# Lesson Notes By Weeks and Term - Senior Secondary 3

Overview of number bases I

Term: 2nd 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