NUMERATION SYSTEMSIN BASES OTHER THAN 10

Pamela Leutwyler

Remember – a numeration system

is a system

for NAMING numbers.

As you change from one system to another

the number does not change

only its name changes

COUNT THE CAMELS

Base 10

Base 10

1 3 10

Base 10

1 3 10

Base 10 Base 7

1 3 10 1 6 7

Base 10 Base 7

1 3 10 1 6 7

Base 10 Base 7

1 3 10 1 6 7

Base 5

2 3 5

Base 10 Base 7

1 3 10 1 6 7

Base 5

2 3 5

Base 10 Base 7

1 3 10 1 6 7

Base 5

2 3 5

Base 3

4 1 3

?

Base 10 Base 7

1 3 10 1 6 7

Base 5

2 3 5

Base 3

1 1 31

Base 10 Base 7

1 3 10 1 6 7

Base 5

2 3 5

Base 3

1 1 31

Base 10 Base 7

1 3 10 1 6 7

Base 5

2 3 5

Base 3

1 1 31

2 3 5 = _______10

1 3 10 = _______3

Imagine a base 4 pebble board

It does not matter what pile you look at –The same rule always holds.

4 pebbles inthis pile equals4 pebbles inthis pile equals

4 pebbles inthis pile equals

1 pebble inthis pile equals1 pebble inthis pile equals

1 pebble inthis pile equals

We think and compute in the base 10.

BASE 10 is the DEFAULT BASE

We will learn algorithms forconverting numerals:

1.) TO THE BASE 10 FROM ANOTHER BASE

2.) TO ANOTHER BASE FROM THE BASE 10

converting TO the base 10:

2 1 4 = _________10

base 4

converting TO the base 10:

2 1 4 = _________10

base 4

24 + 1

9

converting TO the base 10:

1 1 1 2 = _________10

base 2

122 + 12 + 1

7

1 2 3 2 4 = ________10

43 42 4 1

( 1 43 ) + ( 2 42 ) + ( 3 4 ) + ( 2 1 )

64 + 32 + 12 + 2

1 1 0

4041

converting FROM the base ten

3 4 10 = __________3

Base 3

33 32 3 1

3 3 4

1 1 - 1

converting FROM the base ten

3 4 10 = __________3

Base 3

33 32 3 1

3 3 4

1 1 - 13

3 - 2

converting FROM the base ten

3 4 10 = __________3

Base 3

33 32 3 1

3 3 4

1 1 - 13

3 - 2

converting FROM the base ten

3 4 10 = __________3

Base 3

33 32 3 1

3 3 4

1 1 - 13

3 - 23

1 - 0

1 0 2 1