Numbers Converter - Convert Binary, Decimal, Hexadecimal, Octal & More
Result:
10 (dec) = 1010 (bin)
How Number System Conversion Works
Input Number
Enter number in source base
Convert to Decimal
Parse using source base
Convert to Target
Convert to target base
Number System Conversion Formulas
Binary to Decimal
Decimal = Σ(digit × 2^position)
Example: 1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 11₁₀
Decimal to Binary
Divide by 2, collect remainders
Example: 11₁₀ ÷ 2 = 5 R1, 5 ÷ 2 = 2 R1, 2 ÷ 2 = 1 R0, 1 ÷ 2 = 0 R1 → 1011₂
Hexadecimal to Decimal
Decimal = Σ(digit × 16^position)
Example: A3₁₆ = 10×16¹ + 3×16⁰ = 163₁₀
Octal to Decimal
Decimal = Σ(digit × 8^position)
Example: 75₈ = 7×8¹ + 5×8⁰ = 61₁₀
Number System Conversion Table
| Decimal | Binary | Hexadecimal | Octal |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 10 | 2 | 2 |
| 3 | 11 | 3 | 3 |
| 4 | 100 | 4 | 4 |
| 5 | 101 | 5 | 5 |
| 6 | 110 | 6 | 6 |
| 7 | 111 | 7 | 7 |
| 8 | 1000 | 8 | 10 |
| 9 | 1001 | 9 | 11 |
| 10 | 1010 | A | 12 |
| 11 | 1011 | B | 13 |
| 12 | 1100 | C | 14 |
| 13 | 1101 | D | 15 |
| 14 | 1110 | E | 16 |
| 15 | 1111 | F | 17 |
Number System Progression Chart
Decimal: 1
Decimal: 8
Decimal: 16
Decimal: 32
Decimal: 64
Decimal: 255
Practice Problems
Problem 1:
Convert 1010₂ to decimal
Solution: 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10₁₀
Problem 2:
Convert 25₁₀ to binary
Solution: 25 ÷ 2 = 12 R1, 12 ÷ 2 = 6 R0, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1 → 11001₂
Problem 3:
Convert FF₁₆ to decimal
Solution: 15×16¹ + 15×16⁰ = 240 + 15 = 255₁₀
Problem 4:
Convert 64₁₀ to octal
Solution: 64 ÷ 8 = 8 R0, 8 ÷ 8 = 1 R0, 1 ÷ 8 = 0 R1 → 100₈
Problem 5:
Convert 111₂ to hexadecimal
Solution: 111₂ = 7₁₀ = 7₁₆
Daily Uses of Number Systems
Computer programming uses binary and hexadecimal for memory addresses
Digital electronics design requires binary and octal number systems
Network administration uses hexadecimal for MAC addresses and IP configuration
Web development uses hexadecimal color codes for CSS styling
Cybersecurity analysis involves converting between different number bases