numeration systems in bases other than 10 pamela leutwyler
TRANSCRIPT
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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