Multiplication and Division in Base 2 – JSS3 Mathematics Lesson Note (Third Term)

TOPIC: MULTIPLICATION AND DIVISION IN BASE TWO

In multiplication, 0 x 0 = 0, 1 x 0 = 0, 1 x 1 = 1.

When there is a long multiplication of binary numbers, the principle of addition can be used to derive the answer. Under division, the principle of subtraction can be used.

Worked Examples:

1.         1110 x 111

Solution:

1.         1110

        X       110

                0000

                1110

              1110    

          1010100

2.         Multiply 11.01 by 1.1 in base two

 Solution:

      1101

      x 11

      1101

     1101      

 100.111

DIVISION IN BASE TWO

Example:

Divide 110010101 by 1111

Solution:

1100101012  ÷  11112 = 110112

Example:

Find the square root of 10100012

Solution:

First, convert it to base 10

10100012 = 1 x 2 6+ 0 + 1 x 2 4+ 0 + 0 + 0 + 1 x 20

     = 64 + 16 + 1 = 81 ten

The square root of 81 = 9ten

2 9 1

2 4 0

2 2 0

 2 1 1

    0    = 10012

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