Base

Introduction

You have been taught to count in base 10. Base 10 means that our counting system has 10 digits: (0123456789). To understand what this means, let's start counting!

0...1...2...3...4...5...6...7...8...9

What happens after 9? We have used all available digits, so we add another digit (1) to the front and start over:

10...11...12...13...14...15...16...17...18...19

// we have run out of numbers, so increase from 1 to become 2 and start over!
20...21...22...23...24...25...26...27...28...29
30...31...32...33...34...35...36...37...38...39
...
90...91...92...93...94...95...96...97...98...99

What happens after 99? We have used all available digits, so let's add another digit (1) to the front and start over:

100...101...102....103...104...105...106...107...108...109
110...111...112....113...114...115...116...117...118...119
120...121...122....123...124...125...126...127...128...129
...
990...991...992....993...994...995...996...997...998...999

What happens after 999? We have used all available digits, so let's add another digit (1) to the front and start over:

1000...1001...1002...1003...1004...1005...1006...1007...1008...1009
1010...1011...1012...1013...1014...1015...1016...1017...1018...1019

With this other method, we can count to infinity if we have enough time.

Lower Base

Base 9

But what about base 9? Base 9 means that there are only 9 digits (012345678). How do you count?

0...1...2...3...4...5...6...7...8

What happens after 8? We have used all available digits, so we add another digit (1) to the front and start over:

10...11...12...13...14...15...16...17...18

// we have run out of numbers, so increase from 1 to become 2 and start over!
20...21...22...23...24...25...26...27...28
30...31...32...33...34...35...36...37...38
...
80...81...82...83...84...85...86...87...88

What happens after 88? We have used all available digits, so let's add another digit (1) to the front and start over:

100...101...102....103...104...105...106...107...108
110...111...112....113...114...115...116...117...118
120...121...122....123...124...125...126...127...128
...
880...881...882....883...884...885...886...887...888

What happens after 888? We have used all available digits, so let's add another digit (1) to the front and start over: