Convert from Binary (Base 2) to Romano (Romano)

¿How to convert from Binary (Base 2) to Romano (Romano)?

Note: To convert a number in binary (base 2) to any other base, we must first convert the binary value to decimal base (base 10), for this we must perform the following steps:

1. Identify each digit of the binary number.
2. Calculate the position of each digit. Start from the rightmost digit, which will have a position of 0. Each digit to the left will have an incremental position of 1 (1, 2, 3, etc.).
3. Calculate the decimal value of each digit by multiplying it by the base (2) raised to the digit's position. For example: digit * 2^position.
4. Add the values obtained in the previous step to obtain the equivalent decimal number.

Applying these steps to the binary number 10011111:

Let's see how to pass the binary number 10011111 to decimal.

1. 1, 0, 0, 1, 1, 1, 1, 1, 1 and 1 are the digits.
2. From the rightmost, the position is 0, 1, 2, 3, 3, 4, 5, 6 and 7.
3. 1 * 2^7 = 128; 0 * 2^6 = 0; 0 * 2^5 = 0; 1 * 2^4 = 16; 1 * 2^3 = 8; 1 * 2^2 = 4; 1 * 2^1 = 2; 1 * 2^0 = 1;
4. 128 + 0 + 0 + 0 + 16 + 8 + 8 + 4 + 2 + 1 = 159 decimal.

So, 10011111 binary = 159 decimal.

To convert the decimal number to a Roman numeral, we must follow a series of rules:

Roman numerals and their basic rules.

1. The Roman numerals I, X, C, and M can repeat up to three times when writing a composite Roman numeral.
2. The Roman numerals V, L, and D can never repeat.
3. If a composite Roman numeral has a number on the right smaller than the one on the left, then both are added. Example: XI: the right number (I = 1) is smaller than the left number (X = 10), so they are added, that is XI = 11.
4. If a composite Roman numeral has a number on the right greater than the one on the left and this is an I, X or C, then the left is subtracted from the right. Example: IX: the right number (X = 10) is greater than the left number (I = 1) and it is also an I, then the left is subtracted from the right, that is IX = 9.
5. If a Roman numeral has a line over it, then its value is multiplied by a thousand. Example: IX

   : the number is 9,000 since it is the Roman numeral representing 9 and with the line over it it is multiplied by a thousand.

Steps to convert the decimal number 159 into a Roman numeral:

1. Break down the number into units, in this case: 100, 50, and 9.
2. Translate using the table, each decimal number to its equivalent Roman numeral. in this case: C=100, L=50 and IX=9.
3. We write the result from highest to lowest unit or from left to right: CLIX.

As a result, we can say that the decimal number 159 is equal to CLIX in Roman numeral.