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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