How do you convert a binary number to its octal equivalent?

To convert a binary number to its octal equivalent, group the binary digits into sets of three, starting from the right, then convert each group to its octal equivalent.

To understand this process in more detail, let's break it down step by step. Binary numbers are base 2, and octal numbers are base 8. The key to converting between these two bases is to recognise that 2^3 equals 8. This means that three binary digits can represent one octal digit.

Start by grouping the binary number into sets of three digits, starting from the right. If the binary number doesn't divide evenly into groups of three, simply add zeros to the left side until it does. For example, if you have the binary number 101101, you would group it as 101 101. If you have the binary number 1101, you would group it as 011 101, adding a zero to the left side.

Next, convert each group of three binary digits to its octal equivalent. The binary numbers 000, 001, 010, 011, 100, 101, 110, and 111 correspond to the octal numbers 0, 1, 2, 3, 4, 5, 6, and 7, respectively. So, using our previous examples, the binary number 101 101 would convert to the octal number 55, and the binary number 011 101 would convert to the octal number 35.

Remember, the key to this process is understanding the relationship between the bases. Because 2^3 equals 8, three binary digits can represent one octal digit. This makes the conversion process straightforward: simply group the binary digits into sets of three, then convert each group to its octal equivalent. This method is a simple and effective way to convert binary numbers to octal numbers.