Binary to Decimal Converter

Home › Number Converter › Binary to Decimal
2
10
2
8
16

Understanding Binary Numbers 🤔

Binary numbers are a fundamental part of computer science and digital electronics. Unlike the decimal system we commonly use (base 10), which consists of digits from 0 to 9, the binary system (base 2) uses only two digits: 0 and 1.

Each digit in a binary number represents a power of 2, with the rightmost digit representing (22), the next representing (21), and so on. The binary number (1011) represents (1 × 23 + 0 × 22 + 1 × 21 + 1 × 20), which equals 11 in decimal.

Importance of Binary to Decimal Conversion 🔄

Converting binary numbers to decimal is crucial for various reasons, especially in computer programming and digital systems. While binary is the language of computers, humans often find it easier to work with decimal numbers.

Therefore, converting binary to decimal allows us to understand and interpret binary data more intuitively and converting long binary numbers with our tool can give you quick results.

How to Convert Binary to Decimal 🧮

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

  1. Start from the rightmost digit and assign powers of 2 to each digit, starting from (2^0).

  2. Multiply each binary digit by its corresponding power of 2.

  3. Sum up all the results to obtain the decimal equivalent.

Example 1: Convert (1001) to Decimal

  1. (1 × 23 + 0 × 22 + 0 × 21 + 1 × 20)
  2. (8 + 4 + 0 + 1) = 13

Example 2: Convert (100111101) to Decimal

  1. (1 × 28 + 0 × 27 + 0 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 0 × 21 + 1 × 20)
  2. (256 + 0 + 0 + 32 + 16 + 8 + 4 + 0 + 1) = 317

Binary to Decimal Conversion Table 📊

Here's a table of binary numbers and their decimal equivalents to help you understand the conversion process:

Binary NumberDecimal Equivalent
(0)2(0)10
(1)2(1)10
(10)2(2)10
(11)2(3)10
(100)2(4)10
(101)2(5)10
(110)2(6)10
(111)2(7)10
(1000)2(8)10
(1001)2(9)10
(10100)2(20)10
(110010)2(50)10
(111111)2(63)10
(1000000)2(64)10

Introducing Our Conversion Tool 🛠️

Our online tool simplifies the process of converting binary to decimal and provides additional outputs for enhanced understanding.

Features:

  1. Binary to Decimal Conversion: Get the decimal equivalent of your binary input.
  2. 2s Complement: Understand the signed representation using the 2's complement.
  3. Octal Value: View the octal representation of the binary input.
  4. Hex Value: See the hexadecimal representation of the binary input.
  5. Grouped Output: Group binary digits by 4 for easier readability.
  6. Step-by-Step Conversion: Follow each step of the conversion process for clarity.

Conclusion 🎉

Converting binary to decimal is a fundamental skill in computer science and digital electronics.

With our tool, you can effortlessly convert binary numbers to decimal and explore additional representations, facilitating a deeper understanding of binary data. Embrace the power of binary and decimal conversion with our intuitive online tool!