# Conversion of Octal Number System to Binary, Decimal and Hexadecimal Number Systems

Here, we are going to learn how to convert Octal Number System to Binary, Decimal and Hexadecimal Number Systems?
Submitted by Saurabh Gupta, on October 19, 2019

### 1) Conversion of Octal Number System to Binary Number System

To convert octal numbers into binary numbers, we can use the relationship between octal and binary numbers.

Octal NumberBinary Number
0000
1001
2010
3011
4100
5101
6110
7111

Example 1: Convert (73.2)8 into ( ? )2

Solution:

Using the table provided above, we can replace octal numbers with their equivalent binary digits.

```    7 = 111
3 = 011
2 = 010
```

Therefore, (73.2)8 = (111 011.010)2

Example 2: Convert (475.62)8 into ( ? )2

Solution:

Using the table provided above, we can replace octal numbers with their equivalent binary digits.

```    4 = 100
7 = 111
5 = 101
6 = 110
2 = 010
```

Therefore, (475.62)8 = (100 111 101.110 010)2

### 2) Conversion of Octal Number System to Decimal Number System

Conversion of octal number into a decimal number can be done using the positional weights by multiplying the positional weights with the corresponding bit and add them all together to obtain the decimal number.

• In an integral part of the octal number, the weights follow the pattern as 80, 81, 82, 83, 84, 85 and so on from right to left.
• In the fractional part of the octal number, the weights follow the pattern as 8-1, 8-2, 8-3, 8-4, 8-5 and so on from left to right.

Example 1: Convert (75.3)8 = ( ? )10

Solution: We multiply each bit with the corresponding positional weight and then add them together to get the result.

Therefore, (75.3)8 = (61.375)10

Example 2: Convert (624.712)8 = ( ? )10

Solution: We multiply each bit with the corresponding positional weight and then add them together to get the result.

Therefore, (624.712)8 = (404.894)10

Example 3: Convert (482.31)8 = ( ? )10

Solution:

Given number (482.31)8 is not an octal number as a range of octal number is from 0 to 7 and the given number includes 8. So, it cannot be converted to a decimal number.

### 3) Conversion of Octal Number System into Hexadecimal Number System

Conversion of the octal number to hexadecimal can only be done using a certain definite path. We first have to convert octal number to binary number and then convert the binary number into hexadecimal number i.e., Octal Number → Binary Number → Hexadecimal Number

Example 1: Convert (35.7)8 into ( ? )16

Solution:

Step 1: Convert octal number to binary number.
Therefore, (35.7)8 = (011101.111)2

Step 2: Convert binary number to a hexadecimal number.
Therefore, (011101.111)2 = (1D.E)16

Therefore, (35.7)8 = (1D.E)16

Note: To know how to convert the binary number into a hexadecimal number?, Read: Conversion of binary number into a hexadecimal number.

Example 2: Convert (73.2)8 into ( ? )16

Solution:

Step 1: Convert octal number to binary number.
Therefore, (73.2)8 = (111011.010)2

Step 2: Convert binary number to a hexadecimal number.
Therefore, (111011.010)2 = (3B.4)16

Therefore, (73.2)8 = (3B.4)16

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