Number System Converter

Convert integers, fractions, and negative two's complement numbers across arbitrary bases (binary, octal, decimal, hex, base 2 to 36) with exact BigInt precision.

LAST VERIFIED: 2026-07-16โ€ข Complies with IEEE Std 754-2019 & Knuth Seminumerical Radix Algorithms
โšก Estimate-First Challenge
Can you guess the Hexadecimal value of Binary 11011010 without calculating?
Quick Test Scenarios
Converted Result (Base 16)
FF
Exact positional value in Base 16.
Binary (Base 2)
11111111
Octal (Base 8)
377
Decimal (Base 10)
255
Hexadecimal (Base 16)
FF
Two's Complement Bitmask (8-bit Binary)Hardware Signed Encoding
11111111
How is this calculated? (See Step-by-Step Polynomial & Division Math)
1. Polynomial Radix Expansion (To Decimal):
N = (2 ร— 10^2) + (5 ร— 10^1) + (5 ร— 10^0) = 255 (Decimal)
2. Successive Division by Target Base (16):
255 / 16 = 15 remainder 15 (F)
15 / 16 = 0 remainder 15 (F)
Scientific Verification & Formula Derivations (Knuth TAOCP & IEEE Std 754)

Polynomial Radix Expansion: Any positional integer representation $N$ in base $b$ maps to scalar magnitude via weighted polynomial summation:N_10 = โˆ‘ (d_i ร— b^i) + โˆ‘ (c_j ร— b^-j), where digits $d_i \in [0, b-1]$.

Exact 64-bit / 256-bit BigInt Precision: Standard web calculators rely on IEEE 754 double floating-point numbers (`parseInt`), which suffer from low-order truncation when integer magnitudes exceed `2^53 - 1` (`9,007,199,254,740,991`). Our engine utilizes exact arbitrary-precision `BigInt` modular arithmetic (`temp % BigInt(targetBase)`) to guarantee zero precision drift across 64-bit and 256-bit word widths.

Primary References:

  • Knuth, Donald E. The Art of Computer Programming, Volume 2: Seminumerical Algorithms (3rd ed., Addison-Wesley, ยง4.4 Radix Conversion).
  • IEEE Std 754-2019, IEEE Standard for Floating-Point Arithmetic, ยง5.12 Radix Conversion.
  • ECMAScript 2026 Language Specification, ยง7.1.4 ToNumber / parseInt Radix Boundaries.

How to Use the Number System Converter

The Number System Converter is a free, easy-to-use tool that helps you get accurate results instantly. Simply enter your values in the input fields above and the results will update in real time.

Step-by-Step Guide

  1. Enter the required values in the input fields provided above.
  2. Adjust the inputs using the sliders or type directly for precision.
  3. View the calculated results displayed below the inputs.
  4. Use the detailed breakdown to understand the numbers better.

Why Use This Calculator?

Manual calculations can be tedious and error-prone. Our number system converter uses precise mathematical formulas to give you reliable results in milliseconds. Whether you are planning, comparing options, or just curious, this tool saves you time and effort.

Results are calculated using industry-standard formulas with full floating-point precision.

Frequently Asked Questions

Yes! All calculators on NumAtlas are completely free to use with no registration required. Use them as many times as you like.
Our calculators use precise mathematical formulas and compute results with full floating-point accuracy. All calculations are performed locally in your browser for instant results.
Absolutely. NumAtlas is fully responsive and works great on phones, tablets, and desktops. The interface adapts to your screen size automatically.