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Bangladesh Army University of Engineering & Technology (BAUET)

The document discusses common number systems including decimal, binary, octal and hexadecimal. It covers how to convert between these number systems using techniques like dividing by the base and keeping track of remainders.

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wagiga3805
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12 views15 pages

Bangladesh Army University of Engineering & Technology (BAUET)

The document discusses common number systems including decimal, binary, octal and hexadecimal. It covers how to convert between these number systems using techniques like dividing by the base and keeping track of remainders.

Uploaded by

wagiga3805
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1

Bangladesh Army University of


Engineering & Technology (BAUET)
Dept. of CSE
Course Code: CSE- 2101
Course Title: Digital Logic Design
Mirza A.F.M.Rashidul Hasan, D.Engg &
Ph.D
Lecture-1
Fundamentals of Digital
Logic System
Digital electronics is the foundation of modern computers
and digital communications.

Massively complex digital logic circuits with millions of


gates can now be built onto a single integrated circuit (IC)
such as a microprocessor.

These IC circuits can perform millions of operations per


second.
Number System
Common Number Systems
Number Systems
• Each number system is associated with a base or radix
-The decimal number system is said to be of base or radix 10

• A number in base r contains r digits 0,1,2,...,r-1


-Decimal (Base 10): 0,1,2,3,4,5,6,7,8,9

• Numbers are usually expressed in positional notation

– MSD: most significant digit


7
– LSD: least significant digit
Common Number Systems

Used by Used in
System Base Symbols humans? computers?
Decimal 10 0, 1, … 9 Yes No
Binary 2 0, 1 No Yes
Octal 8 0, 1, … 7 No No
Hexa- 16 0, 1, … 9, No No
decimal A, B, … F
Conversion Among Bases

Decimal Octal

Binary Hexadecimal
Decimal Number
Weight

• 12510 => 5 x 100 = 5


2 x 101 = 20
1 x 102 = 100
125
Base
Binary to Decimal
Binary Decimal

Technique
• Multiply each bit by 2n, where n is the “weight” of the bit
• The weight is the position of the bit, starting from 0 on the right
• Add the results
Bit “0”

1010112 => 1 x 20 = 1
1 x 21 = 2
0 x 22 = 0
1 x 23 = 8
0 x 24 = 0
1 x 25 = 32
4310
Decimal to Binary
12510 = ?2 2 125
2 62 1
2 31 0
12510 = 11111012
2 15 1
2 7 1
2 3 1
2 1 1
0 1

Technique
• Divide by two, keep track of the remainder
• First remainder is bit 0 (LSB, least-significant bit)
• Second remainder is bit 1
• Etc.
Decimal to Octal

Decimal Octal

Binary Hexadecimal
Decimal to Octal
• Technique
– Divide by 8
– Keep track of the remainder
Example
123410 = ?8

8 1234
8 154 2
8 19 2
8 2 3
0 2

123410 = 23228

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