Digital Logic Design
Download
Report
Transcript Digital Logic Design
Digital Logic & Design
Dr. Waseem Ikram
Lecture 01
Analogue Quantities
Continuous Quantity
Intensity of Light
Temperature
Velocity
Digital Values
Discrete set of values
Continuous Signal
45
40
temperature 0C
35
30
25
20
15
10
5
0
1
2
3
4
5
6
7
8
time
9
10
11
12
13
14
15
Continuous Signal
45
42
40
temperature 0C
35
35
34
41
37
30
29
25
25
20
25
23
22
18
15
10
7
5
1
0
1
4
2
2
3
4
5
6
7
8
time
9
10
11
12
13
14
15
Digital Representation
45
42
40
temperature 0C
35
35
34
41
37
30
29
25
25
20
25
23
22
18
15
10
7
5
1
0
1
4
2
2
3
4
5
6
7
8
9
samples
10
11
12
13
14
15
Under Sampling
45
40
temperature 0C
35
30
25
20
15
10
5
0
1
3
5
7
9
samples
11
13
15
Electronic Processing
Analogue Systems
Digital Systems
Representing quantities in Digital Systems
Representing Digital Values
39 0C ?
8
GND
a4
4
a3
3
0
b4
7
b3
6
b2
a2
2
a1
1
6.25 x 1018 ?
39mV
1mV = 1
Vcc1
0
b1
5
Digital
System
6.25 x 1015 V !!
Digital Systems
Two Voltage Levels
Two States
On/Off
Black/White
Hot/Cold
Stationary/Moving
Binary Number System
Binary Numbers
Representing Multiple Values
Combination of 0v & 5v
Merits of Digital Systems
Efficient Processing & Data Storage
Efficient & Reliable Transmission
Detection and Correction of Errors
Precise & Accurate Reproduction
Easy Design and Implementation
Occupy minimum space
Information Processing
Numbers
Text
Formula and Equations
Drawings and Pictures
Sound and Music
Logic Gates
Building Blocks
AND, OR and NOT Gates
NAND, NOR, XOR and XNOR Gates
Integrated Circuits (ICs)
Logic Gate Symbol and ICs
NAND Gate IC
GND
6
5
4
3
2
7400
1
XNOR Gate
8
9
XOR Gate
10
NOR Gate
11
NAND Gate
12
NOT Gate
13
OR Gate
Vcc
AND Gate
Combinational Circuits
Combination of Logic Gates
Adder Combinational Circuit
Adder Combinational Circuit
Sum
Carry
Functional Devices
Functional Devices
Adders
Comparators
Encoders/Decoders
Multiplexers/Demultiplexers
Sequential Circuits
Memory Element
Current & Previous State
Flip-Flops
Counters & Registers
Block Diagram of a Sequential Circuit
Input
1
2
1
a1
a2
b1
Combinational
Logic Circuit
a1
b2
b1
Memory Element
5
6
5
Output
Programmable Logic Devices (PLDs)
Configurable Hardware
Combinational Circuits
Sequential Circuits
Low chip count
Lower Cost
Short development time
Memory
Storage
RAM (Random Access Memory)
Read-Write
Volatile
ROM (Read-Only Memory)
Read-Only
Non-Volatile
A/D & D/A Converters
Processing of Continuous values
Conversion
Analogue to Digital A/D
Digital to Analogue D/A
Industrial Control Application
Digital Industrial Control
Digital
*/*
x1
u1
A/D
Converter
Controller
Thermocouple
Reaction
Vessel
Heater
Control
*/*
x1
u1
D/A
Converter
Summary
Continuous Signals
Digital Representation in Binary
Information Processing
Logic Gates
Summary
Combinational & Sequential Circuits
Programmable Logic Devices (PLDs)
Memory (RAM & ROM)
A/D & D/A Converters
Number Systems and Codes
Decimal Number System
Caveman Number System
Binary Number System
Hexadecimal Number System
Octal Number System
Decimal Number System
Ten unique numbers 0,1..9
Combination of digits
Positional Number System
275 = 2 x 102 + 7 x 101 + 5 x 100
Base or Radix 10
Weight 1, 10, 100, 1000 ….
Representing Fractions
Fractions can be represented in decimal number
system in a manner
= 3 x 102 + 8 x 101 + 2 x 100 + 9 x 10-1
+ 1 x 10-2
= 300 + 80 + 2 + 0.9 + 0.01
= 382.91
Caveman Number System
∑, ∆, >, Ω and ↑
Base – 5 Number System
∆Ω↑∑ = 220
Caveman Number System
Decimal Number
Caveman Number
Decimal Number
Caveman Number
0
∑
10
>∑
1
∆
11
>∆
2
>
12
>>
3
Ω
13
>Ω
4
↑
14
>↑
5
∆∑
15
Ω∑
6
∆∆
16
Ω∆
7
∆>
17
Ω>
8
∆Ω
18
ΩΩ
9
∆↑
19
Ω↑
Caveman Number System
Mr. Caveman is using a base 5 number system.
Thus the number ∆Ω↑∑ in decimal is
= ∆ x 5 3 + Ω x 5 2 + ↑ x 51 + ∑ x 5 0
= ∆ x 125 + Ω x 25 + ↑ x 5 + ∑ x 1
= (1) x 125 + (3) x 25 + (4) x 5 + (0) x 1
= 125 + 75 + 20 + 0 = 220
Binary Number System
Two unique numbers 0 and 1
Base – 2
A binary digit is a bit
Combination of bits to represent larger values
Binary Number System
Decimal Number
Binary Number
Decimal Number
Binary Number
0
0
10
1010
1
1
11
1011
2
10
12
1100
3
11
13
1101
4
100
14
1110
5
101
15
1111
6
110
16
10000
7
111
17
10001
8
1000
18
10010
9
1001
19
10011
Combination of Binary Bits
Combination of Bits
100112 = 1910
= (1 x 24) + (0 x 23) + (0 x 22) + (1 x 21)
+ (1 x 20)
= (1 x 16) + (0 x 8) + (0 x 4) + (1 x 2)
+ (1 x 1)
= 16 + 0 + 0 + 2 + 1
= 19
Fractions in Binary
Fractions in Binary
1011.1012 = 11.625
= (1 x 23) + (0 x 22) + (1 x 21) + (1 x 20)
+ (1 x 2-1) + (0 x 2-2) + (1 x 2-3)
= (1 x 8) + (0 x 4) + (1 x 2) + (1 x 1)
+ (1 x 1/2) + (0 x 1/4) + (1 x 1/8)
= 8 + 0 + 2 + 1 + 0.5 + 0 + 0.125
= 11.625
Floating Point Notations
Decimal-Binary Conversion
Binary to Decimal Conversion
Sum-of-Weights
Adding weights of non-zero terms
Decimal to Binary Conversion
Sum-of-Weights (in reverse)
Repeated Division by 2
Decimal to binary conversion using
Sum of weight
Number
Weight
Result after subtraction
Binary
392
256
392-256=136
1
136
128
136-128=8
1
8
54
0
8
32
0
8
16
0
8
8
0
4
0
0
2
0
0
1
0
8-8=0
1
Decimal-Binary Conversion
Binary to Decimal Conversion
Sum-of-Weights
Adding weights of non-zero terms
100112
(1 24 ) (0 23 ) (0 22 ) (1 21 )
(1 2 )
0
Terms 16,0,0.2 and 1
19
Decimal-Binary Conversion
Binary to Decimal Conversion
Sum-of-Weights
Adding weights of non-zero terms
Decimal-Binary Conversion
Binary to Decimal Conversion
Sum-of-Weights
Adding weights of non-zero terms
100112 16 2 1 19
1011.1012 8 2 1 1
2
8
11 5
8
11.625
Lecture No. 1
Number Systems
A Summary