Hexadecimal to Decimal

A Hexadecimal to Decimal Converter is a tool designed to convert numbers from the hexadecimal system (base-16) into the decimal system (base-10). The hexadecimal system uses 16 symbols: 0–9 and A–F, where A represents 10, B represents 11, up to F representing 15. The decimal system is the standard base-10 system used in daily life.

This conversion is crucial in fields like programming, digital electronics, and data representation.

Conversion Principle:

To convert hexadecimal to decimal:

• Multiply each digit in the hexadecimal number by 16 raised to the power of its position, counting from right to left (starting at 0).
• Add all the results to get the decimal equivalent.

Example:

Hex: 2F

→ (2 × 16¹) + (F × 16⁰)

→ (2 × 16) + (15 × 1) = 32 + 15 = 47

Common Uses for Hexadecimal to Decimal Conversion:

• Programming: Used for memory addresses, machine code, and debugging tools.
• Web Design: Color codes (e.g., #FF5733) are in hex but may need decimal equivalents.
• Digital Electronics: Register values and low-level instructions use hex but operate in binary or decimal.
• Data Encoding: Cryptographic keys and hash functions often use hexadecimal formats.
• Education: Essential in teaching number systems and computer architecture.

Key Features of Hexadecimal to Decimal Converter:

• Precision: Converts all valid hex inputs including fractions and large values.
• Instant Output: Real-time conversion while typing.
• Handles Fractions: Supports hexadecimal floating point (e.g., 1A.F).
• Simple Interface: User-friendly for students, programmers, and professionals.
• No Manual Calculation: Saves time by avoiding errors in conversions.
• Supports Copy-Paste: Ideal for use in coding and documentation.

This tool provides a fast, reliable, and user-friendly way to translate hexadecimal values into decimal format.

Enter a Hexadecimal Number:

Example: 1A, FF, 3B.4.

Get Instant Result:

The decimal equivalent will display automatically.

Use as Needed:

Ideal for software development, electronics, and learning base conversions.

Formula:

Decimal = (dₙ × 16ⁿ) + (dₙ₋₁ × 16ⁿ⁻¹) + ... + (d₀ × 16⁰)

Example 1: Hex: 3E

→ (3 × 16¹) + (E × 16⁰) = (3 × 16) + (14 × 1) = 48 + 14 = 62

Example 2: Hex: A2

→ (A × 16¹) + (2 × 16⁰) = (10 × 16) + 2 = 160 + 2 = 162

Example 3 (with fraction): Hex: 2.B

→ Integer part: 2 × 16⁰ = 2

→ Fractional part: B = 11 → 11 × 16⁻¹ = 11 × 0.0625 = 0.6875

→ Decimal = 2.6875

Hex

Decimal

0

0

1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9

A

10

B

11

C

12

D

13

E

14

F

15

Steps to Convert Hexadecimal to Decimal:

For Integer Part:

1. Write down the hex number.
2. Convert each hex digit to its decimal equivalent.
3. Multiply each by 16 raised to its position power.
4. Sum the values.

For Fractional Part:

1. Multiply each digit after the point by 16 raised to a negative power.
2. Sum these with the integer result.

Formula:

Decimal = Σ (hex_digit × 16^position)