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JSS3: MATHEMATICS - 1ST TERM

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  1. Binary Number System I | Week 1
    5Topics
    |
    1 Quiz
  2. Binary Number System II | Week 2
    6Topics
    |
    1 Quiz
  3. Word Problems I | Week 3
    4Topics
    |
    1 Quiz
  4. Word Problems with Fractions II | Week 4
    1Topic
    |
    1 Quiz
  5. Factorisation I | Week 5
    4Topics
    |
    1 Quiz
  6. Factorisation II | Week 6
    3Topics
    |
    1 Quiz
  7. Factorisation III | Week 7
    3Topics
    |
    1 Quiz
  8. Substitution & Change of Subject of Formulae | Week 8
    2Topics
    |
    1 Quiz
  9. Simple Equations Involving Fractions | Week 9
    3Topics
    |
    1 Quiz
  10. Word Problems | Week 10
    1Topic
    |
    1 Quiz
Lesson 2, Topic 1
In Progress

Binary Arithmetic Operations – Addition

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Binary Arithmetic Operations

Basic arithmetic operations of addition, subtraction, multiplication, and division are carried out in their bases similar to base 10.

Addition & Subtraction:

To add in base two note that; 

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 10 (which is 0 carry 1)

Remember that in base 10, 1 + 1 = 2, But 2 in base 2 is 10. therefore, in binary 1 + 1 = 10.

a. Examples Add 111two and 101two

Screen Shot 2021 09 14 at 12.11.28 PM

Answer = 1100two

Alternative Explanation

Screen Shot 2021 09 14 at 1.04.32 PM

1st Column (from right to left) = 1 + 1 = 2. How many twos are there in 2?\( \frac{2}{2} \) = 1 remainder 1 remainder 0. Write 0 and carry 1 to column 2.

2nd Column = 1 + 1 + 0 = 2. How many twos are there in 2?\( \frac{2}{2} \) = 1 remainder 0. Write 0 and carry 1 to column 3.

3rd Column = 1 + 1 + 1 = 3. How many twos are there in 3?\( \frac{3}{2} \) = 1 remainder 1. Write 1 and carry 1 to column 4.

4th column = 1…Write 1.

Answer = 11002

b. Add 1101two + 10001two + 1011two

Screen Shot 2021 09 14 at 1.10.06 PM

Alternative Explanation

1st Column (from right to left) = 1 + 1 + 1 = 3. How many twos are there in 3?\( \frac{3}{2} \) = 1 remainder 1. Write 1 and carry 1 to column 2.

2nd Column = 1 + 0 + 0 + 1 = 2. How many twos are there in 2?\( \frac{2}{2} \) = 1 remainder 0. Write 0 and carry 1 to column 3.

3rd Column = 1 + 1 + 0 + 0 = 2. How many twos are there in 2?\( \frac{2}{2} \) = 1 remainder 0. Write 0 and carry 1 to column 4.

4th Column = 1 + 1 + 0 + 1 = 3. How many twos are there in 3?\( \frac{3}{2} \) = 1 remainder 1. Write 1 and carry 1 to column 5.

5th Column = 1 + 1 = 2. How many twos are there in 2?\( \frac{2}{2} \) = 1 remainder 0. Write 0 and carry 1 to column 6.

6th Column = +1 …. Write 1.

Answer = 1010012

c. 1.1011two  + 10.1001two  + 10.01two

Screen Shot 2021 09 14 at 1.42.19 PM

Alternative Explanation

1st Column (from right to left) = 1 + 1 + 0 = 2. How many twos are there in 2? \( \frac{2}{2} \) = 1 remainder 0. Write 0 and carry 1 to column 2.

2nd Column = 1 + 1 + 0 + 0 = 2. How many twos are there in 2? \( \frac{2}{2} \) = 1 remainder 0. Write 0 and carry 1 to column 3.

3rd Column = 1 + 0 + 0 + 1 = 2. How many twos are there in 2? \( \frac{2}{2} \) = 1 remainder 0. Write 0 and carry 1 to column 4.

4th Column = 1 + 1 + 1 + 0 = 3. How many twos are there in 3? \( \frac{3}{2} \) = 1 remainder 1. Write 1 and carry 1 to column 5.

5th Column = 1 + 1 + 0 + 0 = 2. How many twos are there in 2? \( \frac{2}{2} \) = 1 remainder 0. Write 0 and carry 1 to column 6.

6th Column = 1 +1 + 1 = 3.How many twos are there in 3? \( \frac{3}{2} \) = 1 remainder 1. Write 1 and carry 1 to column 7.

7th column = 1…Write down 1

Answer = 110.10002

d. 1011two + 1101two

Screen Shot 2020 11 27 at 10.16.11 PM

e. 10011two + 1101two + 111two

Screen Shot 2020 11 27 at 10.16.20 PM

Work To Do

1. 10011 + 1101

2. 1011 + 1101 + 101

Answers

1. 100000two

2. 11101two

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