CONV_UNIT
Binary
- Binary
- Octal
- Decimal
- Hex
Octal
- Binary
- Octal
- Decimal
- Hex
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OUTPUT_LOG
RESULT_VALUE (click to copy):
Awaiting input...
SYSTEM_MANUAL
Positional numbering systems define a digit's value based on its place in a string. While Decimal (Base 10) is our everyday human standard, computer hardware relies on Binary (Base 2) to represent fundamental ON/OFF states. Octal (Base 8) and Hexadecimal (Base 16) work as binary shortcuts: they allow us to group 3 or 4 bits into a single character, making it much easier to read memory addresses and CPU instructions.
Base Management
The CONV_UNIT module provides instant conversion for both whole numbers and decimals across bases 2, 8, 10, and 16.
Fractional Precision
Noverflow's algorithm ensures high accuracy by calculating the fractional part through repeated multiplications, matching the limits of hardware registers.
Quick Guide to Manual Calculation
1. From any Base to Decimal (Weighted Method):
Multiply each digit by the base raised to its position index (starting from 0 for the first digit to the left of the decimal point).
Example: 110.1₂ = (1×2²) + (1×2¹) + (0×2⁰) + (1×2⁻¹) = 4 + 2 + 0 + 0.5 = 6.5₁₀
2. From Decimal to any Base (Division/Multiplication):
For whole numbers: divide the number by the target base repeatedly and read the remainders from bottom to top.
For fractions: multiply the decimal part by the base; the whole number part of the result is your next digit. Repeat until you hit 0 or reach your desired precision.
3. Direct Jumps (Powers of 2):
When switching between Binary, Octal, and Hex, you don't need to go through decimal first.
Octal: group bits in 3s (e.g., 111₂ = 7₈).
Hexadecimal: group bits in 4s (e.g., 1010₂ = A₁₆).