Hex to Decimal

Introduction  

Table of Contents  

• What is Hex to Decimal Conversion?
• Hex to Decimal Definition
• Hex to Decimal Table
• How to Convert Hex to Decimal Manually
• Hex to Decimal Converter Tools
• Hex to Decimal Calculator Benefits
• Hex to Decimal Conversion Examples
• Applications of Hex to Decimal Conversion
• Common Misconceptions
• Fun Facts
• Solved Examples
• Conclusion
• FAQs on Hex to Decimal

What is Hex to Decimal Conversion?

Hex to decimal is the process of converting numbers from base-16 (hexadecimal) to base-10 (decimal).

Hexadecimal includes digits from 0 to 9 and letters A to F, where:  

• A = 10  

• B = 11  

• C = 12  

• D = 13  

• E = 14  

• F = 15  

Decimal numbers are more familiar and are used in everyday math.  

Conversion is necessary for interpreting machine-level data in a human-readable form.  

Hex to Decimal Definition

The hex to decimal conversion translates a hexadecimal number into its decimal equivalent.  

For example, hex 1A becomes decimal 26.  

This is done by multiplying each digit in the hex number by powers of 16 and adding the results.  

Hex to Decimal Table

Below is a hex to decimal table for quick reference:  

This hex-to-decimal table helps during manual conversions.  

How to Convert Hex to Decimal Manually

Formula:

Decimal Value = Σ (Digit × 16^Position)

(Read the hex number right to left; rightmost position = 0.)

Quick note: Hex digits 0–9 keep their values. A=10, B=11, C=12, D=13, E=14, F=15.

Steps :

Write the hexadecimal number.

Example: 2F

Label positions from the right, starting at 0.

For 2F: F → position 0, 2 → position 1.

Convert each hex digit to its decimal value.

F = 15, 2 = 2

Write each term as (digit × 16^position).

For 2F: (2 × 16^1) and (15 × 16^0)

Calculate each power of 16 you need.

16^0 = 1, 16^1 = 16, 16^2 = 256, 16^3 = 4096, … (use as many as positions you have)

Multiply each digit by its 16^position value.

2 × 16^1 = 2 × 16 = 32

15 × 16^0 = 15 × 1 = 15

Add all the results to get the decimal value.

32 + 15 = 47

Final Answer :

2F (hex) = 47 (decimal)

Hex to Decimal Calculator Benefits

• A hex to decimal calculator performs the same function but usually has extra features.  

• It may display steps, binary equivalents, and explanations.  

• It is often built into scientific calculators or software.  

Use Cases for Hex to Decimal Calculator:  

• In coding and debugging, hexadecimal memory addresses are used.  

• In digital electronics, for address decoding.  

• In data analysis tools that work with hexadecimal formats.  

Using a hex to decimal calculator helps you understand conversion logic while saving time.  

Hex to Decimal Conversion Examples

Here are some common hex to decimal examples:  

These examples help illustrate how to convert hex to decimal.  

Applications of Hex to Decimal Conversion

Hex to decimal conversions are used in:  

• Computer Programming: Memory locations, colour codes (e.g., #FF5733), data encoding.  

• Network Engineering: MAC addresses are often in hexadecimal.  

• Digital Electronics: Hex values simplify circuit programming.  

• Game Development: Debugging coordinates or object IDs.  

• Cybersecurity: Analysing hex dumps of files.  

Understanding how to convert hex to decimal is important in various tech areas.  

Common Misconceptions

• Hex Numbers Are Just Letters  

Misconception: Letters like A-F are just the alphabet.  

Fact: They represent numbers 10 -15.  

• Hex to Decimal Is Difficult  

Misconception: The process is hard and confusing.  

Fact: With a hex to decimal table, it’s simple.  

• You Always Need a Calculator  

Misconception: Manual conversion is impossible.  

Fact: Small numbers can be easily converted by hand.  

• One-to-One Mapping Between Hex and Decimal  

Misconception: Each hex number maps directly to a single decimal digit.  

Fact: A hex digit can represent values up to 15. 

• Decimal and Hex Use the Same Symbols  

Misconception: They function similarly.  

Fact: Decimal is base-10; hex is base-16.  

Fun Facts

• HTML Colour Code: Use Hex  

For example, #FFFFFF (white) and #000000 (black) are hexadecimal representations.  

• Memory Addresses Are Written in Hex  

Hex makes it easier to read and shorten binary data.  

• MAC Addresses  

Network hardware uses hex-coded identifiers like 00:1A:2B:3C:4D:5E.  

• Hex Saves Space  

One hex digit represents 4 binary digits (bits), reducing clutter.  

• Video Games and Hacking  

Hex editing tools allow you to change game data or file properties.  

The hex to decimal concept is present in many tech fields!  

Solved Examples

Example 1: Convert 1C (hex) to decimal

Step 1: Write with place values → 1C = (1 × 16¹) + (C × 16⁰)
Step 2: Convert hex letters → C = 12
Step 3: Evaluate powers → 16¹ = 16, 16⁰ = 1
Step 4: Multiply → 1 × 16 = 16, 12 × 1 = 12
Step 5: Add → 16 + 12 = 28

Answer: 1C (hex) = 28 (decimal)

Example 2: Convert A3 (hex) to decimal

Step 1: Write with place values → A3 = (A × 16¹) + (3 × 16⁰)
Step 2: Convert hex letters → A = 10
Step 3: Evaluate powers → 16¹ = 16, 16⁰ = 1
Step 4: Multiply → 10 × 16 = 160, 3 × 1 = 3
Step 5: Add → 160 + 3 = 163

Answer: A3 (hex) = 163 (decimal)

Example 3: Convert 7D (hex) to decimal

Step 1: Write with place values → 7D = (7 × 16¹) + (D × 16⁰)
Step 2: Convert hex letters → D = 13
Step 3: Evaluate powers → 16¹ = 16, 16⁰ = 1
Step 4: Multiply → 7 × 16 = 112, 13 × 1 = 13
Step 5: Add → 112 + 13 = 125

Answer: 7D (hex) = 125 (decimal)

Example 4: Convert F0 (hex) to decimal

Step 1: Write with place values → F0 = (F × 16¹) + (0 × 16⁰)
Step 2: Convert hex letters → F = 15
Step 3: Evaluate powers → 16¹ = 16, 16⁰ = 1
Step 4: Multiply → 15 × 16 = 240, 0 × 1 = 0
Step 5: Add → 240 + 0 = 240

Answer: F0 (hex) = 240 (decimal)

Example 5: Convert 2B (hex) to decimal

Step 1: Write with place values → 2B = (2 × 16¹) + (B × 16⁰)
Step 2: Convert hex letters → B = 11
Step 3: Evaluate powers → 16¹ = 16, 16⁰ = 1
Step 4: Multiply → 2 × 16 = 32, 11 × 1 = 11
Step 5: Add → 32 + 11 = 43

Answer: 2B (hex) = 43 (decimal)

Conclusion

Understanding hex to decimal conversion is important in computing and electronics. Whether you are learning how to convert hex to decimal manually or using a calculator, mastering this skill is essential. A hex to decimal table can help you see patterns and perform quicker conversions. The importance of converting hex to decimal goes beyond academics; it is used daily in programming, networking, and digital systems. Keep practising with real examples to strengthen your understanding of this key number system!

Frequently Asked Questions on Hex to Decimal 

1. How do I convert hex to decimal?

Answer: Multiply each hex digit by 16^n16^n16^n (from right to left) and add the results.

2. What is the decimal equivalent of the hexadecimal number 1A3?

Answer: 1A3 (hex) = 419 (decimal).

3. What is 43 dec in hex?

Answer: 43 (decimal) = 2B (hex).

4. What is the hex formula?

Answer: Decimal = Σ (Hex digit × 16^position).

Explore how Hex becomes Decimal effortlessly with Orchids The International School.