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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

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Base 10

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1 3 10

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Base 10 1 3 10

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Base 10Base 7 1 3 10 1 6 7

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Base 10Base 7 1 3 10 1 6 7

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Base 10Base 7 1 3 10 1 6 7 Base 5 2 3 5

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Base 10Base 7 1 3 10 1 6 7 Base 5 2 3 5

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Base 10Base 7 1 3 10 1 6 7 Base 5 2 3 5 Base 3 4 1 3 ?

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Base 10Base 7 1 3 10 1 6 7 Base 5 2 3 5 Base 3 1 1 3 1

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Base 10Base 7 1 3 10 1 6 7 Base 5 2 3 5 Base 3 1 1 3 1

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Base 10Base 7 1 3 10 1 6 7 Base 5 2 3 5 Base 3 1 1 3 1 2 3 5 = _______ 10 1 3 10 = _______ 3

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Imagine a base 4 pebble board It does not matter what pile you look at The same rule always holds. 4 pebbles in this pile equals 4 pebbles in this pile equals 4 pebbles in this pile equals 1 pebble in this pile equals 1 pebble in this pile equals 1 pebble in this pile equals

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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 base 4 2 4 + 1 9

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converting TO the base 10: 1 1 1 2 = _________ 10 base 2 1 2 2 + 1 2 + 1 7

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1 2 3 2 4 = ________ 10 4343 4242 41 ( 1 4 3 ) + ( 2 4 2 ) + ( 3 4 ) + ( 2 1 ) 64 + 32 + 12 + 2 1 1 0 4040 4141

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converting FROM the base ten 3 4 10 = __________ 3 Base 3 3 3232 31 3 3 4 1 1 - 1

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converting FROM the base ten 3 4 10 = __________ 3 Base 3 3 3232 31 3 3 4 1 1 - 1 3 3 - 2

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converting FROM the base ten 3 4 10 = __________ 3 Base 3 3 3232 31 3 3 4 1 1 - 1 3 3 - 2

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converting FROM the base ten 3 4 10 = __________ 3 Base 3 3 3232 31 3 3 4 1 1 - 1 3 3 - 2 3 1 - 0 1 0 2 1