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Octal to Decimal Converter



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Converting an Octal Number to Decimal

The octal numeral system (base-8) is used in computing and digital systems. It uses digits from 0 to 7. The decimal system (base-10) is the standard numeral system used in everyday life. Converting an octal number to its decimal equivalent involves understanding the positional value of each digit in the octal number. Each position represents a power of 8, starting from the rightmost digit (which represents \(8^0\)) and moving left.

For example, the octal number 345 can be converted to decimal by calculating:

\(3 \times 8^2 + 4 \times 8^1 + 5 \times 8^0\)

This becomes:

\(3 \times 64 + 4 \times 8 + 5 \times 1 = 192 + 32 + 5 = 229\)

Thus, the decimal equivalent of 345 is 229.

Examples

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

1. Convert the octal number 345 to decimal.

Answer

First, we identify the given number:

Given:

  • Octal: 345

Next, we calculate the decimal value by applying the powers of 8 to each digit:

Steps:

  • 3 = 3, so \(3 \times 8^2 = 3 \times 64 = 192\)
  • 4 = 4, so \(4 \times 8^1 = 4 \times 8 = 32\)
  • 5 = 5, so \(5 \times 8^0 = 5 \times 1 = 5\)

We then sum these values to get the decimal equivalent:

  • \(192 + 32 + 5 = 229\)

The final decimal value is:

Decimal Equivalent:

229

Result:

∴ The decimal equivalent of the octal number 345 is 229.

2. Convert the octal number 52 to decimal.

Answer

We start by identifying the number:

Given:

  • Octal: 52

Next, we calculate the decimal value by applying the powers of 8 to each digit:

Steps:

  • 5 = 5, so \(5 \times 8^1 = 5 \times 8 = 40\)
  • 2 = 2, so \(2 \times 8^0 = 2 \times 1 = 2\)

We then sum these values to get the decimal equivalent:

  • \(40 + 2 = 42\)

The final decimal value is:

Decimal Equivalent:

42

Result:

∴ The decimal equivalent of the octal number 52 is 42.

3. Determine the decimal equivalent of the octal number 701.

Answer

First, we identify the given number:

Given:

  • Octal: 701

Next, we calculate the decimal value by applying the powers of 8 to each digit:

Steps:

  • 7 = 7, so \(7 \times 8^2 = 7 \times 64 = 448\)
  • 0 = 0, so \(0 \times 8^1 = 0\)
  • 1 = 1, so \(1 \times 8^0 = 1 \times 1 = 1\)

We then sum these values to get the decimal equivalent:

  • \(448 + 0 + 1 = 449\)

The final decimal value is:

Decimal Equivalent:

449

Result:

∴ The decimal equivalent of the octal number 701 is 449.

4. Convert the octal number 16 to decimal.

Answer

We start by identifying the number:

Given:

  • Octal: 16

Next, we calculate the decimal value by applying the powers of 8 to each digit:

Steps:

  • 1 = 1, so \(1 \times 8^1 = 1 \times 8 = 8\)
  • 6 = 6, so \(6 \times 8^0 = 6 \times 1 = 6\)

We then sum these values to get the decimal equivalent:

  • \(8 + 6 = 14\)

The final decimal value is:

Decimal Equivalent:

14

Result:

∴ The decimal equivalent of the octal number 16 is 14.