Binary Numbers (Base 2) JSS3 Mathematics Lesson Note

TOPIC: BINARY NUMBERS (BASE 2 NUMBERS)

•             Addition in base 2

•             Subtraction in base 2

•             Multiplication & Division in base 2 

 ADDITION IN BASE TWO

We can add binary numbers in the same way as we separate with ordinary base 10 numbers. 

 The identities to remember are:-

0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 10, 1 + 1 + 1 = 11, 1 + 1 + 1 + 1 = 100

Worked Examples

Simplify the following

1.          1110 + 1001 2. 1111 + 1101 + 101

Solutions:

1.          1110

 +    1001

       10111

 2.          1111

  +     1101

           101

            100001

Note: 11 take 1 carry 1 

         10 take 0 carry1

         100 take 0 carry 10

EVALUATION

1.          Simplify the following 101 + 101 +111

2.          10101 + 111

ADDITION IN DECIMALS

In decimals, the binary points are placed underneath each other in the same way as in ordinary decimals.

Example:

1.               1.1011two +   10.1001two  +  10.01

2.               10.001two+   101.111

Solution:

1.               1  .  1011

             10.  1001

              10  .0100 

110.  1000 two

2.             101.111

                   10.001

                   1000.000                                 

SUBTRACTION IN BASE TWO

The identities to remember on subtraction are: 0 – 0 = 0, 1 – 0 = 1, 10 – 1 = 1, 11 – 1 = 10, 100 – 1 = 11

Worked Examples

Simplify the following:-

(a) 1110 – 1001 (b) 101010 – 111

Solutions:

(a) 1110

        –   1001

              101

(b) 101010

         –       111

                1110

SUBTRACTION IN BICIMAL

Example

101.101two – 11.011two

      101.101

        11.011

       10.010two

EVALUATION

1.          10111÷110

2.          10001 x 11

READING ASSIGNMENT

New Gen Maths Book 3, chapter 1 Exercise 1e pg 18 Nos 1-12

Essential Mathematics for J.S.S.3 Pg 8-10

WEEKEND ASSIGNMENT

1.          Express 3426 as a number in base 10. (a) 342     (b) 3420    (c) 134

2.          Change the number 10010 to base 10 (a) 18      (b) 34         (c) 40

3.          Express in base two the square of 11 (a) 1001  (b)  1010    (c)  1011

4.          Find the value of (101)2 in base two        (a) 1010  (b) 1111    (c)  1001

5.          Multiply 1000012 by 11              (a) 1001  (b) 1100011  (c)  10111

THEORY

1.          Calculate 1102 x (10112 + 10012 – 1012)

2.          Convert 110111 to base five