How to Convert Hexadecimal to Decimal and Vice Versa?

Q: What about negative hexadecimal numbers?

Yes! In fact, there exist some special forms or notations like two’s complement as seen in computers which indicates that hex notation may well denote negative quantities.

Q: Is there another base commonly used in computing?

Yes, computers use among others decimal, binary (base-2) and octal (base-8). Each one has different usages as well as varying degrees of representation quality.

ElevatEd
Math
July 10, 2024

Introduction to Hexadecimal & Decimal

The Hexadecimal system is the one that has 16 digits and uses 0 to 9 and A-F letters, this is due to its application in computing where it can represent large binary numbers more compactly. On the other hand, decimal is the base-10 system with which people are most familiar on an everyday basis.

It is a basic requirement for professions related to computer science and digital electronics. To learn more about coding from a young age explore 98thPercentile and master the concepts. Let's start with the first step of conversion.

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Hexadecimal to Decimal

There are sixteen symbols used in hexadecimal numbers: 0-9, A-F. Here’s how to convert a hexadecimal number into a decimal.

Example: Convert 2F3 (hexadecimal) to decimal.

Identify each digit and its position:

2F3

Assign each digit a power of 16, starting from 0 on the right:

2 × 16^2
F × 16^1
3 × 16^0

Convert hexadecimal digits to decimal values:

2 = 2
F = 15
3 = 3

Calculate the decimal value for each digit:

2 × 16^2 = 2 × 256 = 512
15 × 16^1 = 15 × 16 = 240
3 × 16^0 = 3 × 1 = 3

Sum the results:

Decimal value = 512 + 240 + 3 = 755

Therefore, 2F3 in hexadecimal is 755 in decimal.

Decimal to Hexadecimal

To convert a decimal number to hexadecimal, use repeated division by 16:

Example: Convert 755 (decimal) to hexadecimal.

Divide the decimal number by 16 and record the quotient and remainder:

755 ÷ 16 = 47 remainder 7

Divide the quotient by 16:

47 ÷ 16 = 2 remainder 15

The remainder 15 is represented by F in hexadecimal.

Divide the new quotient by 16:

2 ÷ 16 = 0 remainder 2

Combine the remainder in reverse order:

Hexadecimal value = 2F7

Therefore, 755 in decimal is 2F7 in hexadecimal.

In various technical fields, it is important to convert between hexadecimal and decimal systems. The process calls for understanding place values and performing mathematical operations to translate between these systems.

The aim of mastering these conversions is that you can effectively work with different number systems used in computing and digital electronics. Learn more about the basics of computing language from an early age with 98thPercentile.

FAQ’s (Frequently Asked Questions)

Q1. Why does computing use hexadecimal?

Ans: It’s because it represents binary values more concisely than any other form; each digit of the former amounting to four binary bits makes it easy to read or write long binary values.

Q2. What about negative hexadecimal numbers?

Ans: Yes! There exist some special forms or notations like two’s complement as seen in computers which indicates that hex notation may well denote negative quantities.

Q3. What are the steps to convert floating point hex to decimals?

Ans: To convert a floating-point hexadecimal number to decimal, you need to separate its integer and fractional parts, convert these parts to decimal numbers, and then combine them. This is more convoluted and may require an understanding of how floating-points are represented.

Q4. Is there another base commonly used in computing?

Ans: Yes, computers use among others decimal, binary (base-2), and octal (base-8). Each one has different usages as well as varying degrees of representation quality.

Q5. Do I need a hexadecimal converter or calculator?

Ans: A hexadecimal converter or calculator will be useful if you work with programming tasks like networking, computer science, etc. It simplifies converting from decimal numbers to hexadecimal ones.