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SS1: MATHEMATICS - 1ST TERM

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  1. Number Base System I | Week 1
    6Topics
    |
    2 Quizzes
  2. Number Base System II | Week 2
    3Topics
    |
    1 Quiz
  3. Number Base System III | Week 3
    2Topics
    |
    1 Quiz
  4. Modular Arithmetic I | Week 4
    2Topics
  5. Modular Arithmetic II | Week 5
    2Topics
  6. Modular Arithmetic III | Week 6
    3Topics
    |
    1 Quiz
  7. Indices I | Week 7
    2Topics
  8. Indices II | Week 8
    1Topic
    |
    1 Quiz
  9. Logarithms I | Week 9
    3Topics
  10. Logarithms II
    1Topic
    |
    1 Quiz
Lesson Progress
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Example 1

Evaluate the following:

1. 111100two + 10111two + 10011two

2. 110.011two + 10.111two + 1.01two 

3. 13047 + 467 + 1304

4. 5D6C16 + 6ABF16 + 3D216

Solution (1)

bin e1601800399682

Explanation

1st Column (from right to left) = 0 + 1 + 1 = 2. How many twos are there in 2? The answer is 1 remainder 0. Write 0 and carry 1 to column 2.

2nd Column = 1 + 0 + 1 + 1 = 3. How many twos are there in 3? The answer is 1 remainder 1. Write 1 and carry 1 to column 3.

3rd Column = 1 + 1 + 1 + 0 = 3. How many twos are there in 3? The answer is 1 remainder 1. Write 1 and carry 1 to column 4.

4th Column = 1 + 1 + 0 + 0 = 2. How many twos are there in 2? The answer is 1 remainder 0. Write 0 and carry 1 to column 5.

5th Column = 1 + 1 + 1 + 1 = 4. How many twos are there in 4? The answer is 2 remainder 0. Write 0 and carry 2 to column 6.

6th Column = 2 + 1 = 3. How many twos are there in 3? The answer is 1 remainder 1. Write 1 and carry 1 to the next column.

This yields 1100110two

Solution (2)

Screen Shot 2020 10 02 at 10.08.40 AM

Explanation

1st Column (from right to left) = 0 + 1 + 1 = 2. How many twos are there in 2? The answer is 1 remainder 0. Write 0 and carry 1 to column 2.

2nd Column = 1 + 1 + 1 + 1 = 4. How many twos are there in 4? The answer is 2 remainder 0. Write 0 and carry 2 to column 3.

3rd Column = 2 + 0 + 1 + 0 = 3. How many twos are there in 3? The answer is 1 remainder 1. Write 1 and carry 1 to column 4.

4th Column = 1 + 0 + 0 + 1 = 2. How many twos are there in 2? The answer is 1 remainder 0. Write 0 and carry 1 to column 5.

5th Column = 1 + 1 + 1 = 3. How many twos are there in 3? The answer is 1 remainder 1. Write 0 and carry 1 to column 6.

6th Column = 1 + 1 = 2. How many twos are there in 2? The answer is 1 remainder 0. Write 0 and carry 1 to column 7.

This yields 1010.110two

Solution (3)

addition base e1601651883536

Explanation

1st Column (from right to left) = 4 + 6 + 6 = 16. How many sevens are there in 16? The answer is 2 remainder 2. Write 2 and carry 2 to column 2.

2nd Column = 2 + 0 + 4 + 2 = 8. How many sevens are there in 8? The answer is 1 remainder 1. Write 1 and carry 1 to column 3.

3rd Column = 1 + 3 + 4 = 8. How many sevens are there in 8? The answer is 1 remainder 1. Write 1 and carry 1 to column 4.

4th Column = 1 + 1 + 1 = 3. How many sevens are there in 3? The answer is 3 is not up to 7. Finally, Write 3.

This yields 3112

Solution (4) | Hex Addition

Binary Addition 2 e1601653032527

Explanation

Hex addition follows the same rules as decimal addition with the only difference being the added numerals A, B, C, D, E, and F. It may be convenient to have the decimal equivalent values of A through F handy when performing hex operations if the values have not yet been committed to memory. Below is an example of hex addition. Work through the example, and refer to the text below it for further details.

Remember A = 10, B = 11, C= 12, D = 13, E = 14, F = 15

1st Column (from right to left) = C + F + 2 = 13 + 15 + 2 = 29. How many sixteens are there in 29? The answer is 1 remainder 13. But D = 13, so write D and carry 1 to column 2.

2nd Column = 1 + 6 + B + D = 1 + 6 + 11 + 13 = 31. How many sixteens are there in 31? The answer is 1 remainder 15. But F = 15, so write F and carry 1 to column 3.

3rd Column = 1 + D + A + 3 = 1 + 13 + 10 + 3 = 27. How many sixteens are there in 27? The answer is 1 remainder 11. But B = 11, so write B and carry 1 to column 4.

4th Column = 1 + 5 + 6 = 12. 12 is not up to 16. So write 12 in this column which is also C.

This yields CBFD16

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