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Hex to Decimal Converter



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Converting a Hexadecimal Number to Decimal

Hexadecimal (hex) is a base-16 numeral system that is widely used in computing and digital electronics. It uses sixteen distinct symbols: 0-9 to represent values zero to nine, and A-F (or a-f) to represent values ten to fifteen. On the other hand, the decimal system is the standard base-10 numeral system that we use in everyday life.

To convert a hexadecimal number to its decimal equivalent, you must understand the positional value of each digit in the hex number. Each position represents a power of 16, starting from the rightmost digit (which represents \(16^0\)) and moving left. The value of the hexadecimal number is the sum of these powers of 16, multiplied by the corresponding hex digit’s value.

For example, the hexadecimal number 1A3 can be converted to decimal by calculating:

\(1 \times 16^2 + A \times 16^1 + 3 \times 16^0\)

Where A represents 10 in decimal. Therefore, the calculation becomes:

\(1 \times 256 + 10 \times 16 + 3 \times 1 = 256 + 160 + 3 = 419\)

Thus, the decimal equivalent of 1A3 is 419.

Examples

Let’s explore some examples to understand how to convert hexadecimal numbers to their decimal equivalents.

1. Convert the hexadecimal number 1A3 to decimal.

Answer

First, we identify the given number:

Given:

  • Hexadecimal: 1A3

Next, we calculate the decimal value by applying the powers of 16 to each digit:

Steps:

  • 1 = 1, so \(1 \times 16^2 = 1 \times 256 = 256\)
  • A = 10, so \(A \times 16^1 = 10 \times 16 = 160\)
  • 3 = 3, so \(3 \times 16^0 = 3 \times 1 = 3\)

We then sum these values to get the decimal equivalent:

  • \(256 + 160 + 3 = 419\)

The final decimal value is:

Decimal Equivalent:

419

Result:

∴ The decimal equivalent of the hexadecimal number 1A3 is 419.

2. Convert the hexadecimal number 4F to decimal.

Answer

We start by identifying the number:

Given:

  • Hexadecimal: 4F

Next, we calculate the decimal value by applying the powers of 16 to each digit:

Steps:

  • 4 = 4, so \(4 \times 16^1 = 4 \times 16 = 64\)
  • F = 15, so \(F \times 16^0 = 15 \times 1 = 15\)

We then sum these values to get the decimal equivalent:

  • \(64 + 15 = 79\)

The final decimal value is:

Decimal Equivalent:

79

Result:

∴ The decimal equivalent of the hexadecimal number 4F is 79.

3. Determine the decimal equivalent of the hexadecimal number B7.

Answer

First, we identify the given number:

Given:

  • Hexadecimal: B7

Next, we calculate the decimal value by applying the powers of 16 to each digit:

Steps:

  • B = 11, so \(B \times 16^1 = 11 \times 16 = 176\)
  • 7 = 7, so \(7 \times 16^0 = 7 \times 1 = 7\)

We then sum these values to get the decimal equivalent:

  • \(176 + 7 = 183\)

The final decimal value is:

Decimal Equivalent:

183

Result:

∴ The decimal equivalent of the hexadecimal number B7 is 183.

4. Convert the hexadecimal number 2C to decimal.

Answer

We start by identifying the number:

Given:

  • Hexadecimal: 2C

Next, we calculate the decimal value by applying the powers of 16 to each digit:

Steps:

  • 2 = 2, so \(2 \times 16^1 = 2 \times 16 = 32\)
  • C = 12, so \(C \times 16^0 = 12 \times 1 = 12\)

We then sum these values to get the decimal equivalent:

  • \(32 + 12 = 44\)

The final decimal value is:

Decimal Equivalent:

44

Result:

∴ The decimal equivalent of the hexadecimal number 2C is 44.