11. Octal Numbers

Octal Numbers are very similar in principle to the previous hexadecimal numbering system except that in Octal a binary number is divided up into groups of only 3 bits, with each group or set of numbers having a distinct value of between "000" (0) and "111" (4+2+1=7) giving a range of just 8, (0, 1, 2, 3, 4, 5, 6, 7) therefore q = "8".

Then the main characteristics of an Octal Numbering System is that there are 8 distinct counting digits from 0 to 7 with each digit having a weight or value of just 8 starting from the least significant bit (LSB).

As the base of an Octal Numbers system is 8, which also represents the number of individual numbers used in the system, the subscript 8 is used to identify a number expressed in octal. For example, 237₈

Like hexadecimal, the octal number system provides a convenient way of converting large binary numbers into smaller groups. However, octal numbers is used less frequently than the more common hexadecimal numbering system and has almost disappeared. As octal uses only eight digits there are no letters used but the conversion from binary or denary follows the same pattern as we have seen for hex.

To count above 7 in octal we add another column and start over again in a similar way to hexadecimal.

0, 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 20, 21....etc

Again do not get confused, 10 or 20 is NOT ten or twenty it is 1 + 0 and 2 + 0 in octal exactly the same as for hexadecimal. With two octal numbers, 77₈ we can count up to 63 in decimal, with three octal numbers, 777₈ up to 511 in decimal and with four octal numbers, 7777₈ up to 4095 in decimal and so on.

Example No1.

Using our previous binary number of 1101010111001111₂ converting it into the octal equivalent is shown as follows.

Binary Digit Value	001101010111001111
Group the bits into three´s starting from the right hand side	001 101 010 111 001 111
Octal Number form	1 5 2 7 1 78

Thus, 001101010111001111₂ in its Binary form is equivalent to 152717₈ in Octal form or 54,735 in decimal.

Next topic will be on Boolean Algebra