Lesson
Title: Conversion of other bases to base 10.
Objective :
At the end of this lesson, you will be able to convert other bases to base 10.
What you should know :
To fully understand this lesson, you should be familiar with,
- Indices: a3 = a x a x a. 83 = 8 x 8 x 8.
- Basic arithmetic operations.
Introduction:
Conversion of other bases to base 10 is done differently from the previous lesson. It involves the user of indices, multiplication, and addition.
Presentation /Steps:
Given, 1. convert 40358 to base 10. (2) 1011012 to base 10.
The following steps will be used to solve the above problems.
Steps:
- Rank the digits of the number to be converted starting with 0 from right to left.
- For every digit in the number, multiply each of the digits by the number base value raised to the power of the rank value. I.e digit x (number base value)rank value + digit x (number base value)rank value ..., and simplify the expression gotten.
- Therefore, the result is the new number in base 10.
Soln: 40358 to base 10.
=> The number base value is 8.
=> Ranking : 43 02 31 50 , the rank values = 3 2 1 0.
=> digit x (number base value)rank value =
4x83 + 0x82 + 3x81 + 5x80
=> 4x(8x8x8) + 0x(8x8) + 3x8 + 5x1.
=> 4 x 512 + 0 x 64 + 24 + 5.
=> 2045 + 0 + 24 + 5 = 2077.
Therefore, 40358 to base 10 = 207710
Soln 2: 1011012 to base 10
=> The number base value is 2.
=> Ranking : 15 04 13 12 01 10 , the rank values = 5 4 3 2 1 0.
=> 1x25 + 0x24 + 1x23 + 1x22 + 0x21 + 1x20
=> 1x(2x2x2x2x2) + 0x(2x2x2x2) + 1x(2x2x2) + 1x(2x2) + 0x2 + 1x1.
=> 1 x 32 + 0 x 16 + 1 x 8 + 1 x 4 + 0x2 + 1x1.
=> 32 + 0 + 8 + 4 + 0 + 1 = 45.
Therefore, 1011012 to base 10 = 4510
Summary / Conclusion :
- In indices, any number raised to power 0 is 1.
- In multiplication, any number multiplied by 0 is 0.