Base Conversion

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.