Calculating in Other Bases Section 4.3 Slide 2 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. Slide
3 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. Slide 4 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. Slide 5 Base Ten Base Two Base Five Base Eight Base Sixteen
00000 11111 210222 311333 4100444 51011055 61101166 71111277
8100013108 9100114119 1010102012A 1110112113B 1211002214C
1311012315D 1411102416E 1511113017F 1610000312010 1710001322112
1810010332213 1910011342314 2010100402415 Slide 6 Example 1: 24 5
List the number before and after the given number, in the given
base. Slide 7 Example 2: 204 5 List the number before and after the
given number, in the given base. Slide 8 Example 3: 67 8 List the
number before and after the given number, in the given base. Slide
9 Example 4: 19 16 List the number before and after the given
number, in the given base. Slide 10 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.
Slide 11 Example 5: 24 5 Convert to decimal (base ten) notation.
Slide 12 Example 6: 40,312 5 Convert to decimal (base ten)
notation. Slide 13 Example 7: 7,036 8 Convert to decimal (base ten)
notation. Slide 14 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. Slide 15 Example 8: 384 Convert from
decimal to base 5 Notation. Slide 16 Example 9: 645 Convert from
decimal to base 5 Notation. Slide 17 Example 10: 1838 Convert from
decimal to base 6 Notation. Slide 18 Section 4.3 Assignment Class
work: Worksheet on teacher website Slide 19 Section 4.3 Part II
Adding, Subtracting, Multiplying, and Dividing in Other Bases Slide
20 NOTE: If you thoroughly understand the concept of place value in
our Hindu-Arabic numeration system, then you can easily modify the
techniquesto compute in other place value systems. Slide 21
Addition Table for Base 5 +01234 0 1 2 3 4 Slide 22 Example 11:
Adding Base 5 342 5 +223 5 Slide 23 Example 12: Adding Base 6 315 6
+524 6 +012345 0 1 2 3 4 5 Slide 24 Example 13: Subtracting Base 5
424 5 - 143 5 Slide 25 Example 14: Subtracting Base 6 325 6 - 131 6
Slide 26 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. Slide 27 Multiplication Table for Base
5 X01234 0 1 2 3 4 Slide 28 Example 15: Multiplying Base 5 34 5 x
42 5 ..Use Galley Method Slide 29 Example 16: Multiplying Base 5
134 5 x 32 5 ..Use Galley Method Slide 30 Example 17: Division in
Base 5 4132 5 23 5 ..1 st need to know multiples of 23 5 Slide 31
Example 18: Division in Base 5 2143 5 32 5 ..1 st need to know
multiples of 32 5 Slide 32 Binary, Octal, and Hexadecimal Notation
TB pg. 226 Base Ten Base Two Base Eight Base Sixteen 0000 1111
21022 31133 410044 510155 611066 711177 81000108 91001119 10101012A
11101113B 12110014C 13110115D 14111016E Slide 33 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.
