Decimal to Binary

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 system through decimal to binary number conversion examples.


Decimal to Binary Conversion Example

Here we will discuss 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 number to binary number, the base of decimal number i.e. 10 will be changed into the base of 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 remainder 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.(image will be uploaded soon)


How to Convert Decimal Number System to Binary Number System?

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

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

2. 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.

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

4. Continue dividing the number till you get the quotient  0

5. 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.


On the basis of 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 are 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.


1. Convert 112₁₀ to binary number system

2. Convert 25673₁₀ to its equivalent binary number.

3. What would be the binary equivalent number of 12999₁₀?

4. Convert 555₁₀ to binary number.


Fun Facts

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

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

  • Most of the computer storage systems such as Compact disc, DVDs use a binary number system to manifest the large files.

  • A set of 8 binary digits is known as bit

  • Sometimes the word ‘period’ is used in place of ‘decimal’ to point out the dot used to separate the position of 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 which can be made from decimal numbers?

a. 9999

b. 10000

c. 999

d. 1000


3. What would be the greatest 4 digit number which 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

FAQ (Frequently Asked Questions)

1. Define Binary Number Systems and list Some of its Applications.

The binary number system also is known as the base-2 system is a way of symbolizing numbers that count through a combination of only two digits i.e. 0 and 1. A single number in a binary digit is known As "Bit". Binary arithmetic operations such as addition, subtraction, multiplication, and division are performed similarly as arithmetic operations are performed in the numeral.


Applications of Binary Number System

Binary numbers are commonly used in common applications. Each coding and language in computers such as java, C++ to write a program or encode any digital data as the computer understands only two digits i.e. 0 and 1. These two digits binary numbers are also used by the computers to symbolize data or information in varied bits of information as computers understand only coded language.

2. Explain Binary Number System Arithmetic Operations

Binary numbers arithmetic operations are performed similarly as arithmetic operations are calculated in numerals. Here are some of the binary number system arithmetic operations:


Binary Addition

Addition of the two binary numbers gives the binary number itself. For example-If we will add two binary numbers 1101 ₂and 1001₂, we will get 10110₂, which is a binary number.


Binary Subtraction

Subtraction of the two binary numbers gives a binary number itself. For example-If we will subtraction two binary numbers 1101 ₂and 1010₂, we will get 0010₂, which is a binary number.


Binary Multiplication

The binary number systems multiplication operations are performed similarly as multiplication is done in numerals. For example-If we will multiply two binary numbers 1101₂ and 1010₂, we will get 10000010₂, which is a binary number.


Binary Division

The binary number systems division operations are performed similarly as the division is done in numerals. For Example- Divide 1010₂ by 2, we will get the quotient value 101, which is a binary number.