Lesson Notes By Weeks and Term - Senior Secondary 3

Term: 2^nd Term

Week: 3

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 I

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 graphic packages	Students pay attention
STEP 2 EXPLANATION	He explains the number bases and lists all the digits of the binary and decimal number base	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

DECIMAL NUMBER SYSTEM

The decimal number system (base10) number system has ten as it base. It uses various symbols called digit for ten distinct value (0,1,3,4,5,6,7,8 and 9) to represent numbers. It requires 10 different types of electronic pulse.

 

The decimal system is a position number system. It has position for unit, tens, hundred e.t.c The position of each digit conveys the multiplier( a power of ten) to be used with the digit- each position has value to ten time of a position to its right.

 

For example:

275 = 2×100 + 7×10 + 5×1

2x 10² + 7 + 10¹ + 5 x 10⁰

 

BINARY NUMBER

The binary number (base 2) number system represents values using symbols typically 0 and 1. In other words, the binary number system is a position number system with a power of two (2).

 

Owing to its relatively straightforward implementation in electronic circuitry, the binary is used internally by virtually in all modern computers.

 

The numerals 0 and 1 have the same meaning in the decimal system, but a different interpretation is placed on the position occupied by a digit.

In the binary number system, the  individual digit represent the coefficient of power 2 rather than 10 as in the decimal number system.

 

For example, the decimal number system 19 is written in the binary representation as 10011

1⁴0³0²1¹1⁰₂ = 1 x 2⁴ +0 x 2³ + 0 x 2² + 1 x 2¹ + 1 x 2⁰

= 16 + 0 + 0 + 2 + 1.

 

Let’s look at base-two, or binary, numbers. How would you write, for instance, 12₁₀ (“twelve, base ten”) as a binary number?

 

You would have to convert to base-two columns, the analogue of base-ten columns. In base ten, you have columns or “places” for 10⁰ = 1, 10¹ = 10, 10² = 100, 10³ = 1000, and so forth.

 

Similarly in base two, you have columns or “places” for 2⁰ = 1, 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, and so forth.

 

The first column in base-two math is the units column. But only “0” or “1” can go in the units column. When you get to “two”, you find that there is no single solitary digit that stands for “two” in base-two math. Instead, you put a “1” in the twos column and a “0” in the units column, indicating “1 two and 0 ones”. The base-ten “two” (2₁₀) is written in binary as 10₂.

A “three” in base two is actually “1 two and 1 one”, so it is written as 11₂. “Four” is actually two-times-two, so we zero out the twos column and the units column, and put a “1” in the fours column; 4₁₀ is written in binary form as 100₂. Here is a listing of the first few numbers:

 

decimal (base 10)	binary (base 2)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16	0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 10000	0 ones 1 one 1 two and zero ones 1 two and 1 one 1 four, 0 twos, and 0 ones 1 four, 0 twos, and 1 one 1 four, 1 two, and 0 ones 1 four, 1 two, and 1 one 1 eight, 0 fours, 0 twos, and 0 ones 1 eight, 0 fours, 0 twos, and 1 one 1 eight, 0 fours, 1 two, and 0 ones 1 eight, 0 fours, 1 two, and 1 one 1 eight, 1 four, 0 twos, and 0 ones 1 eight, 1 four, 0 twos, and 1 one 1 eight, 1 four, 1 two, and 0 ones 1 eight, 1 four, 1 two, and 1 one 1 sixteen, 0 eights, 0 fours, 0 twos, and 0 ones

 

CONVERSION BETWEEN BINARY AND DECIMAL NUMBERS

Converting between binary and decimal numbers is fairly simple, as long as you remember that each digit in the binary number represents a power of two.

 

EXAMPLE 1

Convert 101100101₂ to the corresponding base-ten number.

 

I will list the digits in order, and count them off from the RIGHT, starting with zero:

 

digits:	1  0   1  1  0  0  1  0  1
numbering:	8  7   6  5  4  3  2  1  0

 

The first row above (labelled “digits”) contains the digits from the binary number; the second row (labelled ” numbering”) contains the power of 2 (the base) corresponding to each digits. I will use this listing to convert each digit to the power of two that it represents:

 

1×2⁸ + 0×2⁷ + 1×2⁶ + 1×2⁵ + 0×2⁴ + 0×2³ + 1×2² + 0×2¹ + 1×2⁰

= 1×256 + 0×128 + 1×64 + 1×32 + 0×16 + 0×8 + 1×4 + 0×2 + 1×1

= 256 + 64 + 32 + 4 + 1

= 357

 

DECIMAL	BINARY
0	0000
1	0001
2	0010
3	0011
4	0100
5	0101
6	0110
7	0111
8	1000
9	1001
10	1010
11	1011
12	1100
13	1101
14	1110
15	1111
100	0100100
512	1000000000

 

 

 

EVALUATION:    1. Explain the following and list the digits

1. binary numbers
2. decimal numbers

2. convert these binary numbers to decimal numbers

1. 101010   b. 11101              c. 1000110

3. Convert these decimal numbers to binary numbers

1. 28   b. 32           c. 67

CLASSWORK: As in evaluation

CONCLUSION: The teacher commends the students positively