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Roman to Hex Converter



Converting a Roman Numeral to Hexadecimal

Roman numerals are an ancient numeral system based on 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 certain rules. On the other hand, the hexadecimal system (base-16) uses digits from 0 to 9 and letters A to F to represent values.

To convert a Roman numeral to its hexadecimal (hex) equivalent, the Roman numeral is first converted to its decimal (base-10) equivalent by summing the values of the individual letters according to the rules of Roman numerals. Once you have the decimal number, you can convert it to hexadecimal.

For example, the Roman numeral XXVII can be converted to decimal as follows:

X = 10, X = 10, V = 5, I = 1, I = 1

Summing these values gives:

10 + 10 + 5 + 1 + 1 = 27

The decimal number 27 is then converted to hexadecimal, which is 1B.

Examples

Let’s explore some examples to understand how to convert Roman numerals to their hexadecimal equivalents.

1. Convert the Roman numeral XXVII to hex.

Answer

First, we identify the given Roman numeral:

Given:

  • Roman: XXVII

Next, we convert the Roman numeral to its decimal equivalent by summing the values of its individual letters:

Steps:

  • X = 10
  • X = 10
  • V = 5
  • I = 1
  • I = 1

The sum is:

Decimal Equivalent:

27

Finally, we convert the decimal number to hexadecimal:

Hexadecimal Equivalent:

1B

Result:

∴ The hexadecimal equivalent of the Roman numeral XXVII is 1B.

2. Convert the Roman numeral XLIV to hex.

Answer

We start by identifying the Roman numeral:

Given:

  • Roman: XLIV

Next, we convert the Roman numeral to its decimal equivalent by summing the values of its individual letters:

Steps:

  • X = 10
  • L = 50
  • I = 1
  • V = 5

Since X is before L, we subtract its value from L:

  • 50 - 10 = 40

And since I is before V, we subtract its value from V:

  • 5 - 1 = 4

The sum is:

Decimal Equivalent:

44

Finally, we convert the decimal number to hexadecimal:

Hexadecimal Equivalent:

2C

Result:

∴ The hexadecimal equivalent of the Roman numeral XLIV is 2C.

3. Determine the hexadecimal equivalent of the Roman numeral CMXCIX.

Answer

First, we identify the given Roman numeral:

Given:

  • Roman: CMXCIX

Next, we convert the Roman numeral to its decimal equivalent by summing the values of its individual letters:

Steps:

  • C = 100
  • M = 1000
  • X = 10
  • C = 100
  • I = 1
  • X = 10

Since C is before M, and X is before C, we subtract their values:

  • 1000 - 100 = 900
  • 100 - 10 = 90
  • 10 - 1 = 9

The sum is:

Decimal Equivalent:

999

Finally, we convert the decimal number to hexadecimal:

Hexadecimal Equivalent:

3E7

Result:

∴ The hexadecimal equivalent of the Roman numeral CMXCIX is 3E7.

4. Convert the Roman numeral LXII to hex.

Answer

We start by identifying the number:

Given:

  • Roman: LXII

Next, we convert the Roman numeral to its decimal equivalent by summing the values of its individual letters:

Steps:

  • L = 50
  • X = 10
  • I = 1
  • I = 1

The sum is:

Decimal Equivalent:

62

Finally, we convert the decimal number to hexadecimal:

Hexadecimal Equivalent:

3E

Result:

∴ The hexadecimal equivalent of the Roman numeral LXII is 3E.