Convert Binary to Decimal

Converting binary to decimal is one of the most fundamental operations in computer science and digital electronics. Binary uses only two digits, 0 and 1, while decimal uses ten digits, 0 through 9.

How the conversion works:

Each digit in a binary number represents a power of 2, starting from the rightmost digit at position 0. To convert, multiply each binary digit by its corresponding power of 2, then sum all the results.

Step-by-step example — converting 11010 to decimal:

1. Write out each digit with its position: 1(4) 1(3) 0(2) 1(1) 0(0)
2. Calculate powers of 2: 1×2⁴ + 1×2³ + 0×2² + 1×2¹ + 0×2⁰
3. Evaluate: 16 + 8 + 0 + 2 + 0 = 26

So 11010₂ = 26₁₀.

Key concepts to remember:

• The rightmost bit is called the least significant bit (LSB) with a weight of 2⁰ = 1.
• The leftmost bit is the most significant bit (MSB) with the highest weight.
• Each position doubles in value from right to left: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and so on.
• Memorizing the first 10 powers of 2 makes mental conversion much faster.

Common binary values: 0000 = 0, 0001 = 1, 0010 = 2, 0100 = 4, 1000 = 8, 1111 = 15, 11111111 = 255. The maximum value of an 8-bit unsigned integer is 255, which is why this number appears frequently in networking and color codes. Understanding binary-to-decimal conversion is essential for working with memory addresses, bitwise operations, and low-level programming.