The converting of binary, octal, and hex numbers to their decimal equivalents is covered as a group later in this section.

BINARY CONVERSION

Earlier in this chapter, we mentioned that the octal and hex number systems are useful to computer programmers. It is much easier to provide data to a computer in one or the other of these systems. Likewise, it is important to be able to convert data from the computer into one or the other number systems for ease of understanding the data.

Binary to Octal

Look at the following numbers:

You can easily see that the octal number is much easier to say. Although the two numbers look completely different, they are equal.

Since 8 is equal to 2³, then one octal digit can represent three binary digits, as shown below:

With the use of this principle, the conversion of a binary number is quite simple. As an example, follow the conversion of the binary number at the beginning of this section.

Write out the binary number to be converted. Starting at the radix point and moving left, break the binary number into groups of three as shown. This grouping of binary numbers into groups of three is called binary-coded octal (BCO). Add 0s to the left of any MSD that will fill a group of three:

Next, write down the octal equivalent of each group:

To convert a binary fraction to its octal equivalent, starting at the radix point and moving right, expand each digit into a group of three:

Add 0s to the right of the LSD if necessary to form a group of three. Now write the octal digit for each group of three, as shown below:

To convert a mixed binary number, starting at the radix point, form groups of three both right and left:

Convert the following binary numbers to octal:

Q.65 10₂.
Q.66 1010₂.
Q.67 101111₂.
Q.68 0.0011₂.
Q.69 0.110011₂.
Q.70 110111.010101₂.