Hex to Decimal Converter

Computer Science & Positional Radix Polynomial Expansion

Hexadecimal (Base-16) represents numbers where the place value of each digit is a power of 16:

• **

• Polynomial Expansion Formula**:

Decimal = Σ_i=0^n-1 d_i · 16^i = d_n-1 16^n-1 + + d_1 16^1 + d_0 16^0

• Hex digits: 0--9, A=10, B=11, C=12, D=13, E=14, F=

15.

• **

• Binary Nibble Alignment**:

Every hex digit maps to a 4-bit binary sequence.

• **

• Standard Hex Benchmarks**:

• 0x2B = (2 × 16) + 11 = 43

• 0xFF = (15 × 16) + 15 = 255

• 0x1000 = 1 × 16^3 = 4,096

• 0xFFFF = 65,535

How to Use This Calculator

Enter your Hexadecimal String (e.g. 1A3F or 0xFF) (e.g. 1A3F) and Hexadecimal Radix Benchmark — choose from Custom Hex String, 1A3F → 6,719 (4-Digit Hex Number), FF → 255 (Max 8-Bit Byte). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Formula Reference: Hex to Decimal Converter

Input variables:

hexadecimalInputString — Hexadecimal String (e.g. 1A3F or 0xFF)

Computed outputs:

decimalIntegerResult — Decimal Integer (Base-10)

polynomialExpansionProof — Polynomial Base-16 Expansion Proof

binaryNibblesRepresentation — Binary 4-Bit Nibbles (Base-2)

octalCodeString — Octal Representation (Base-8)

rgbColorChannels — RGB Color Channels (if 6-digit hex)

Mathematical relationships extracted from calculation logic:

cleanHex = s.replace(/^0[xX]/, '').replace(/[^0-9a-fA-F]/g, '').toUpperCase() || '0'

power = n - 1 - i

paddedBin = binStr.padStart(Math.ceil(binStr.length / 4) * 4 || 4, '0')

nibbles = paddedBin.match(/.1,4/g).join(' ')

Standard: NIST Handbook 44 and BIPM SI unit definitions

Worked Example

A web designer converting the hex color 0xFFFFFF verifies that 15 × 16^5 + 15 × 16^4 + + 15 × 16^0 = 16,777,215, corresponding to RGB(255, 255, 255).

Understanding Your Result

Unit conversion precision: round to the same number of significant figures as your original measurement. Converting 6 feet to meters gives 1.8288 m — but if your measurement was approximate (±1 inch), expressing more than 2 decimal places is false precision. For international trade and technical specifications, SI units (meters, kilograms, liters) are the standard. US customary units (feet, pounds, gallons) differ from Imperial UK units: 1 US gallon = 3.785 L vs. 1 UK gallon = 4.546 L.