JSS 2 FIRST TERM WEEK NINE 2023 LESSON NOTE

 

JSS 2

TOPIC: NUMBER BASE

Objective:

At the end of this lesson, you should be able to:

1.       Define number base system

2.       List different number system

3. Perform conversion of numbers from one base to another

Introduction

Number based system is the character representations in computer. Its translator converts instructions passed into the computer to machine-readable language, which is in the form of 0s and 1s. these are called binary digits because it is binary number system (base 2) that has such digits only in its counting system. The word bit is formed from binary digits. In most cases 0 represents OFF and 1 represents ON.

 

Number base System

There are different number systems depending on the one being used at any particular time and place. E.g.

Base 10 is called Decimal Number System.

Base 2 is called Binary Number System.

Base 2 is called Octal Number System.

Base 16 is called Hexadecimal System.

The number system and their digits are expressed below

Bases

Name

Digits

NO. of digits

2

Binary

0,1

2

8

Octal

0,1,2,3,4,5,6,7

8

10

Decimal

0,1,2,3,4,5,6,7,8,9

10

12

Duo-decimal

0,1,2,3,4,5,6,7,8,9,A,B

12

16

Hexadecimal

0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

16

 

Conversion of Numbers from one base to another.

a.      Decimal to others:  to convert from base 10 to any number system, the given number is divided by the base number being converted to until it is no longer divisible. E.g.

8

345

8

43     r     1

8

5       r      3

 

0       r      5

Convert 345 to base 2 and base 8      

2

345

2

172     r     1

2

86       r      0

2

43       r      0

2

21       r      1

2

10       r      1

2

5         r       0

2

2         r       1

2

1         r        0

 

0         r        1

 

 

 

                                                                                             Therefore 34510 = 5318


Therefore 34510  = 1010110012




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