How to Learn / Do Octal / Base 8 / Base Eight Number System. And Lots of Math Examples. A Mathematics Lesson.

The octal (base 8) number system is just a convenient way to use the binary (base 2) number system. It is highly recommended that one understand binary before proceeding to octal. You will be glad you did.

If you understand the binary (base 2) number system, then you already understand the octal (base 8) number system. You just don’t know that you know yet.

We use the decimal (base 10) number system in our day-to-day living. Base 10 has ten numbers (0-9) and orders of magnitude that are times ten. The lowest-order number represents itself times one. The next-order number represents itself times ten. The next order number represents itself times 10x10 or itself times 100. The next order number represents itself times 10x10x10 or itself times 1000. And so on.

An example would be the number 2375. This number means that there are:

five 1’s,

seven 10’s,

three 100’s

and two 1000’s.

Which represents 5 + 70 + 300 + 2000; for a total of 2375.

The octal (base 8) number system...

...uses the same structure, the only difference being the order of magnitude. Base 8 has eight numbers (0-7) and orders of magnitude that are times eight. The lowest-order number represents itself times one. The next-order number represents itself times eight. The next order number represents itself times 8x8 or itself times 64. The next order number represents itself times 8x8x8 or itself times 512. And so on.

An example would be the number 4075. This number means that there are:

five 1’s,

seven 8’s,

no 64’s,

and four 512’s.

Which represents 5 + 56 + 0 + 2048; for a total of 2109.

Other octal (base 8) examples are:

0=0

1=1

2=2

7=7

10=8

11=9

12=10

13=11

14=12

15=13

16=14

17=15

20=16

25=21

34=28

50=40

55=45

77=63

100=64

165=117

200=128

534=348

1000=512

1100=576