Transcript Document

NUMERATION SYSTEMS
IN 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
1
Base 7
3
10
1
6
7
Base 10
1
Base 7
3
10
1
6
7
Base 10
Base 7
1
3
10
2
3
5
Base 5
1
6
7
Base 10
Base 7
1
3
10
2
3
5
Base 5
1
6
7
Base 10
1
Base 7
3
10
1
6
7
Base 3
Base 5
2
3
5
4
1
3
Base 10
1
Base 7
3
1
10
6
7
Base 3
Base 5
2
3
5
1
1
1
3
Base 10
1
Base 7
3
1
10
6
7
Base 3
Base 5
2
3
5
1
1
1
3
Base 10
1
Base 7
3
1
10
235 =
6
7
_______10
1 3 10 = _______3
Base 3
Base 5
2
3
5
1
1
1
3
Imagine a base 4 pebble board
It does not matter what pile you look at –
The same rule always holds.
11 pebble
pebbles
in
pebble in
in 444pebbles
pebblesin
in
1this
pebble
in
pile
equals
this
this
pile
equals
this
pile
thispile
pileequals
equals
this pile equals
equals
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
converting TO the base 10:
2 1 4 = _________10
base 4
converting TO the base 10:
2 1 4 = _________
9
10
24
+
base 4
1
converting TO the base 10:
1 1 1 2 = _________
7
10
122
+
12
base 2
+
1
43
42 4
1
1 1 0 10
1 2 3 2 4 = ________
41
40
( 1  43 ) + ( 2  42 ) + ( 3  4 ) + ( 2  1 )
64
+
32
+
12
+
2
converting FROM the base ten
3 4 10 = __________3
33
32
11 - 1
3 34
Base 3
3
1
converting FROM the base ten
3 4 10 = __________3
33
32
3 - 2
3 11 - 1
3 34
Base 3
3
1
converting FROM the base ten
3 4 10 = __________3
33
32
3 - 2
3 11 - 1
3 34
Base 3
3
1
converting FROM the base ten
1021 3
3 4 10 = __________
33
32
1 - 0
3
3 - 2
3 11 - 1
3 34
Base 3
3
1