Decimal Equivalent (Base 10)
22
Positional Value Contribution
Conversion Breakdown Table
| Position (n) | Binary Digit (b) | Positional Weight (2^n) | Contribution (b * 2^n) |
|---|
Binary to Decimal Conversion Tool
Understanding Binary to Decimal Conversion
At the core of every digital system lies the binary numbering system. While humans communicate using the decimal system (Base-10), computers process information using binary (Base-2), representing data as sequences of 0s and 1s. This converter bridges the gap, allowing you to translate machine code into human-readable integers instantly.
The Logic: Positional Notation
Unlike the decimal system where each digit represents a power of 10, in the binary system, each position represents a power of 2. Reading from right to left, the first digit represents \(2^0\), the second \(2^1\), the third \(2^2\), and so on. To convert a binary string to a decimal number, we multiply each bit by its corresponding power of 2 and sum the results.
General Formula:
Where \(b_i\) is the bit value (0 or 1) at position \(i\), and \(n\) is the position index starting from 0 on the right.
Calculation Example
Let's take the binary number 1101 as an example. To find its decimal equivalent, we break it down by position:
- 1st bit (Right): \(1 \times 2^0 = 1\)
- 2nd bit: \(0 \times 2^1 = 0\)
- 3rd bit: \(1 \times 2^2 = 4\)
- 4th bit (Left): \(1 \times 2^3 = 8\)
Mathematical Representation:
Why is this Important?
Understanding binary conversion is fundamental for software development and network engineering. It is crucial for understanding IP addressing (Subnetting), memory allocation, and low-level hardware programming. When you configure a Subnet Mask like 255.255.255.0, you are essentially working with groups of 8 binary bits converted to decimal.