A short presentation on how to count in another base number system, such as base8 or base6.

1. Base Jumping
Part 1
Counting in Base X

2. What you know
already
Counting the old fashioned way

3.  You know that 125 is one hundred and
twenty-five. That’s a good start!
 You know it because at infant school,
someone told you about ones, tens, and
hundreds
 125 has 5 ones, 2 tens and 1 hundred
 The positions of the individual numbers in
125 matter. They tell us if we are talking
about ones, tens or hundreds
Hundreds Tens Ones
1 2 5

4.  To count, we start in the right most column and count
from 0 to 9; a total of 10 possible digits
 When we get to 9, to go higher we have to add 1 to the
next column and start again at 0 in the right column
 We repeat this for each column as we count higher and
higher
 Because we have 10 possible digits in each column,
each column is 10 times larger than the column before it
(to the right)
Hundreds Tens Ones
8
9
1 0
1 1

5.  10 digits for each column
 Each column 10 times larger than the last
 You’ve guessed it, this is the Base 10
number system!
Hundreds Tens Ones
1 2 5
 To show we are working in the base10
system, we can write 12510 instead of just
125

6. Taking it further
General rules we already know

7.  Now we have learned a little more Math than
when we were children, we can express
ones, tens and hundreds in a different way
 We know that hundreds or 100 can be
expressed as 102 (ten to the power of 2)
 Tens can be expressed as 101
Hundreds Tens Ones
1 2 5
 Ones can be expressed 100, because any
number raised to the power of 0 is always 1

8. So, what do we know…?

9.  Rule 2: We can create a table to help us
count in that number system
 Rule 3: Each column in the table has a
name that is made up of the base number
raised to a power. The power increases by
one for each column as we move from right
to left, starting with base0
 Rule 4: Each cell in the table is able to hold
a single digit from 0 up to the base number -
1
 Rule 1: We know what number system a
number is from when it is written in the
format numberbase

10. Let’s see these rules again using another base
system as an example. Base 8…
 Rule 5: When a cell reaches the highest digit
it can take, we add 1 to the next column to
the left and start again at 0 in the original cell
we were counting in

11. Our first Base
Jump
Counting in Base8

12.  Rule 1: We know what number system a
number is from when it is written in the
format numberbase
1248 = 124 in the base8 number system

13.  Rule 2: We can create a table to help us
count
1248

14. 82 81 80
1248
 Rule 3: Each column in the table has a
name that is made up of the base number
raised to a power. The power increases by
one for each column as we move from right
to left, starting with base0

15. 82 81 80
6
7
1248
 Rule 4: Each cell in the table is able to hold
a single digit from 0 up to the base number -
1

16. 82 81 80
6
7
1 0
1248
 Rule 5: When a cell reaches the highest digit
it can take, we add 1 to the next column to
the left and start again at 0 in the original cell
we were counting in

17. You survived!
Counting in baseX

18.  The rules you learned can be applied to any
base number
 Did you know that the ancient Babylonians
counted in Base6? That’s why we have 60
seconds in a minute and 60 minutes in an
hour.
 Can you count in base6 out loud?
(Answers on the next slide)
 That’s all there is to counting in another
base number system
 Try counting in base6 on a piece of paper.

19. 1
2
3
4
5
10
11
12
13
14
15
20
21
22
Etc, etc
Base6

20. Base Jumping: Part (2) will look at converting to and from
Base10