An octal-to-binary conversion is done to convert an octal number (base 8) to its equivalent binary number (base 2). Here are the methods to convert an octal number to its binary counterpart.
Direct Method: Using Table
The octal number system has 8 digits from 0 to 7, represented in their equivalent binary using 3 bits.
Let us convert (363)8 into its binary number.
Step 1: Grouping 363 into individual digits, we have 3, 6, and 3.
Step 2: Now, we find their corresponding binary numbers using the conversion table.
Octal Number
Binary Number
0
000
1
001
2
010
3
011
4
100
5
101
6
110
7
111
By converting each octal digit of (363)8 to their binary numbers, we get
Octal Value
3
6
3
Binary Value
011
110
011
Here, we observe that each octal digit gives us a 3-bit binary number. Otherwise, we add zeros to maintain the correct number of digits.
Step 3: Taking the values from the first to last, (363)8 equals (011110011)2 or (11110011)2.
For Fractional Octal Numbers
Similarly, we convert the fractional octal numbers into their corresponding binary.
Now, converting (452.01)8 to its equivalent binary, we get
For the Integral Part:
4 → 100, 5 → 101, and 2 → 010
For the Fractional Part:
0 → 000 and 1 → 001
Thus, (452.01)8 = (100101010.000001)2
Convert (53)8 into binary using the conversion table.
Solution:
Grouping 53 into individual digits, we have 5 and 3. By converting each octal digit of (53)8 to the binary, we get (5)8 = (101)2 (3)8 = (011)2 Placing the values from the first to last, (53)8 equals (101011)2.
Octal Value
5
3
Binary Value
101
011
Indirect Method: Without Using Table
There is another way by which each digit in any octal number is represented to its corresponding binary number without using the octal-to-binary conversion table.
Let us convert an octal number (73)8 into its corresponding binary.
First, we convert 73 into a decimal number and then decimal to binary.
Step 1: Octal to Decimal
While converting (73)8 to its decimal number, we multiply each digit from the right by the corresponding powers of 8, as shown.
Octal Value
7
3
Decimal Value
7 × 81
3 × 80
Now, on adding the values, we get the decimal number
(7 × 81) + (3 × 80) = 56 + 3 = 59
Step 2: Decimal to Binary
Now, converting (59)10 into its corresponding binary, we get
Thus, (73)8 = (111011)2.
Convert (347)8 into its corresponding binary.
Solution:
By converting (347)8 into its corresponding decimal, we get (3 × 82) + (4 × 81) + (7 × 80) = 192 + 32 + 7 = 231 Now, by converting (231)10 into its corresponding binary, we get Thus, (347)8 = (11100111)2.
