72/2 36 0 0 36/2 18 0 0 18/2 9 0 0 9/8 4 1 1 4/2 2 0 0 2/2 1 0 0 1/2 0 1 1 (MSB)

Hence, 145₁₀ = 10010001₂

2. How to convert 112 into the Binary Number System?

Solution:

 Division of Decimal Number by 2 Quotient Remainder Binary 112/2 56 0 0 56/2 28 0 0 28/2 14 0 0 14/2 7 0 0 7/2 3 1 1 3/2 1 1 1 1/2 0 1 1

Hence, 112₁₀ = 1110000₂

### Decimal to Binary Problems

Here is some questions given below regarding the Decimal to Binary Conversion for the students to solve. Solving the questions, again and again, will help them to solve the problem speedily. With this, they will be able to solve the questions accurately and score good marks in their examination.

• Convert 112₁₀ to Binary Number System

• Convert 25673₁₀ to its equivalent binary number.

• What would be the binary equivalent number of 12999₁₀?

• Convert 555₁₀ to binary number.

### Fun Facts

• Decimal Number System is also known as base ten or binary numeral system.

• The Chinese counting rod system and Hindu-Arabic numeral system are the only two positional decimal systems in ancient civilization.

• Most computer storage systems such as Compact disc DVDs use a Binary Number System to manifest large files.

• A set of 8 binary digits is known as a bit

• Sometimes the word ‘period’ is used in place of ‘decimal’ to point out the dot used to separate the position of the number in the Decimal Number System.

### Quiz Time

1. How many unique symbols are there in Binary Number Systems?

a. 15

b. 7

c. 2

d. 9

2. What would be the greatest 4 digit number that can be made from decimal numbers?

a. 9999

b. 10000

c. 999

d. 1000

3. What would be the greatest 4 digit number that can be made from binary numbers?

a. 16

b. 13

c. 14

d. 15

4. Convert 100₁₀ to the Binary Number System.

a. 1100100

b. 1000100

c. 1111100

d. 1100101

### Importance of Decimal to Binary Conversion Method

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### Conclusion:

After reading this, you will be in a position to recognize if the given number is binary or decimal, you will know definitions of both the two, you will learn how they can be interconverted, the formula needed to do that, and the importance of this conversion. To fuel your enthusiasm further, fun facts have been added for you to read and have an enjoyable learning experience. Apart from this many questions have been provided towards the end for you to test your understanding of the topic. This write-up has been prepared very holistically for you to understand and excel in the exams.