# Lesson Notes By Weeks and Term - Junior Secondary School 3

MULTIPLICATION AND DIVISION IN BASE TWO

SUBJECT: MATHEMATICS

CLASS:  JSS 3

DATE:

TERM: 1st TERM

REFERENCE BOOKS

• New General Mathematics by M. F Macrae et al bk 3
• Essential Maths by AJS OluwasanmiBk 3

WEEK FOUR

TOPIC: MULTIPLICATION AND DIVISION IN BASE TWO

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

When there is 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

1.   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 = 81ten

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

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