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Decimal to Binary Calculator
Decimal to binary converter is an online converter that converts the decimal number to binary number. Decimal numbers have a lot of importance because it is a standard system that is most commonly used in our daily life. It has a base \(10\) and consists of the numbers from \(0 \text{to} 9\). It is one of the oldest numeral systems in the world. While on the other hand, the binary system is the backbone of IT and computer engineering. It is widely used in computer programming and networking. It has a base \(10\) and consists of \(0 \text{and} 1\). The decimal to binary calculator converts the base \(10\) numbers to base \(2\) numbers.
In this post, we will explain the concept of converting decimal to binary, how to use decimal to binary converter, and much more.
How to use decimal to the binary calculator?
The binary number converter makes the conversion process very smooth. It takes the input from the user and converts the decimal number to binary instantly. Manual decimal to binary conversion can take time because it is a complex process, but the above calculator makes the binary conversion in seconds. You can use this calculator for academic as well as other purposes. To use this calculator, follow the below steps:
- Enter the decimal number in the given input box.
- Switch the Digital grouping bottom to Yes if you want the digital grouping in the output.
- Press the Calculate button to see the output in the binary number.
It would convert the given decimal number to the binary number and implement the digital grouping if you switched the button to Yes. You will get the output in a binary number, binary signed 2’s complement, and a hex number as well. If you want a reverse conversion, you can use our binary to decimal converter anytime.
How to convert decimal to binary?
Manually converting a decimal number to a binary can be a bit tricky because it has a lot to do with divisions and remainders. You can use the above converter to convert to binary. For your understanding, we will explain step by step method for this conversion. Follow the steps below to convert a decimal number to a binary number:
- Write down the decimal number that you want to convert to the binary number.
- Divide the decimal number by \(2\) and write down the Write the remainder of this division on the right side.
- Now, divide the answer of the last division again by \(2\) and write down the answer. Write the remainder of this division on the right side again.
- Repeat this division until the answer is zero.
- The remainders are the output of this conversion, but you have to combine them in the right manner. Write down the remainders from bottom to top. The remainder digits at the bottom are most significant, and those on top are least significant bits.
Example:
Convert the decimal \(15_{10}\) to binary number.
Solution:
Step 1: Write down the decimal number that you want to convert to the binary number.
\(15_{10}\)
Step 2: Divide the decimal number by \(2\) and write down the answer. Write the remainder of this division on the right side.
| Division by 2 | Quotient | Remainder |
| 15/2 | 7 | 1 |
Step 3: Now, divide the answer of the last division again by \(2\) and write down the answer. Write the remainder of this division on the right side again.
| Division by 2 | Quotient | Remainder |
| 7/2 | 3 | 1 |
Step 4: Repeat this division until the answer is zero.
| Division by 2 | Quotient | Remainder |
| 3/2 | 1 | 1 |
| 1/2 | 0 | 1 |
Step 5: Write down the remainders from bottom to top. The remainder digits at the bottom are most significant, and those on top are least significant bits.
\(\left(1111\right)_2\)
So, the binary equivalent of \(15_{10}\) is \(\left(1111\right)_2\).
Convert \(24_{10}\) to binary number
Step 1: Write down the decimal number that you want to convert to the binary number.
\(24_{10}\)
Step 2: Divide the decimal number by \(2\) and write down the answer. Write the remainder of this division on the right side.
| Division by 2 | Quotient | Remainder |
| 24/2 | 12 | 0 |
Step 3: Now, divide the answer of the last division again by \(2\) and write down the answer. Write the remainder of this division on the right side again.
| Division by 2 | Quotient | Remainder |
| 12/2 | 6 | 0 |
Step 4: Repeat this division until the answer is zero.
| Division by 2 | Quotient | Remainder |
| 6/2 | 3 | 0 |
| 3/2 | 1 | 1 |
| 1/2 | 0 | 1 |
Step 5: Write down the remainders from bottom to top. The remainder digits at the bottom are most significant, and those on top are least significant bits.
\(\left(11000\right)_2\)
The binary equivalent of \(24_{10}\) is \(\left(11000\right)_2\).