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Last updated on October 6, 2025
Decimal to binary conversion is a fundamental concept in computer science and digital electronics. The conversion process involves dividing the decimal number by 2 and recording the remainder. In this topic, we will learn the formula for converting decimal numbers to binary.
To convert a decimal number to binary, follow these steps: divide the number by 2, record the remainder, and continue dividing the quotient by 2 until you reach zero. The binary number is the sequence of remainders read from bottom to top.
The process of converting a decimal number to binary involves repeated division by 2. Here’s the formula:
1. Divide the decimal number by 2.
2. Record the remainder (0 or 1).
3. Update the quotient to be the integer result of the division.
4. Repeat steps 1-3 until the quotient is zero.
5. The binary equivalent is the remainders read in reverse order.
Let's convert the decimal number 13 to binary:
1. 13 divided by 2 gives a quotient of 6 and a remainder of 1.
2. 6 divided by 2 gives a quotient of 3 and a remainder of 0.
3. 3 divided by 2 gives a quotient of 1 and a remainder of 1.
4. 1 divided by 2 gives a quotient of 0 and a remainder of 1.
5. Therefore, the binary equivalent of 13 is 1101.
Decimal to binary conversion is crucial in computer science. It allows us to represent numerical data in a format that computers can process efficiently. Understanding this conversion is fundamental for programming, digital circuit design, and data representation in computing systems.
Decimal to binary conversion might seem complex, but with practice, it becomes easier. Here are some tips: -
Decimal to binary conversion is applied in various real-life scenarios:
Mistakes in decimal to binary conversion can lead to incorrect results. Here are some common errors and how to avoid them:
Convert the decimal number 8 to binary.
The binary representation of 8 is 1000.
1. 8 divided by 2 gives a quotient of 4 and a remainder of 0.
2. 4 divided by 2 gives a quotient of 2 and a remainder of 0.
3. 2 divided by 2 gives a quotient of 1 and a remainder of 0.
4. 1 divided by 2 gives a quotient of 0 and a remainder of 1.
5. Therefore, the binary equivalent of 8 is 1000.
Convert the decimal number 19 to binary.
The binary representation of 19 is 10011.
1. 19 divided by 2 gives a quotient of 9 and a remainder of 1.
2. 9 divided by 2 gives a quotient of 4 and a remainder of 1.
3. 4 divided by 2 gives a quotient of 2 and a remainder of 0.
4. 2 divided by 2 gives a quotient of 1 and a remainder of 0.
5. 1 divided by 2 gives a quotient of 0 and a remainder of 1.
6. Therefore, the binary equivalent of 19 is 10011.
Convert the decimal number 5 to binary.
The binary representation of 5 is 101.
1. 5 divided by 2 gives a quotient of 2 and a remainder of 1.
2. 2 divided by 2 gives a quotient of 1 and a remainder of 0.
3. 1 divided by 2 gives a quotient of 0 and a remainder of 1.
4. Therefore, the binary equivalent of 5 is 101.
Convert the decimal number 24 to binary.
The binary representation of 24 is 11000.
1. 24 divided by 2 gives a quotient of 12 and a remainder of 0.
2. 12 divided by 2 gives a quotient of 6 and a remainder of 0.
3. 6 divided by 2 gives a quotient of 3 and a remainder of 0.
4. 3 divided by 2 gives a quotient of 1 and a remainder of 1.
5. 1 divided by 2 gives a quotient of 0 and a remainder of 1.
6. Therefore, the binary equivalent of 24 is 11000.
Convert the decimal number 2 to binary.
The binary representation of 2 is 10.
1. 2 divided by 2 gives a quotient of 1 and a remainder of 0.
2. 1 divided by 2 gives a quotient of 0 and a remainder of 1.
3. Therefore, the binary equivalent of 2 is 10.
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
: He loves to play the quiz with kids through algebra to make kids love it.