Decimal to Binary Converter Calculator

About Decimal to Binary Converter

A Decimal to Binary Converter is a simple and efficient tool for converting numbers from decimal (base 10) to binary (base 2). The Decimal to Binary Converter resource is invaluable for students and professionals dealing with Computer Science, Mathematics, or Engineering concepts. By using the JAIN (Deemed-to-be University) tool, you can easily convert decimal to binary, saving time and ensuring accuracy. With just a few clicks, this calculator provides the binary equivalent of any decimal number you input, offering clarity and convenience.

Why Use Decimal to Binary Converter Available at the Website of JAIN (Deemed-to-be University)

The Decimal to Binary Calculator provided by JAIN (Deemed-to-be University) is designed for user-friendliness and precision. It eliminates the need for manual calculations, making complex conversions straightforward. This tool is ideal for students, educators, and professionals managing assignments or research. Whether you are working on assignments or conducting research, this online resource ensures precision and saves valuable time. 

Start exploring the power of this innovative and reliable Decimal to Binary Converter today! Just fill in a decimal number in the appropriate field called “Enter Decimal Number” and click on the “Convert” button. The decimal number will instantly get converted to a binary number. 

What are Decimal Numbers?

A decimal number consists of two parts: a whole number and a fractional part. Decimal numbers, represented in the base-10 system, range from 0 to 9 and are fundamental to calculations in everyday life, including counting, measuring, and financial transactions.

Decimal numbers can also be defined as numbers which are expressed in the base-10 system. This system consists of 10 digits, ranging from 0 to 9. For example, numbers like 5, 23, and 198 are all decimal numbers. 

Each digit in a decimal number holds a place value based on powers of 10, making it easy to interpret and manipulate large values. Decimal numbers are fundamental to everyday calculations, forming the basis of counting, measuring, and financial transactions.

What are Binary Numbers?

Binary numbers use the base-2 system, consisting of only two digits: 0 and 1. Each digit represents a power of 2, making this system fundamental to computer science for data representation and processing. For example, the binary number 101 equals 5 in decimal (1 × 2² + 0 × 2¹ + 1 × 2⁰).

Each binary digit, or bit, corresponds to a power of 2, starting from the rightmost bit. For example, the binary number 101 represents 1 × 2² + 0 × 2¹ + 1 × 2⁰, which equals 5 in decimal. Binary numbers form the language of computers, enabling them to execute instructions and store information effectively.

How to Convert Decimal to Binary

Converting decimal numbers to binary involves dividing the decimal number repeatedly by 2 and recording the remainder. 

To convert a decimal number to binary, follow these steps:

1. Divide the decimal number by 2.

2. Record the remainder (0 or 1).

3. Repeat until the quotient becomes 0.

4. Write the remainder in reverse order to obtain the binary equivalent.

For example, to convert the decimal number 10 to binary:

• 10 ÷ 2 = 5 remainder 0

• 5 ÷ 2 = 2 remainder 1

• 2 ÷ 2 = 1 remainder 0

• 1 ÷ 2 = 0 remainder 1

Reversing all remainders gives the binary number 1010.

Decimal to Binary Conversion Table

Here is a quick reference table showing the binary equivalents of decimal numbers from 0 to 15:

This table helps illustrate the relationship between decimal and binary systems, serving as a quick reference for conversions.

Decimal to Binary Conversion Examples

Example 1: Convert 25 to Binary

1. 25 ÷ 2 = 12 remainder 1

2. 12 ÷ 2 = 6 remainder 0

3. 6 ÷ 2 = 3 remainder 0

4. 3 ÷ 2 = 1 remainder 1

5. 1 ÷ 2 = 0 remainder 1

When the remainders are reversed, the binary equivalent of 25 is 11001.

Example 2: Convert 7 to Binary

1. 7 ÷ 2 = 3 remainder 1

2. 3 ÷ 2 = 1 remainder 1

3. 1 ÷ 2 = 0 remainder 1

Reversing the remainders, the binary equivalent of 7 is 111.

FAQs

How do you convert a number from decimal to binary?

Divide the decimal number by 2 repeatedly, record every remainder, and write them in reverse to get the binary form.

How do you convert a negative decimal number to a binary number?

Convert the absolute value to binary, invert the digits, and add 1 using two's complement representation.

How do you convert 0.75 into binary?

Multiply 0.75 by 2 repeatedly, record the whole numbers, and write them in sequence: 0.75 = 0.11 in binary.

How do you convert 0.1 to binary?

Repeatedly multiply 0.1 by 2, recording the whole numbers. The binary representation of 0.1 is approximately 0.000110011...

What is 0.5 in binary?

The binary form of 0.5 is 0.1.