1. Calculating in Other Bases
Section 4.3
Calculating in Other Bases

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.

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.

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.

5. Base Ten
Base Two
Base Five
Base Eight
Base Sixteen 1 2 10 3 11 4
100 5
101 6
110 7
111 12 8
1000 13 9
1001 14
1010 20 A
1011 21 B
1100 22 C
1101 23 15 D
1110 24 16 E
1111 30 17 F
10000 31
10001 32 18
10010 33 19
10011 34
10100 40

6. Example 1: 245
List the number before and after the given number, in the given base.

7. Example 2: 2045
List the number before and after the given number, in the given base.

8. Example 3: 678
List the number before and after the given number, in the given base.

9. Example 4: 1916
List the number before and after the given number, in the given base.

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.

11. Example 5: 245
Convert to decimal (base ten) notation.

12. Example 6: 40,3125
Convert to decimal (base ten) notation.

13. Example 7: 7,0368
Convert to decimal (base ten) notation.

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.

15. Example 8: 384
Convert from decimal to base 5 Notation.

16. Example 9: 645
Convert from decimal to base 5 Notation.

17. Example 10: 1838
Convert from decimal to base 6 Notation.

18. Section 4.3 Assignment
Class work:
Worksheet on teacher website

19. Section 4.3 Part II
Adding, Subtracting, Multiplying, and Dividing in Other Bases

20. 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.”

21. Addition Table for Base 5+ 1 2 3 4

22. Example 11: Adding Base 5

23. Example 12: Adding Base 6 + 1 2 3 4 5

24. Example 13: Subtracting Base 5

25. Example 14: Subtracting Base 6

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.

27. Multiplication Table for Base 5X 1 2 3 4

28. Example 15: Multiplying Base 5
345 x 425…..Use Galley Method

29. Example 16: Multiplying Base 5
1345 x 325…..Use Galley Method

30. Example 17: Division in Base 5
41325  235……..1st need to know multiples of 235

31. Example 18: Division in Base 5
21435  325……..1st need to know multiples of 325

32. Binary, Octal, and Hexadecimal Notation
Base Ten
Base Two
Base Eight
Base Sixteen 1 2 10 3 11 4
100 5
101 6
110 7
111 8
1000 9
1001
1010 12 A
1011 13 B
1100 14 C
1101 15 D
1110 16 E
TB pg. 226

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.