Convert from Binary (Base 2) to Hexadecimal (Base 16)

¿How to convert from Binary (Base 2) to Hexadecimal (Base 16)?

Note: To convert a number in binary (base 2) to any other base, we must first convert the binary value to decimal (base 10). Follow these 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 position of the digit. For example: digit * 2^position.
4. Add up the values obtained in the previous step to get the equivalent decimal number.

Applying these steps to the binary number 10011111:

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

1. 1, 0, 0, 1, 1, 1, 1, and 1 are the digits.
2. Starting from the rightmost, the positions are 0, 1, 2, 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 + 16 + 8 + 4 + 2 + 1 = 159 decimal.

Therefore, 10011111 binary = 159 decimal.

To convert a decimal number (base 10) to hexadecimal (base 16), follow these steps:

1. Divide the decimal number by 16.
2. Take the quotient and divide it by 16 again.
3. Repeat this process until the quotient is less than 16.
4. Assign a letter to each remainder if the remainder is greater than 9.
5. Numbers 10, 11, 12, 13, 14, and 15 are represented by the letters A, B, C, D, E, and F, respectively.
6. Write down the remainders obtained in reverse order to how they were calculated.

Applying these steps to the decimal number 159:

1. 159 / 16 = 9 with a remainder of 15.
2. 9 / 16 = 0 with a remainder of 9.
3. 15 is represented as F.
4. 9 is represented as 9.