The octal number system consists of eight digits from 0 to 7. Numbers 8 and 9 are excluded from the octal number system. It is denoted by A8, where A is a number from 0 to 7. For example, 2348, 7648, 32678, etc., are some numbers represented in the octal number system.
In a binary number system, two numbers are used to represent everything. 0 and 1 are the primary bases of the binary number system. It is denoted by A2, where A is 0 or 1. For example, 0101012, 1110002, etc., are numbers represented in a binary number system. These are commonly used in computers and electronic devices.
We cannot convert binary to octal directly. We have to convert the binary number to decimal and then that decimal to the octal number system. We need to perform the following steps to convert binary to octal number system-
Convert 1010101₂ to octal number system
We have the binary number as 10101012. We need to convert it to a decimal number first.
We need to raise it to the power of 2n-1.
10101012 = (1 * 26) + (0 * 25 ) + (1 * 24) + (0 * 23) + (1 * 22) + (0 * 21) + (1 * 20)
= 64 + 0 + 16 + 0 + 4 + 0 + 1
= 64 + 21 = 85
This 85 is the required decimal form.
Now, we need to divide 85 by 8 and write the corresponding number on the right hand side. We get,
We need to write the remainder from bottom to top to get the required octal number. Therefore, the required octal number is 1258.
We can convert binary to octal by grouping the numbers. Perform the following steps to convert the number system by another method-
|Octal Number||Binary Number|
Convert 1010111100₂ to octal number system
We need to make pairs of these binary numbers in triplets, starting from the right hand side.
We get, 1 010 111 100. We need to add 0s to the left to complete the left over triplet.
We get, 001 010 111 100
From the table above, we will get the corresponding octal number for these binary numbers.
Therefore, the required octal number is 1274₈.