Binary to Octal Formula
An octal number is a system of numbers that has a base of 8 and uses digits from 0 to 7. The octal number system was initially used as a computer programming language at an early age. In the octal number system, after 7, the numbers start from 10 to 17, then 20 to 27, and so on. They do not contain digits such as 8 and 9. We have two types of methods to convert a binary number into an octal number, i.e., by converting binary to octal directly, and the other one is converting binary to decimal, and then converting the obtained decimal into octal.
Binary number |
Octal Number |
Binary number |
Octal Number |
---|---|---|---|
000 |
0 |
1000 |
10 |
001 |
1 |
1001 |
11 |
010 |
2 |
1010 |
12 |
011 |
3 |
1011 |
13 |
100 |
4 |
1100 |
14 |
101 |
5 |
1101 |
15 |
110 |
6 |
1110 |
16 |
111 |
7 |
1111 |
17 |
For example, convert (10110110)2 to octal.
Solution:
Method 1:
Step 1: Starting at the right end, divide the given binary number into a pair of three digits.
10-110-110
Step 2: We can notice that the first group doesn’t have three digits. So add zeros on the left. Now, substitute the value of the octal number into it.
010-110-110
(010)2 = (2)8
(110)2 = (6)8
(110)2 = (6)8
Step 3: Now, combine all digits.
010-110-110 = 2-6-6 = 266
Therefore, the binary number (10110110)2 in the octal system is 266.
Method 2:
It is a long process as we have to perform two conversions, i.e., from binary to decimal and again from decimal to octal.
Step 1: Converting the binary number (10110110)2 to decimal
(1 × 27) + (0 × 26) + (1 × 25) + (1 × 24) + (0 × 23) + (1 × 22) + (1 × 21) + (0 × 20)
= 128 + 0 + 32 + 16 + 0 + 4 + 2 + 0 = (182)10
Step 2: Now, divide the obtained decimal number 8.
Therefore, the binary number (10110110)2 in the octal system is 266.
Binary Formula
Binary formulas are formulas that are used to convert binary numbers to other number systems. A binary number system is a system of numbers that has a base of 2 and uses only two digits, “0 and 1”. It is one of the four types of number systems and is most commonly employed by computer languages like Java and C++. “Bi” in the word “binary” stands for “two.” Some examples of binary numbers are (11)2, (1110)2, (10101)2, and so on.
In this article, we discuss the arithmetic operations of binary numbers and the conversion formulae to convert binary numbers into other three-number systems.
Table of Content
- Binary Formula
- Arithmetic Operation on Binary Numbers
- Binary to Decimal Formula
- Decimal to Binary Formula
- Binary to Octal Formula
- Binary to Hexadecimal Formula
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