Binary to Decimal Conversion

This section explains the process of converting numbers from binary $base-2$ to decimal $base-10$ format through systematic decomposition and calculation.

Example: Converting 1101₂ to decimal

1. Decompose into powers of 2: 1101₂ = 1 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰
2. Calculate: 8 + 4 + 0 + 1 = 13₁₀

Definition: Binary to decimal conversion involves multiplying each digit by its corresponding power of 2 and summing the results.

Highlight: When converting from binary to decimal, each position represents a power of 2, starting from 2⁰ on the right.

Vocabulary: Base-2 (Binary) - A number system using only 0 and 1 digits Base-10 (Decimal) - The standard number system using digits 0-9 Base-16 (Hexadecimal) - A number system using digits 0-9 and letters A-F

Example: Converting 13₁₀ to binary through successive division:

1. Divide by 2 repeatedly until quotient becomes 0
2. Read remainders from bottom to top Result: 13₁₀ = 1101₂

The page also covers conversion between binary and hexadecimal systems:

Highlight: For binary to hexadecimal conversion:

1. Group binary digits in sets of 4 (add leading zeros if needed)
2. Convert each group to its hexadecimal equivalent

Example: Converting 11110010112 to hexadecimal:

1. Group: 0011 1100 1011
2. Convert: 3CB₁₆

For hexadecimal to binary conversion:

Definition: Each hexadecimal digit converts to exactly 4 binary digits

Example: Converting 13₁₆ to binary: 1₁₆ = 0001₂ 3₁₆ = 0011₂ Therefore, 13₁₆ = 00010011₂