Convert from Roman (Rom) to Binary (Base 2)

¿How to convert from Roman (Rom) to Binary (Base 2)?

Note: To convert a number in the Roman numeral system to any other base, we first need to convert the Roman numeral to decimal (base 10). Follow these steps:

Roman Numerals and Their Basic Rules.

1. The Roman numerals I, X, C, and M can be repeated up to three times when writing a composite Roman numeral.
2. The Roman numerals V, L, and D cannot be repeated.
3. If a composite Roman numeral has a smaller number to the right than to the left, then both are added. Example: XI: The number on the right (I = 1) is smaller than on the left (X = 10), so they are added, i.e., XI = 11.
4. If a composite Roman numeral has a larger number to the right and it is I, X, or C, then the left is subtracted from the right. Example: IX: The number on the right (X = 10) is larger than on the left (I = 1), and it's I, so the left is subtracted from the right, i.e., IX = 9.
5. If a Roman numeral has a line over it, its value is multiplied by a thousand. Example: IX

   : the number is 9,000, as it's the Roman numeral representing 9 and the line over it multiplies it by a thousand.

Applying the steps to the Roman numeral "CLIX":

1. C = 100, L = 50, I = 1, X = 10
2. We observe I = 1 before X = 10, so I is subtracted from X;
3. Add 100 + 50 + (10 - 1) = 159.

The Roman numeral "CLIX" is equivalent to 159 in decimal.

Note: To convert a decimal number (base 10) to binary number (base 2), follow these steps:

1. Repeatedly divide the decimal number by 2 and record the remainders of the divisions.
2. The process ends when the result of the division is 0.
3. The remainders of the divisions must be written in reverse order as they represent the weights of the corresponding binary digits.

Applying these steps to the decimal number 159:

Below is an example of how to convert the decimal number 159 to binary:

1. Divide 159 by 2: 159 ÷ 2 = 79 with a remainder of 1.
2. Divide 79 by 2: 79 ÷ 2 = 39 with a remainder of 1.
3. Divide 39 by 2: 39 ÷ 2 = 19 with a remainder of 1.
4. Divide 19 by 2: 19 ÷ 2 = 9 with a remainder of 1.
5. Divide 9 by 2: 9 ÷ 2 = 4 with a remainder of 1.
6. Divide 4 by 2: 4 ÷ 2 = 2 with a remainder of 0.
7. Divide 2 by 2: 2 ÷ 2 = 1 with a remainder of 0.
8. Divide 1 by 2: 1 ÷ 2 = 0 with a remainder of 1.

The remainders of the divisions are written in reverse order: 10011111.

Therefore, the number 159 in decimal converts to 10011111 in binary.