Base system
24
NUMERATION SYSTEMS IN BASES OTHER THAN 10 Pamela Leutwyler
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Transcript of Base system
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
