In contrast to the decimal system, the rules for writing numbers in the binary and octal systems are different. In the octal number system, we use 0 to 7 digits to write numbers, whereas in the binary system, we only use 0 and 1. Each number written in one number framework can be changed over completely to another, by applying some arrangement of rules.
We have learned about the various kinds of numbers in mathematics, such as rational numbers, real numbers, whole numbers, natural numbers, and so on. The number system is used in a slightly different way in the digital world. The four most prevalent types of the number system are as follows:
In this article, we will learn how to convert the binary number system to the octal number system, which has a base of 8 and is represented by (n) 8; the binary number system has a base of 2 and is represented by (n) 2; the decimal number system has a base of 10 and is represented by (n) 10; and the hexadecimal number system has a base of 16 and is represented by (n) 16. Let’s start!
Meaning of Binary Number System
The computer system that only uses the numbers 0 and 1 is closely related to the binary number system. Binary numbers only deal with the digits 0 and 1 and the base 2, which is 2. This number framework doesn’t manage different numbers, for example, 2,3,4,5, etc. In the binary number system, a bit is a digit that can be either 0 or 1. A few examples of binary numbers include (01101) 2, (01000010) 2, and (11000101)
Meaning of Octal Number System
The octal number system uses a base of 8 and digits from 0 to 7. The octal number system does not include numbers like 8 and 9. Similar to the binary system, the octal number system, which has digits from 0 to 7, is used in minicomputers. Some octal numbers, like (76/8), (121/8), and (350/8), are examples.
Octal to Binary Conversion
Directly converting from binary to octal is not an option because octal numbers are used in electronics while binary numbers are used in computers as bits or bytes. When converting from binary to octal, there are two types of approaches.
1st Method: The steps for converting from binary to decimal and then from decimal to octal are listed below.
Step 1: Step 2: Identify the binary number: By multiplying each digit by 2n-1, where n is the position of the digit from right, you can convert binary to decimal.
Step 3: For the given binary number, the derived answer is the decimal number. Step 4: Partition the decimal number by 8
Stage 5: Note the remaining steps in Step 6: Step 7: Add the quotient to the previous two steps until it reaches zero. Step 8: Write the remaining words in the opposite order. The answer is the binary number’s required octal number, such as: Make an octal number of the binary number (1011112) 2.
Solution: First, convert the binary number to a decimal number using method 1.
( 1011101 ) 2 = (1 x 26) + (0 x 25) + (0 x 24) + (0 x 23) + (0 x 22) + (0 x 21) + (1 x 20) = 64 + 0 + 16 + 8 + 4 + 0 + 1 = 93 ( 1011101 ) 2 = ( 93 ) 10 The next step is to divide 93 by 8 to turn the decimal number into an octal number.
Method 2: Divide 93 by 8 to get 5 as a remainder and 11 as a quotient. Divide 11 by 8 to get 3 as a remainder and 1 as a quotient. Divide 8 to get 1 as a remainder and 0 as a quotient. Collect the remainders in reverse order to get 1 3 5. Using grouping to convert from binary to octal: the necessary steps are listed below.
Step 1: Distinguish the paired number for example the digits ought to be either 0 or 1 with base 2.
Step 2: Beginning on the right side, arrange all of the 0 to 1 in a set of three.
Step 3: If it does not form a group of three, add zeros to the left. There must be three digits in each group.
Step 4: For precise numbers, consult the binary to octal conversion table.
Step 5: The octal number is that number once it is obtained. Binary to Octal Conversion Table Make an octal number of the binary number (01110101) 2.
Solution: Set the binary number into three groups of three numbers using grouping.
= 001 110 101 = 1 6 5
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