NUMERATION SYSTEMS

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NUMERATION SYSTEMS IN BASES OTHER THAN 10
Pamela Leutwyler
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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
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COUNT THE CAMELS
4
Base 10
5
Base 10
1 3 10
6
Base 10
1 3 10
7
Base 10
Base 7
1 3 10
1 6 7
8
Base 10
Base 7
1 3 10
1 6 7
9
Base 10
Base 7
1 3 10
1 6 7
Base 5
2 3 5
10
Base 10
Base 7
1 3 10
1 6 7
Base 5
2 3 5
11
Base 10
Base 7
1 3 10
1 6 7
Base 3
Base 5
4 1 3
2 3 5
12
Base 10
Base 7
1 3 10
1 6 7
Base 3
Base 5
1 1 3
1
2 3 5
13
Base 10
Base 7
1 3 10
1 6 7
Base 3
Base 5
1 1 3
1
2 3 5
14
Base 10
Base 7
1 3 10
1 6 7
2 3 5 _______10
1 3 10 _______3
Base 3
Base 5
1 1 3
1
2 3 5
15
Imagine a base 4 pebble board
It does not matter what pile you look at The
same rule always holds.
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We think and compute in the base 10. BASE 10 is
the DEFAULT BASE We will learn algorithms
for converting numerals 1.) TO THE BASE 10
FROM ANOTHER BASE 2.) TO ANOTHER BASE FROM THE
BASE 10
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converting TO the base 10
2 1 4 _________10
base 4
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converting TO the base 10
2 1 4 _________10
9
2?4 1
base 4
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converting TO the base 10
1 1 1 2 _________10
7
1?22 1?2 1
base 2
20
43
42
4
1
1 1 0
1 2 3 2 4 ________10
40
41
( 1 ? 43 ) ( 2 ? 42 ) ( 3 ? 4 ) (
2 ? 1 )
64 32
12 2
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converting FROM the base ten
3 4 10 __________3
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converting FROM the base ten
3 4 10 __________3
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converting FROM the base ten
3 4 10 __________3
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converting FROM the base ten
1 0 2 1
3 4 10 __________3
1 - 0
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