Binary To Decimal Converter: Fast and Simple Calculation
Binary To Decimal Converter
Binary to Decimal Converter is a free online tool that allows you to convert binary numbers to decimal. Converting from binary to decimal is a common task in everyday life. Here, GeeksforGeeks offers a free, easy-to-use, and reliable online binary-to-decimal conversion tool to make this process easy and accurate. It acts as a fast, convenient, and general-purpose calculator suitable for any field, including computer science. Moreover, it helps students and professionals solve various everyday problems efficiently.
What is Binary to Decimal?
Binary to Decimal conversion helps in changing a binary number to its decimal form. Binary numbers use base 2 and are commonly used in computer programming. On the other hand, decimal numbers use base 10 and are used for routine calculations and calculations in daily life.
What is Binary System?
Binary system is a method of writing numbers using only two digits: 0 and 1. Its base is 2. Ancient Indian, Chinese and Egyptian civilizations used this system for various purposes. Today, binary numbers play an important role in electronics and computer programming.
What is Decimal System?
Decimal number system is the number system that we use in our daily life. Its base is 10 and it uses ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. This system allows us to easily perform all routine calculations, calculations and arithmetic operations.
How to Use Binary Converter?
Now, let’s see how to use Binary Converter. For example, we will convert the number -87 from decimal to binary.
Select the number of bits. For this example, 8 bits works well because it covers the range from
−128 to 127.
Enter your decimal value in the input box under the Decimal to Binary section. The calculator will show the result:
The binary of the positive version of our number, i.e. 87, is:
0101 0111.
The one’s complement is:
1010 1000.
The two’s complement is:
1010 1001.
One’s and two’s complement are calculated as explained above, by flipping all the bits for the opposite number and adding 1 for the two’s complement.
The converter also works the other way around – from binary to decimal. Simply enter your binary number in the appropriate field, and the decimal value will appear immediately below.
How to Convert Binary to Decimal
Follow these simple steps to convert binary numbers to their decimal form.
- Step 1: Write down the binary number and note the power of 2, counting from right to left, starting with 0.
- Step 2: Match each binary digit (from right to left) with its matching power of 2, making sure that the first digit (MSB) multiplies the highest power of 2.
- Step 3: Multiply each digit by its power of 2, and then add all the results together.
- Step 4: The sum you get is the decimal equivalent of the binary number.
Binary to Decimal Conversion Steps
- First, note down the given binary number and raise each digit starting from the right to the power of 2 (starting from power 0).
- Next, combine each binary digit from right to left with its corresponding power of 2, making sure that the first binary digit (MSB) is multiplied by the highest power of 2.
- Multiply each digit by its corresponding power of 2 and sum all the results.
- This will give the decimal equivalent of the simple binary number.
Let’s look at this conversion through an example.
Example of Binary to Decimal Conversion:
Convert the binary number (1101)₂ to decimal.
Solution:
Given binary number = (1101)₂
Now, multiply each digit from MSB to LSB by raising it to the power of 2.
1 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰
= 8 + 4 + 0 + 1
= 13
Binary to Decimal Formula
To convert a binary number to decimal, we need to multiply each digit of the binary number by a power of 2, starting from right to left with 0, and then add all the results to get its decimal value. You can also use a binary calculator to quickly perform this conversion without manual calculation.
Decimal Number = nth bit × 2n-1
Binary to Decimal Formula
n = bnq + bn-1qn-2 +………+ b2q2 +b1q1 +b0q0 + b-1q-1 + b-2q-2
Binary to Decimal Table
| Binary | Decimal |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 10 | 2 |
| 11 | 3 |
| 100 | 4 |
| 101 | 5 |
| 110 | 6 |
| 111 | 7 |
| 1000 | 8 |
| 1001 | 9 |
| 1010 | 10 |
| 1011 | 11 |
| 1100 | 12 |
FAQs: Questions And Answers
Q1. What are the rules for converting binary to decimal?
To convert a binary number to decimal, raise each binary digit to the power of 2, starting with 2⁰ for the rightmost digit. Multiply each binary digit by its corresponding power of 2, then add all the powers together to get the decimal value.
Q2. Why do we convert binary to decimal?
We convert binary to decimal because humans find decimal numbers easier to read and understand, since decimal is the standard system used in everyday life, while computers naturally work with binary numbers.
Q3. What is the fastest way to convert binary to decimal?
Converting Binary to Decimal Using the Binary Method
Step 1: Write the binary number and start with the leftmost digit. Double the previous result and add the current digit.
Step 2: Repeat the same for the next digit in the sequence.
Step 3: Continue doubling and adding for all digits until the last digit.
Q4. What is the purpose of binary to decimal conversion?
Binary to decimal conversion is important in computer programming. Computers work in binary (0 and 1), while humans can understand decimal numbers more easily. This conversion bridges the communication between human-readable numbers and machine-readable code.
