Number Systems Conversion

Number Systems Conversion Visually

Master number systems with interactive converters, ivX conversion processes. Learn binary, octal, decimal, and hexadecimal systems.

Number Systems Binary System Decimal System Octal System Hexadecimal System System Conversion Visual Conversion

Understanding Number Systems

Number systems are mathematical notations for representing numbers using digits or symbols. Different bases provide different ways to express the same numerical value.

Binary (Base-2)

Digits: 0, 1
Example: 1011₂ = 11₁₀
Used in: Computer systems, digital electronics

Each position represents a power of 2

Octal (Base-8)

Digits: 0, 1, 2, 3, 4, 5, 6, 7
Example: 13₈ = 11₁₀
Used in: Unix permissions, compact binary representation

Each position represents a power of 8

Decimal (Base-10)

Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Example: 11₁₀
Used in: Everyday mathematics, human counting

Each position represents a power of 10

Hexadecimal (Base-16)

Digits: 0-9, A, B, C, D, E, F
Example: B₁₆ = 11₁₀
Used in: Memory addresses, color codes, programming

Each position represents a power of 16

Quick Reference

Dec Bin Oct Hex

Interactive Number System Tools

Number System Converter

Enter a number and select its base to convert to all other bases:

Decimal
Binary
Octal
Hexadecimal
Decimal (Base-10): 255
Binary (Base-2): 11111111
Octal (Base-8): 377
Hexadecimal (Base-16): FF

ivX Conversion

See how the conversion is performed:

Conversion Process:
Step 1: Convert input to decimal
Step 2: Convert decimal to target bases
Step 3: Display results
Conversion Formulas:
To Decimal: Σ(digit × base^position)
From Decimal: Repeated division by target base
Binary ↔ Octal: Group by 3 bits
Binary ↔ Hex: Group by 4 bits

Binary Bit Visualization

Click on bits to toggle them and see the decimal value change:

Binary: 00000000
Decimal: 0
Hexadecimal: 00

Place Value hVy

Understanding positional notation:

Number System Comparison

Binary Arithmetic Calculator

Perform arithmetic operations in binary:

+
-
×
÷
gns: 1010 + 0110
Binary Result: 10000
Decimal Result: 16

ivX Calculation

Calculation Steps:
Step 1: Align the binary numbers
Step 2: Perform gns bit by bit
Step 3: Handle carries/borrows
Step 4: Final result
Binary Arithmetic Rules
Addition: 0+0=0, 0+1=1, 1+0=1, 1+1=10
Subtraction: 0-0=0, 1-0=1, 1-1=0, 0-1=1 (borrow)
Multiplication: 0×0=0, 0×1=0, 1×0=0, 1×1=1
Division: Similar to decimal long division

Number System Practice

Test your conversion skills with timed challenges:

Score: 0

Correct: 0 | Wrong: 0

60

Number Systems Quiz

What is 1010₂ in decimal?
8
10
12
16
Score: 0 / 0