Why Convert from 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 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 image will be uploaded soon)
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.
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:
Hence, 145₁₀ = 10010001₂
2. How to convert 112 into the Binary Number System?
Solution:
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
You may be wondering when the internet is flooded with the importance of Decimal to Binary Conversion Method then why should you refer to Vedantu's website only? Well, it is a very valid question.
At Vedantu we ensure that all the content brought to you is prepared by experts only who have relevant expertise in the subject. They curate the information in such a way that it is friendly for students as well as beginners. This will help you to understand the topic from the very basics and later you can build upon it.
Apart from the reliability of the materials, all these are made available to you for absolutely free. No hidden charges are involved. You need not even sign-up as these are part of open source information by Vedantu and can be accessed by anyone.
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.
FAQs on Decimal to Binary
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.
3. Where can I find authentic information on the Decimal to Binary Conversion Method for free?
You can find authentic information on the Decimal to Binary Conversion Method on Vedantu’s website as well as a mobile application for free. Content brought to you is tailor-made by subject matter experts of Vedantu. These experts have been teaching this topic for many years. This information brought to you is not free but also authentic and reliable. You can find information on other math topics which have been made available to you by Vedantu for free.
4. Is it possible to study the Decimal to Binary Conversion Method in one night?
The concept involved in Decimal to Binary Conversion Method is not very difficult thus it can be covered in one night. But like any other concept in math, you need enough practice to apply in the exam or elsewhere. Practicing and perfecting this topic may take time and cannot be conquered in one night. You should dedicate enough time to this topic as it forms a very fundamental concept of mathematics. Start early and try to solve problems such as conversions are needed.
5. Where is the Decimal to Binary Conversion Method used?
Decimal to Binary Conversion is used at various places. Firstly they are used in exams to report answers in the questioned format. It is used in higher standards as well. These conversions are used when solving complex mathematical problems. Such conversions can make such calculations simple and doable. These conversions and calculations associated with them are used in astrophysics as well. Calculations involved in spaced technology involve binary calculations. Thus this topic holds a lot of significance whether you are a school student studying are given for your exams or you are a rocket scientist.
6. How many questions do I need to practice to master the Decimal to Binary Conversion Method?
Number of sums that one needs to solve to gain a command over the Decimal to Binary Conversion Method varies from student to student. Generally, it suggested solving enough problems such that a variety of problems are covered. You may want to start with simple problems after learning the concept for the first time. Slowly you can move towards more complex problems. Cover at least 9-10 problems of each type. Focus on both, the accuracy and precision of your answers. If you still find the topic difficult, revisit the concept and solve more problems again.
7. Is Decimal to Binary Conversion Method useful in higher classes?
The answer to this question is yes. Decimal to Binary Conversion Method, Solved Examples, Quiz FAQs is very useful in higher classes. In higher standards, students have access to calculators but still, they are expected to know the logic and reason behind these conversions. These conversions form a basic part of quantitative aptitude and are needed in various entrance exams because these exams do not allow calculators. Thus we can safely conclude that concepts taught in Vedantu will stay with you for a very long time and will come in handy at many places in the future.