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Number System Conversion

The document outlines four primary numbering systems used in digital electronics: Decimal, Binary, Octal, and Hexadecimal. It provides examples of conversions between these systems, illustrating how to convert numbers from one system to another, including step-by-step solutions. Additionally, it emphasizes the ease of converting between binary and hexadecimal systems due to their structural similarities.

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24 views13 pages

Number System Conversion

The document outlines four primary numbering systems used in digital electronics: Decimal, Binary, Octal, and Hexadecimal. It provides examples of conversions between these systems, illustrating how to convert numbers from one system to another, including step-by-step solutions. Additionally, it emphasizes the ease of converting between binary and hexadecimal systems due to their structural similarities.

Uploaded by

teddy.re
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Conversions Between Numbering systems

1
Number Systems

There are four systems of arithmetic which


are often used in digital electronics.

Decimal Number System


Binary Number System
Octal Number System
Hexa Decimal System
Decimal System
In the decimal system there are 10 digits:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
EX: 230

And thus the base is 10.


Binary System
Computers use binary system, binary system
uses 2 digits:

0, 1

And thus the base is 2.


Hexadecimal System
Hexadecimal System uses 16 digital
values:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
And thus the base is 16.
Note:
Hexadecimal numbers are compact and
easy to read.
It is very easy to convert numbers from
binary system to Hexadecimal system and
vice-versa, every 4 bits
Octal Number System

Also known as the Base 8 System


Uses digits 0 - 7
Readily converts to binary
Groups of three (binary) digits can be used to
represent each octal digit
(0010)2 = (2)16 =(2)10 (B)16 = (1011)2
REFERENCE TABLE
Example 1
Convert the decimal number (12)10 into binary number.
Solution:

1- Generate Series 16 8 4 2 1
x x x x x
2- Convert to binary
0 1 1 0 0

3- Sum 0 + 8 + 4 + 0 + 0 = 12

12 10 = (01100)2 = (1100)2

https://www.youtube.com/watch?v=rsxT4FfRBaM
Example 2
Convert the binary number 1010102 into decimal number.
Solution:

1-Binary Number 1 0 1 0 1 0

2-Generate Series 32 16 8 4 2 1

3- Sum 32 + 0 + 8 +0 + 2 + 0 = 42

(101010)2 = 42 10

https://www.youtube.com/watch?v=VLflTjd3lWA
Least significant bit
Example 3
Convert a binary number 101101012 into a
Hexadecimal number. Extract from Reference Table

101101012 = B516

https://www.youtube.com/watch?v=tSLKOKGQq0Y
Example 4
Convert a Hexadecimal number (2F)16 Extract from Reference Table
to binary number:

1-Hex Digits 2 F

2-Convert to Decimal 2 15

3-Convert to Binary 8 4 2 1 8 4 2 1

0010 1111

(2F)16 = (00101111)2

https://www.youtube.com/watch?v=D_YC6DSPpQE
Example 5
Convert the decimal number (28)10 into Hexadecimal number.
Solution:
Convert Decimal à Binary then convert Binary à Hexa
Extract from Reference Table
Step1: Generate series 32 16 8 4 2 1

Step 2: Convert to binary 0 1 1 1 0 0


8 4 2 1 8 4 2 1

Step 3: Group bits in four 0001 1100


Step 4: Convert 0+0+0+1 8+4+0+0

Step 5: Hex digits 1 C


28 10 = (1C)16
Example 6
Convert Hexadecimal number 4F16 to its decimal equivalent:
Extract from Reference Table
Solution:
Convert Hexa à Binary then convert Binary à decimal

4 F
1-Convert each digit to
decimal 4 15
8 4 2 1
8 4 2 1

2-Convert each group to 0100 1111


binary
128 64 32 16 8 4 2 1

3-Generate series 0100 1111

4-Sum 0+64+0+0+8+4+2+1

79
(4F)16 = (79)10

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