the Octal System

For this section, let’s take (65)₈ for example.

Conversion of Octal to Decimal

Octal Number	6	5
Significance of each bit	81	80
Weighted value	6(8) = 40	5(1) = 5
Solved Multiplication	48	5

Therefore = (65)₈ = 48 + 5 = 53

Conversion of Octal fraction to decimal fraction

Take (0.5)₈ for an example.

Octal number	5
Significance of bit	8-1
Weighted value	5(8-1)
Solved multiplication	0.625

Therefore, (0.5)₈ = 0.625, and (65.5)₈ = 53.625

Conversion of Octal to Binary

When converting octal to binary, we follow these steps:

1.       Convert each octal digit to its 3-bit equivalent.

2.                    Combine the numbers

(65)₈

Octal number	6	5
Binary number	110	101

Combine them: 110101₂

8-bit binary number = 00110101₂

Conversion of octal fraction to binary fraction

0.5₈

Octal number	5
Binary number	101

Therefore (0.5)₈ = 0.101 and (65.5)₈ = (110101.101)₂

-Xin Lin