Binary to Decimal Converter

Convert Binary to Decimal

Enter a binary number below to convert it to decimal. Our converter handles binary numbers of any length.

Please enter a valid binary number (0s and 1s only).

How to Convert Binary to Decimal

Converting binary numbers to decimal is a fundamental operation in computer science and digital systems. Here's a comprehensive guide on how to perform this conversion:

Conversion Formula

The formula for converting a binary number to decimal is:

\[ d = b_n \times 2^n + b_{n-1} \times 2^{n-1} + ... + b_1 \times 2^1 + b_0 \times 2^0 \]

Where:

  • \(d\) is the decimal value
  • \(b_i\) represents each digit of the binary number (0 or 1)
  • \(n\) is the position of the digit (starting from 0 for the rightmost digit)

Conversion Steps

  1. Identify each digit in the binary number.
  2. Multiply each digit by 2 raised to the power of its position.
  3. Sum up all the resulting values.

Example Conversion

Let's convert the binary number 1010 to decimal.

Step 1: Identify Digits

1010 = 1 × 2³ + 0 × 2² + 1 × 2¹ + 0 × 2⁰

Step 2: Calculate Each Term

1 × 2³ = 1 × 8 = 8

0 × 2² = 0 × 4 = 0

1 × 2¹ = 1 × 2 = 2

0 × 2⁰ = 0 × 1 = 0

Step 3: Sum Up

8 + 0 + 2 + 0 = 10

Final Result

Therefore, 1010 in binary = 10 in decimal

Visual Representation

Binary to Decimal Conversion Process 1010 Binary Input 1 × 2³ = 8 0 × 2² = 0 1 × 2¹ = 2 0 × 2⁰ = 0 Convert 8 + 0 + 2 + 0 = 10 Decimal Result Position weights: 2³ 2² 2¹ 2⁰ Values: 8 4 2 1

This diagram illustrates the process of converting the binary number 1010 to its decimal equivalent 10.

Article Navigation