Converting octal to binary is easier than you think. Since 23 = 8, all you have to do is convert each octal digit to its corresponding three- bit binary equivalent using the following table:
Octal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Binary: | 000 | 001 | 010 | 011 | 100 | 101 | 110 | 111 |
Now concatenate all the three-bit binary numbers together. For example, to convert 7118 to binary, use the following facts:
78 | = | 1112 |
18 | = | 0012 |
18 | = | 0012 |
Thus,
7118 = 1110010012
Exercise: Convert 7558 to binary.Example: Convert 6448 to binary:
68 | = | 1102 |
48 | = | 1002 |
48 | = | 1002 |
and so
6448 = 1101001002
Example: Convert 1101101002 to octal:
1102 | = | 68 |
1102 | = | 68 |
1002 | = | 48 |
and so
1101101002 = 6648
Exercise: Convert 1111010012 to octal.Note: Since 24 = 16, converting from hexadecimal (base 16) to binary is just as easy. In this case, there are four bits for every hexadecimal digit.