Digital System Design. Lecture 1 – Digital Systems and Information. Md. Saiful Islam Lecturer, Institute of Information Technology University of Dhaka. 2009 IIT, DU. Overview. Digital Systems and Computers Organization of a Digital Computer Information Representation Number Systems
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Lecture 1 – Digital Systems and Information
Md. Saiful Islam
Lecturer, Institute of Information Technology
University of Dhaka
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
Discrete
Information
Inputs
Discrete
Processing
Outputs
System
System State
Digital Systems (3)Takes a set of discrete information inputs and discrete internal information (system state) and generates a set of discrete information outputs.
2009 IIT, DU
Digital computers replaced analog computers:
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
Time
Continuous in value & time
Analog
Digital
Discrete in value & continuous in time
Asynchronous
Discrete in value & time
Synchronous
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2009 IIT, DU
Magnetic Field Direction
Surface Pits/Light
Electrical Charge
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j = Presentation 1
i = n  1
å
å
+
i
j
(Number)r
=
A
r
A
r
i
j
i = 0
j =  m
(Integer Portion)
(Fraction Portion)
+
Number Systems – Representation(
)
(
)
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2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
Carries 00
Augend 01100 10110
Addend +10001+10111
Sum
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Z Presentation
Z
0
1
0
1
1
0
1
0
X
X
0
0
0
0
1
1
1
1
BS
BS
11
0 0
1 1
1 0
0 1
0 0
0 0
1 1
 Y
 Y
0
0
1
1
0
0
1
1
Single Bit Binary Subtraction with Borrow 2009 IIT, DU
Borrows00
Minuend 10110 10110
Subtrahend 10010 10011
Difference
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2009 IIT, DU
Note that there is no negative zero in two’s complement format.
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
Binary Number Presentation
000
001
010
011
101
110
111
Nonnumeric Binary CodesColor
Red
Orange
Yellow
Green
Blue
Indigo
Violet
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2009 IIT, DU
2009 IIT, DU
There are over 8,000 ways that you can chose 10 elements from the 16 binary numbers of 4 bits. A few are useful:
Decimal
8,4,2,1
Excess3
8,4,

2,

1
Gray
0
0000
0011
0000
0000
1
0001
0100
0111
0100
2
0010
0101
0110
0101
3
0011
0110
0101
0111
4
0100
0111
0100
0110
5
0101
1000
1011
0010
6
0110
1001
1010
0011
7
0111
1010
1001
0001
8
1000
1011
1000
1001
9
1001
1
100
1111
1000
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU
Given a BCD code, we use binary arithmetic to add the digits:
8
1000
Eight
+5
+0101
Plus 5
13
1101
is 13 (> 9)
Note that the result is MORE THAN 9, so must be represented by two digits!
To correct the digit, subtract 10 by adding 6 modulo 16.
8
1000
Eight
+5
+0101
Plus 5
13
1101
is 13 (> 9)
+0110
so add 6
carry = 1
0011
leaving 3 + cy
0001  0011
Final answer (two digits)
If the digit sum is > 9, add one to the next significant digit
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0
0001 1000 1001 0111
+ 0010100100000101
2009 IIT, DU
Chapter 1 41
2009 IIT, DU
2009 IIT, DU
Even Parity
Odd Parity
Message
Parity
Parity
Message


000
000


001
001


010
010


011
011


100
100


101
101


110
110


111
111


2009 IIT, DU
Decimal
8,4,2,1
Gray
0
0000
0000
1
0001
0100
2
0010
0101
3
0011
0111
4
0100
0110
5
0101
0010
6
0110
0011
7
0111
0001
8
1000
1001
9
1001
1000
2009 IIT, DU
2009 IIT, DU
2009 IIT, DU