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Octal to Roman Converter



Converting an Octal Number to Roman Numerals

The octal numeral system (base-8) uses digits from 0 to 7 and is commonly used in computing. Roman numerals, on the other hand, are an ancient numeral system that uses combinations of letters from the Latin alphabet: I, V, X, L, C, D, and M. Each of these letters has a specific value, and the total value of a Roman numeral is calculated by summing these values, with adjustments made according to specific rules.

To convert an octal number to its Roman numeral equivalent, the octal number is first converted to its decimal (base-10) equivalent. Once you have the decimal number, it is then converted to Roman numerals.

For example, the octal number 124 can be converted to decimal as follows:

1 × 8^2 + 2 × 8^1 + 4 × 8^0 = 64 + 16 + 4 = 84

The decimal number 84 is then converted to Roman numerals, which is LXXXIV.

Examples

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

1. Convert the octal number 124 to Roman numerals.

Answer

First, we identify the given octal number:

Given:

  • Octal: 124

Next, we convert the octal number to its decimal equivalent:

Steps:

  • 1 × 8^2 = 64
  • 2 × 8^1 = 16
  • 4 × 8^0 = 4

The sum is:

Decimal Equivalent:

84

Finally, we convert the decimal number to Roman numerals:

Roman Numeral Equivalent:

LXXXIV

Result:

∴ The Roman numeral equivalent of the octal number 124 is LXXXIV.

2. Convert the octal number 52 to Roman numerals.

Answer

We start by identifying the octal number:

Given:

  • Octal: 52

Next, we convert the octal number to its decimal equivalent:

Steps:

  • 5 × 8^1 = 40
  • 2 × 8^0 = 2

The sum is:

Decimal Equivalent:

42

Finally, we convert the decimal number to Roman numerals:

Roman Numeral Equivalent:

XLII

Result:

∴ The Roman numeral equivalent of the octal number 52 is XLII.

3. Determine the Roman numeral equivalent of the octal number 701.

Answer

First, we identify the given octal number:

Given:

  • Octal: 701

Next, we convert the octal number to its decimal equivalent:

Steps:

  • 7 × 8^2 = 448
  • 0 × 8^1 = 0
  • 1 × 8^0 = 1

The sum is:

Decimal Equivalent:

449

Finally, we convert the decimal number to Roman numerals:

Roman Numeral Equivalent:

CDXLIX

Result:

∴ The Roman numeral equivalent of the octal number 701 is CDXLIX.

4. Convert the octal number 16 to Roman numerals.

Answer

We start by identifying the number:

Given:

  • Octal: 16

Next, we convert the octal number to its decimal equivalent:

Steps:

  • 1 × 8^1 = 8
  • 6 × 8^0 = 6

The sum is:

Decimal Equivalent:

14

Finally, we convert the decimal number to Roman numerals:

Roman Numeral Equivalent:

XIV

Result:

∴ The Roman numeral equivalent of the octal number 16 is XIV.