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.