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Binary to Roman Converter



Converting a Binary Number to Roman Numerals

The binary numeral system (base-2) uses only two digits: 0 and 1. It is the foundation of all binary code and digital systems. Roman numerals are an ancient numeral system that uses combinations of letters from the Latin alphabet: I, V, X, L, C, D, and M, each representing specific values. To convert a binary number to Roman numerals, we first convert the binary number to its decimal (base-10) equivalent and then convert that decimal number to Roman numerals.

For example, the binary number 11011100 can be converted to decimal as follows:

1 × 2^7 + 1 × 2^6 + 0 × 2^5 + 1 × 2^4 + 1 × 2^3 + 1 × 2^2 + 0 × 2^1 + 0 × 2^0

The sum is:

128 + 64 + 16 + 8 + 4 = 220

The decimal number 220 is then converted to Roman numerals, which is CCXX.

Examples

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

1. Convert the binary number 11011100 to Roman numerals.

Answer

First, we identify the given binary number:

Given:

  • Binary: 11011100

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

Steps:

  • 1 × 2^7 = 128
  • 1 × 2^6 = 64
  • 0 × 2^5 = 0
  • 1 × 2^4 = 16
  • 1 × 2^3 = 8
  • 1 × 2^2 = 4
  • 0 × 2^1 = 0
  • 0 × 2^0 = 0

The sum is:

Decimal Equivalent:

220

Finally, we convert the decimal number to Roman numerals:

Roman Numeral Equivalent:

CCXX

Result:

∴ The Roman numeral equivalent of the binary number 11011100 is CCXX.

2. Convert the binary number 1010 to Roman numerals.

Answer

We start by identifying the binary number:

Given:

  • Binary: 1010

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

Steps:

  • 1 × 2^3 = 8
  • 0 × 2^2 = 0
  • 1 × 2^1 = 2
  • 0 × 2^0 = 0

The sum is:

Decimal Equivalent:

10

Finally, we convert the decimal number to Roman numerals:

Roman Numeral Equivalent:

X

Result:

∴ The Roman numeral equivalent of the binary number 1010 is X.

3. Determine the Roman numeral equivalent of the binary number 100101.

Answer

First, we identify the given binary number:

Given:

  • Binary: 100101

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

Steps:

  • 1 × 2^5 = 32
  • 0 × 2^4 = 0
  • 0 × 2^3 = 0
  • 1 × 2^2 = 4
  • 0 × 2^1 = 0
  • 1 × 2^0 = 1

The sum is:

Decimal Equivalent:

37

Finally, we convert the decimal number to Roman numerals:

Roman Numeral Equivalent:

XXXVII

Result:

∴ The Roman numeral equivalent of the binary number 100101 is XXXVII.

4. Convert the binary number 1111 to Roman numerals.

Answer

We start by identifying the number:

Given:

  • Binary: 1111

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

Steps:

  • 1 × 2^3 = 8
  • 1 × 2^2 = 4
  • 1 × 2^1 = 2
  • 1 × 2^0 = 1

The sum is:

Decimal Equivalent:

15

Finally, we convert the decimal number to Roman numerals:

Roman Numeral Equivalent:

XV

Result:

∴ The Roman numeral equivalent of the binary number 1111 is XV.