# Lesson Notes By Weeks and Term - Senior Secondary 3

Overview of number bases II

Term: 2nd Term

Week: 4

Class: Senior Secondary School 3

Age: 17 years

Duration: 40 minutes of 2 periods each

Date:

Subject:      Computer studies and ICT

Topic:-       Overview of Number bases II

SPECIFIC OBJECTIVES:

At the end of the lesson, pupils should be able to

1. List all digits in number bases
2. Convert from one base to another

INSTRUCTIONAL TECHNIQUES: Identification, explanation, questions and answers, demonstration, videos from source

INSTRUCTIONAL MATERIALS: Videos, loud speaker, pictures, Data Processing for senior Secondary Education by Hiit Plc, WAPB Computer Studies for Senior Secondary III by Adekunle et al, On-line Materials.

INSTRUCTIONAL PROCEDURES

PERIOD 1-2

 PRESENTATION TEACHER’S ACTIVITY STUDENT’S ACTIVITY STEP 1 INTRODUCTION The teacher reviews the previous lesson on binary and decimal number bases Students pay attention STEP 2 EXPLANATION He explains the number bases and lists all the digits of the octal and hexadecimal number bases Students pay attention and participates STEP 3 DEMONSTRATION He then performs some calculations on conversion from one base to another Students pay attention and participate STEP 4 NOTE TAKING The teacher writes a summarized note on the board The students copy the note in their books

NOTE

NUMBER BASE SYSTEM

OCTAL NUMBER SYSTEM

The octal number system is a base 8 number system, and uses the digits from 0 to 7.

Programs often display in an octal format because it can be translate relatively in binary format, each digit in the octal number system represents a power of base 8.

For example the binary representation for decimal 74 is 1001010, which group into 1001010, so the octal representation is 112

1128 = 1 x 82 + 1 x 81 + 2 x 80

= (1 x 64) + (1 x 8) + (2 x 1)

= 64 + 8 + 2

= 74.

So, the decimal equivalent of octal number 1128 is 7410. Since there are only 8 digit (0-8) in the octal number system, 3 bits are sufficient to represent an octal number in a binary digits.

 OCTAL BINARY 0 000 1 001 2 101 3 011 4 100 5 101 6 110 7 111

With this table, it is easy to translate octal and binary system for example

658 = 110 1012

178 = 001 1112

HEXADECIMAL NUMBER SYSTEM

In the hexadecimal number system is a number with a base of 16, usually written using symbols 0-9 and A-F.

For example, the decimal number 79 whose binary representation is 01001111 can be written as 4F in hexadecimal ( 4 = 0100, F = 1111 ) for example 1FF16 = 1 x 132 + F x 161 + F x 160

= 1 x 256 + 15 x 16 + 16 x 1

= 511.

Thus, the decimal equivalent of hexadecimal number 1FF16 is 51110. Since there are only 16 digits in the hexadecimal number system, 4 bits are sufficient to represent any hexadecimal number in binary.

The current decimal number system was first introduced to the computing world in 1963 by international business machine (IBM). An early version that used the digit 0-9 and u-2 was introduced in 1956, in the Bendix G-15 computer

The table given below displays the binary and decimal equivalent of some hexadecimal numbers

 HEXADECIMAL BINARY DECIMAL 0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 0101 5 6 0110 6 7 0111 7 8 1000 8 9 1001 9 A 1010 10 B 1011 11 C 1100 12 D 1101 13 E 1110 14 F 1111 15

The hexadecimal number 4B3A translates the following binary number.

4                      B              3                      A

0100                        1011               0011               1010

EVALUATION:    1. Explain the following and list the digits

1. octal number base
2. hexadecimal number base

2a. Convert 418 to a binary number.  b. Convert 108 to a binary number.

3a. Convert A2B16 to an equivalent binary number.

b. Convert E16to an equivalent binary number.

c. Convert 3016to an equivalent binary number.

CLASSWORK: As in evaluation

CONCLUSION: The teacher commends the students positively