Hex to Decimal Converter

He­x to decimal converter

Hex to decimal converter is used for the conversions of Hexadecimal numbers to decimal numbers easily.

What are Decimal Numbers?

Decimal numbers are also known as base-10 numbers. These are the numbers we use in our everyday lives. They consist of ten digits (0 to 9) and follow a positional notation system.

Each digit's position represents a power of 10, with the rightmost digit having a value of 10⁰, the next one on the left has 10¹, and so on.

Decimal Number System

The decimal number system is the most familiar to us, as we use it for counting and arithmetic. It allows us to express quantities simply and intuitively.

Place Value in Decimal System

The place value of a digit in a decimal number is crucial for understanding its magnitude. For instance, the digit "5" in the number "573" holds a place value of 5 units, while the digit "7" has a place value of 70 (7 tens).

What are Hexadecimal Numbers?

Hexadecimal numbers AKA base-16 numbers are commonly used in computer science and programming. They consist of sixteen digits (0 to 9 and A to F).

Where:

• A represents 10
• B represents 11
• C represents 12
• D represents 13
• E represents 14
• F represents 15

Hexadecimal Number System:

The hexadecimal system is vital in digital systems, as it allows for compact representation and simplification of complex binary numbers.

Hexadecimal to Decimal Conversion:

Understanding how to convert hexadecimal numbers to decimal form will aid us in various real-world applications.

Solved examples:

Converting Decimal to Hexadecimal:

Converting decimal to hexadecimal involves dividing the decimal number by 16 repeatedly and noting the remainder. The remainder is then converted to hexadecimal digits.

Example 1:

Convert the decimal number 312 to hexadecimal

Solution:

 (Using remainder method)

Step 1:

312 / 16 = 19 with a remainder of 8 (8 in hexadecimal)

Step 2:

19 / 16 = 1 with a remainder of 3 (3 in hexadecimal)

Step 3:

1 / 16 = 0 with a remainder of 1 (1 in hexadecimal)

The hexadecimal representation of 312 is 138.

Converting Hexadecimal to Decimal

Converting hexadecimal to decimal involves multiplying each digit by the respective power of 16 and summing the results.

Example 1:

Convert the hexadecimal number 1A7 to a decimal number

Solution:

Step 1: Multiply the existing numbers with the power of 16 separately.

= 1 * 16² + 10 * 16¹ + 7 * 16⁰

= 256 + 160 + 7

= 423.

The decimal representation of 1A7 is 423.