Algebra Know-It-ALL

After the first revolution, you keep the V and then start adding symbols to its right: VI,

VII, VIII. But when you get past VIII (which stands for the number eight), a problem occurs.

The number nine is not represented as VIV, although technically it could be. It’s written as

IX, but X is not on the clock face. The orderliness of this system falls apart before you even

get twice around!

The octal system

Now imagine an eight-hour clock as shown in Fig. 1-5C. This shows how the base-eight or

octal numeration system works. Use the same upward-counting scheme as you did with the

ten-hour clock. But skip the digits 8 and 9. They do not exist in this system. When you finish

the first revolution and are ready to start the second, place a 1 to the left of the digits shown,

so you count

... 5, 6, 7, 10, 11, 12, ...

The string of three dots is called an ellipsis. It indicates that a pattern continues for a

while, or perhaps even forever, saving you from having to do a lot of symbol scribbling. (You’ll

12 Counting Methods

(^01)
2
3
4
5
6
9 8 7
A
B
C
D
E
F
D
0
1
2
3
4
5
6
7
C
I
II
IV III
V
B
0 1 2 3 4 5
6
7
8
9
A
Figure 1- 5 Clock-like representations of digits in base-ten or
decimal (A), Roman base-five (B), base-eight or
octal (C), and base-sixteen or hexadecimal (D).
As you count, proceed clockwise.