1-48BINARY CONVERSIONEarlier in this chapter, we mentioned that the octal and hex number systems are useful to computerprogrammers. 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 numbersystems for ease of understanding the data.Binary to OctalLook at the following numbers:10111001001101_{2}27115_{8}You can easily see that the octal number is much easier to say. Although the two numbers lookcompletely different, they are equal.Since 8 is equal to 2^{3}, 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 thebinary number into groups of three as shown. This grouping of binary numbers into groups of three iscalled 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:

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