Transcript Chapter 5 sec 3

Calculating in Other Bases
CHAPTER 5 SEC 3
Bases
 The Babylonian had a base of 60.
 The Mayan system used a base of
20.
 The Hindu-Arabic we use today is
in base 10.
 What other bases do we use everyday ?
 Base 2 (the binary)
The
use of computers and cell phone.
The only numbers that are used are
zeros and ones.
Other bases
 Base 2
1,
102, 112, 1002, 1012, 1102, …
 Base 5
1, 2, 3, 4, 105, 115, 125, 135, 145, 205, …
 How about base 7?
 Each number has a place holder, for
example given the number 4859 . The
subscript 9 is the base that we will have to
work in. The 5 is the ones, the 8 is the tens,
and the 4 is in the hundreds.
 What we want to do is to expand,
 4x92 + 8x91 + 5x90
 = 4x81 +72+5 = 324+77 = 401
 What we are going to be trying to do is
to convert a different base into base 10.
 For example, covert 24, 4567 into base-
10.
Hindu-Arabic into a different base.
Write 768 into base 5.
724/5 = 144r4
144/5 = 28 r 4
28/5 = 5 r 3
5/5 = 1 r 0
1/5 = 1
 Now we read the remainders in reverse
order. Therefore our number is
10,3445.
Addition
Base 6 Addition
+
0
1
2
3
4
5
0
0
1
2
3
4
5
1
1
2
3
4
5
106
2
2
3
4
5
106
116
3
3
4
5
106
116
126
4
4
5
106
116
126
136
5
5
106
116
126
136
146
Try these problems
 5536 + 2456
12426
 13256 – 4536
4326
Multiplication
Multiplication base 6
x
0
1
2
3
4
5
0
0
0
0
0
0
0
1
2
0
0
1
2
2
4
3
106
4
126
5
146
3
4
0
0
3
4
106
126
136
206
206
246
236
326
5
0
5
146
236
326
416