Binary and octal are two commonly used numeral systems in computer science. While consists of only two digits (0 and 1), octal uses eight digits (0 through 7). Converting a binary to octal can be done in a few simple steps, which we will discuss in detail in this article.

Step 1: Group the Binary Digits

The first step in ing a binary number to octal is to group the binary digits in sets of three, starting from the rightmost digit. If there are not enough digits to form a set of three, add zeros to the left side to complete a set. For example, if we have the binary number 10011010, we group it like this: 001 001 010.

Step 2: Convert Each Group to its Octal Equivalent

Next, we need to convert each group of three binary digits to its octal equivalent. To do this, we can use the following table which shows the binary to octal conversion for all possible three-bit groups:

Binary Octal
000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7

Using the above table, we can convert our binary number 10011010 to octal as follows:

001 001 010
1 1 2

Therefore, our binary number 10011010 equals the octal number 112.

Step 3: Remove Leading Zeros

Finally, we should remove any leading zeros from the octal number. For example, if the octal number is 011, we should remove the leading zero and it as 11. If the octal number is just zero, we should leave it as is.

Example: Convert 1011010100 from binary to octal

Step 1: Group the Binary Digits

We group the binary digits in sets of three, starting from the rightmost digit.

1 0 1 1 0 1 0 0
101 101 010 0

Step 2: Convert Each Group to its Octal Equivalent

We convert each group to its octal equivalent using the binary to octal conversion table.

101 101 010 0
5 5 2 0

Therefore, our binary number 1011010100 equals the octal number 5520.

Step 3: Remove Leading Zeros

In this example, we don’t have any leading zeros to remove from the octal number.

In conclusion, converting a binary number to octal is a simple process that requires grouping the binary digits in sets of three, converting each group to its octal equivalent using a conversion table, and removing any leading zeros from the resulting octal number. By following these simple steps, you can easily convert binary to octal and vice versa.

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