How to Convert Hexadecimal to Decimal: Step-by-Step Guide
The concept of hex to decimal plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. This conversion is important when dealing with different number systems used in digital electronics, programming, and computer science.
What Is Hex to Decimal?
A hex to decimal conversion means changing a number from the hexadecimal (base-16) system to the decimal (base-10) system. Hexadecimal uses the digits 0–9 and the letters A–F (which stand for 10–15). You’ll find this concept applied in areas such as digital electronics, computer programming, and information technology.
Key Formula for Hex to Decimal
Here’s the standard formula:
\( \text{Decimal Value} = \sum_{i=0}^{n-1} (\text{Hex Digit}_i \times 16^i) \)
where the rightmost digit is multiplied by \(16^0\), the next by \(16^1\), and so on, moving left.
Cross-Disciplinary Usage
Hex to decimal is not only useful in Maths but also plays an important role in Physics, Computer Science, and daily logical reasoning. Students preparing for JEE or NEET will see its relevance in number system conversion questions, programming, and understanding memory addresses in computers.
Step-by-Step Illustration
- Write down the hex number. For example: 1A3
- Assign decimal values to each hex digit:
1 = 1, A = 10, 3 = 3
- Starting from the right, multiply each digit by 16 raised to the appropriate power:
1 × 16² A × 16¹ 3 × 16⁰
- Add up all the results:
(1 × 256) + (10 × 16) + (3 × 1)
- Do the calculation:
256 + 160 + 3 = 419
- Final Answer: Hex 1A3 = Decimal 419
Hex to Decimal Conversion Table
| Hex Digit | Decimal Value |
|---|---|
| 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 |
Solved Examples
| Hex Number | Conversion Steps | Decimal Value |
|---|---|---|
| 2C7 |
2 × 16² + 12 × 16¹ + 7 × 16⁰ = 2 × 256 + 12 × 16 + 7 × 1 = 512 + 192 + 7 |
711 |
| 1A7D |
1 × 16³ + 10 × 16² + 7 × 16¹ + 13 × 16⁰ = 1 × 4096 + 10 × 256 + 7 × 16 + 13 × 1 = 4096 + 2560 + 112 + 13 |
6781 |
| 7CF |
7 × 16² + 12 × 16¹ + 15 × 16⁰ = 7 × 256 + 12 × 16 + 15 × 1 = 1792 + 192 + 15 |
1999 |
Speed Trick or Vedic Shortcut
Here’s a quick shortcut for small hex to decimal conversions: Remember that each hex digit’s place (from right) is worth 1, 16, 256, 4096, etc. Multiply and add. For digit A–F, just use A=10, B=11, …, F=15.
Memory tip: Remember these hex-letter values: A=10, B=11, C=12, D=13, E=14, F=15.
Tricks like these are handy for fast checks in exams. Vedantu’s live classes teach other time-saving strategies for conversions and logical reasoning.
Try These Yourself
- Convert 3B2 to decimal
- Find the decimal value of F5
- Convert (1F4)₁₆ to decimal
- What is the decimal equivalent of ABC?
- Convert 10A0 to decimal
Frequent Errors and Misunderstandings
- Forgetting to use the correct value for hex letters (A–F).
- Assigning powers in the wrong direction (left-to-right vs right-to-left).
- Not multiplying each digit by the right power of 16.
- Adding instead of multiplying at some steps.
Relation to Other Concepts
The idea of hex to decimal connects closely with decimal number system and other base conversions. Mastering this helps you understand how computers store data, programming logic for IP addresses, and number systems questions in competitive exams.
Classroom Tip
A quick way to remember hex to decimal is to write a place value table for powers of 16, then fill in digit values and add up. Teachers at Vedantu use colored blocks or digital calculators in class to help you visualize place values and stay accurate.
We explored hex to decimal—from definition, formula, examples, mistakes, and connections to other subjects. Continue practicing with Vedantu to become confident in solving problems using this concept!
For more on related number systems and conversions, check out: Hexadecimal Number System, Decimal Number System, Number System, Decimal to Hex Conversion
FAQs on Hex to Decimal Conversion Made Simple
1. What is hex to decimal conversion?
Hex to decimal conversion is the process of changing a number written in the hexadecimal (base 16) numbering system to an equivalent number in the decimal (base 10) system. Each digit in a hexadecimal number represents a power of 16, while in decimal, each digit represents a power of 10. Students often use this conversion in mathematics and computer science for understanding data representation. At Vedantu, students receive clear conceptual explanations and step-by-step guidance to master such number system conversions.
2. How do you convert a hexadecimal number to a decimal number?
To convert a hexadecimal number to a decimal number:
- Start from the rightmost digit of the hex number.
- Multiply each digit by $16^n$, where n is the position of the digit from the right (starting at 0).
- Add up all the products to get the decimal value.
For example, to convert $1A3$ in hexadecimal to decimal:
- $3 imes 16^0 = 3 imes 1 = 3$
- $A imes 16^1 = 10 imes 16 = 160$ (as A = 10)
- $1 imes 16^2 = 1 imes 256 = 256$
Total sum: $256 + 160 + 3 = 419$. At Vedantu, detailed conversion steps and practice worksheets are provided for better understanding.
3. Why is hexadecimal used in computers?
The hexadecimal system is frequently used in computers and digital systems because:
- It can represent large binary numbers more compactly, since one hex digit corresponds to four binary digits (bits).
- It is easier for humans to read and understand compared to lengthy binary sequences.
- Hexadecimal simplifies programming, debugging, and memory addressing tasks.
In Vedantu’s live online classes, students learn the significance of number systems in computer hardware and software contexts.
4. What is the decimal equivalent of hexadecimal 'FF'?
To find the decimal equivalent of the hexadecimal number 'FF':
- The digit F in hexadecimal represents 15 in decimal.
- So, $'FF' = 15 imes 16^1 + 15 imes 16^0 = 15 imes 16 + 15 imes 1 = 240 + 15 = 255$.
Therefore, the decimal equivalent of 'FF' is 255. Vedantu provides practice problems and interactive explanations for mastering such conversions.
5. What are the steps to convert decimal to hex?
To convert a decimal number to hexadecimal:
- Divide the decimal number by 16.
- Write down the remainder (this is the least significant digit in hex).
- Divide the quotient again by 16 and record the next remainder.
- Repeat until the quotient is zero.
- The hexadecimal number is the remainders read in reverse order.
For example, to convert decimal 156: $156 \div 16 = 9$ remainder $12$ (C in hex), $9 \div 16 = 0$ remainder $9$. So, 156 in hex is 9C. Vedantu's stepwise approach ensures conceptual clarity in these topics.
6. How do you convert a hexadecimal fraction to decimal?
To convert a hexadecimal fraction to decimal:
- Convert the integer part as usual.
- For the fractional part, multiply each digit by $16^{-n}$, where n represents the position after the decimal point (starting from 1).
For example, to convert $2.A$ (hex) to decimal:
- Integer part: $2 imes 16^0 = 2$
- Fractional part: $A imes 16^{-1} = 10 imes 0.0625 = 0.625$
Sum: $2 + 0.625 = 2.625$. Vedantu tutors explain such decimals and number systems in detail, with interactive examples for clarity.
7. What is the difference between binary, octal, decimal, and hexadecimal number systems?
Binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16) are different positional number systems:
- Binary: Digits 0, 1. Used internally by computers for computation.
- Octal: Digits 0-7. Sometimes used in digital electronics.
- Decimal: Digits 0-9. Everyday number system.
- Hexadecimal: Digits 0-9, A-F. Common in programming and computer memory representation.
Vedantu’s learning modules cover all number systems and teach students how to convert between them efficiently.
8. How is hex to decimal conversion useful for students preparing for board exams?
Hex to decimal conversion is essential for board exam preparation in subjects like Mathematics and Computer Science because:
- It appears in curriculum-mandated chapters on number systems and digital logic.
- It strengthens understanding of data representation and coding methods.
- It enhances problem-solving skills for competitive and entrance exams.
With Vedantu’s expert-led classes and practice material, students build a strong foundation in hex-decimal conversions for both school and competitive success.
9. Can Vedantu help me practice more problems on hex to decimal conversions?
Absolutely! Vedantu offers:
- Live interactive classes explaining hexadecimal to decimal (and vice versa) concepts.
- Practice worksheets with a variety of questions.
- Step-by-step solutions and personalized doubt solving for each topic.
Vedantu aims to ensure students gain confidence and accuracy in number system conversions through personalized feedback and targeted practice sessions.
10. What are some common mistakes students make when converting hexadecimal to decimal numbers?
Students may make errors such as:
- Misinterpreting alphabetical digits: Confusing A-F values in hexadecimal.
- Incorrect place values: Using base 10 powers instead of base 16.
- Omitting digits: Skipping a digit or place while calculating.
With Vedantu’s guided learning and error-analysis sessions, students can avoid these mistakes and master conversion methods quickly and accurately.
