Transcript Section 4.3

Section 4.3
Calculating in Other Bases
Objectives
 Change numerals in bases other than ten to base
ten.
 Change base ten numerals to numerals in other
bases.
 Add and Subtract in bases other than ten.
 Multiply and Divide in bases other than ten.
Key Terms
 Digital – a word used in computer technology
and refers to a method of encoding numbers,
letters, visual images, and sounds using a base
two system.
 Binary – base two system.
 Octal System – base eight.
 Hexadecimal System – base sixteen.
Background
 As you have seen, so far, most numeral systems are
based on powers of ten, except for the Babylonian and
Mayan system.
 Babylonian system based on powers of 60.
 Mayan system based on powers of 20.
 Other societies around the world, including ours, use
bases 2, 3, 4, 5, or 8.
 Computers, DVD players, and cell phones use bases 2, 8,
and 16.
Base
Ten
Base
Two
Base
Five
Base
Eight
Base
Sixteen
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0
1
10
11
100
101
110
111
1000
1001
1010
1011
1100
1101
1110
1111
10000
0
1
2
3
4
10
11
12
13
14
20
21
22
23
24
30
31
0
1
2
3
4
5
6
7
10
11
12
13
14
15
16
17
20
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
10
17
18
19
20
10001
10010
10011
10100
32
33
34
40
21
22
23
24
12
13
14
15
Example 1: 245
 List the number before and after the given
number, in the given base.
Example 2: 2045
 List the number before and after the given
number, in the given base.
Example 3: 678
 List the number before and after the given
number, in the given base.
Example 4: 1916
 List the number before and after the given
number, in the given base.
Section 4.3 Assignment
 Class work:
 TB pg. 228/1 – 10
 Remember you must write the problem and show ALL work,
when necessary, to receive credit for the assignment.
Example 5: 245
 Convert to decimal (base ten) notation.
Example 6: 40,3125
 Convert to decimal (base ten) notation.
Example 7: 7,0368
 Convert to decimal (base ten) notation.
Section 4.3 Assignment
 Class work:
 TB pg. 228/12 – 22
 Remember you must write problems and show ALL work to
receive credit for the assignment.
Example 8: 384
 Convert from decimal to base 5 Notation.
Example 9: 645
 Convert from decimal to base 5 Notation.
Example 10: 1838
 Convert from decimal to base 6 Notation.
Section 4.3 Assignment
 Class work:
 Worksheet on teacher website
Section 4.3 Part II
Adding, Subtracting, Multiplying, and
Dividing in Other Bases
NOTE:
 “If you thoroughly understand the concept of
place value in our Hindu-Arabic numeration
system, then you can easily modify the
techniques…to compute in other place value
systems.”
Addition Table for Base 5
+
0
1
2
3
4
0
1
2
3
4
Example 11: Adding Base 5
 3425 +2235
Example 12: Adding Base 6
 3156 +5246
+
0
1
2
3
4
5
0
1
2
3
4
5
Example 13: Subtracting Base 5
 4245 - 1435
Example 14: Subtracting Base 6
 3256 - 1316
Section 4.3 Assignment II
 Class work:
 TB pg. 229/44 – 56 Even
 Remember you must write problems and show ALL work to
receive credit for this assignment.
Multiplication Table for Base 5
X
0
1
2
3
4
0
1
2
3
4
Example 15: Multiplying Base 5
 345 x 425…..Use Galley Method
Example 16: Multiplying Base 5
 1345 x 325…..Use Galley Method
Example 17:
Division in Base 5
 41325  235……..1st need to know multiples of 235
Example 18:
Division in Base 5
 21435  325……..1st need to know multiples of 325
Binary, Octal, and Hexadecimal Notation
 TB pg. 226
Base
Ten
Base
Two
Base
Eight
Base
Sixteen
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
0
1
10
11
100
101
110
111
1000
1001
1010
1011
1100
1101
1110
0
1
2
3
4
5
6
7
10
11
12
13
14
15
16
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
Section 4.3 Assignment II
 Class work:
 Worksheet Online
 Multiplying and Dividing in other Bases
 Remember you must show ALL work to receive credit for the
assignment.