Transcript Convert from decimal to binary

Introduction to
Microcomputers
Computer
numbering
Systems
Prepared by: Hani Al-Mohair
Introduction to Binary Numbers
How Computers Store Numbers
• Computer systems are constructed of digital electronics. That
means that their electronic circuits can exist in only one of two
states: on or off. Most computer electronics use voltage levels
to indicate their present state. For example, a transistor with
five volts would be considered "on", while a transistor with no
voltage would be considered "off." Not all computer hardware
uses voltage, however. CD-ROM's, for example, use
microscopic dark spots on the surface of the disk to indicate
"off," while the ordinary shiny surface is considered "on."
Hard disks use magnetism, while computer memory uses
electric charges stored in tiny capacitors to indicate "on" or
"off."
Cont.
• These patterns of "on" and "off" stored inside the
computer are used to encode numbers using the
binary number system. The binary number system is a
method of storing ordinary numbers such as 42 or
365 as patterns of 1's and 0's. Because of their digital
nature, a computer's electronics can easily manipulate
numbers stored in binary by treating 1 as "on" and 0
as "off." Computers have circuits that can add,
subtract, multiply, divide, and do many other things to
numbers stored in binary.
Converting from Decimal to Binary
• Computer numbering Systems:
• Decimal
• Binary
• Octal
• Hexadecimal.
Binary Truth
Table
• 0 = Off
• 1 = On
Convert from decimal to binary:
(30) =?
(56)= ?
(267)= ?
De
0
1
2
3
4
5
6
7
8
9
8
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
1
1
1
1
0
0
2
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
From Binary to Decimal
• Fill the blanks:
• Computers use binary numbers and human use decimal
numbers.
Convert from Binary to decimal:
(0111)2 = ?
(0001)2=?
(1001)2=?
(1100)2=?
(1110)2=?
From Binary to Hexadecimal
•
•
•
•
•
•
A
B
C
D
E
F
10
11
12
13
14
15
16
17
18
19
1A
1B
1C
1D
1E
1F
20