Convert from Binary (Base 2) to Octal (Base 8)

¿How to convert from Binary (Base 2) to Octal (Base 8)?

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.

Note: To convert a decimal number (base 10) to an octal number (base 8), follow these steps:

1. Divide the decimal number by 8 and record the remainders of the divisions until the division result is 0.
2. The remainders from the divisions should be written in reverse order as they were obtained, as they represent the weights of the corresponding octal digits.

Here's an example of converting the decimal number 159 to octal:

1. Divide 159 by 8: 159 ÷ 8 = 19 with a remainder of 7.
2. Divide 19 by 8: 19 ÷ 8 = 2 with a remainder of 3.
3. Divide 2 by 8: 2 ÷ 8 = 0 with a remainder of 2.

The remainders of the divisions are written in reverse order: 237.

Therefore, the decimal number 159 converts to 237 in octal.