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
- Decompose into powers of 2: 1101₂ = 1 × 2³ + 1 × 2² + 0 × 2¹ + 1 × 2⁰
- 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:
- Divide by 2 repeatedly until quotient becomes 0
- 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:
- Group binary digits in sets of 4 (add leading zeros if needed)
- Convert each group to its hexadecimal equivalent
Example: Converting 11110010112 to hexadecimal:
- Group: 0011 1100 1011
- 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
