1. 4.3
Other Bases

2. Bases
Any counting number greater than 1 may be used as a base for a positional-value numeration system.
If a positional-value system has a base b,
then its positional values will be
… b4, b3, b2, b, 1.
Hindu-Arabic system uses base 10.

3. Example: Converting from Base 8 to Base 10
Convert to base 10.
Solution:

4. Example: Converting from Base 5 to Base 10
Convert 425 to base 10.
Solution:

5. P. 190 # 8

6. Example: Convert to Base 3
Solution:
The place values in the base 3 system are
…, 36, 35, 34, 33, 32, 3, 1 or
…, 729, 243, 81, 27, 9, 3, 1.
The highest power of the base that is less than or equal to 342 is 243.

7. Example: Convert to Base 3 continued
Successive division by the powers of the base gives the following result.

8. Example: Convert to Base 3 continued
The remainder, 0, is less than the base, 3, so further division is necessary.

9. p. 190 # 30

10. Homework
P. 190 # 5 – 55 eoo
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