w9 sfe3013 digital sv
TRANSCRIPT
-
7/28/2019 w9 Sfe3013 Digital Sv
1/37
SFE3013BASIC ELECTRONICS
-
7/28/2019 w9 Sfe3013 Digital Sv
2/37
- DIGITAL ELECTRONICS NUMERATION SYSTEMS
(Numbers and Coding Systems)
-
7/28/2019 w9 Sfe3013 Digital Sv
3/37
DIGITAL ELECTRONICS
CHAPTER OUTLINE
1. Analog and Digital Signals
3. Logic Gates
4. Combining Logic gates
2. Numbers and Coding Systems
5. Simplifying Logic gates
6. Flip-Flops
-
7/28/2019 w9 Sfe3013 Digital Sv
4/37
1. Differentiate between analog and digital
signals.
2. Convert numbers between the numbersystems.
-
7/28/2019 w9 Sfe3013 Digital Sv
5/37
Numerical Presentation
The quantities that are to be measured,monitored, recorded, processed and
controlled are analog and digital,
depending on the type of system used.
There are basically two ways of
representing the numerical value ofquantities: analog and digital.
-
7/28/2019 w9 Sfe3013 Digital Sv
6/37
Digital circuits are electric circuits based on anumber ofdiscrete voltage levels.
Digital circuits are the most common physical
representation ofBoolean algebra and are thebasis of all digital computers.
To most engineers, the terms "digital circuit","digital system" and "logic" are interchange-able in the context of digital circuits.
1. Analog and Digital Signals
-
7/28/2019 w9 Sfe3013 Digital Sv
7/37
Most digital circuits use two voltagelevels labeled "Low"(0) and "High"(1).
Computers, electronic clocks, andprogrammable logic controllers (used
to control industrial processes) are
constructed of digital circuits.
-
7/28/2019 w9 Sfe3013 Digital Sv
8/37
Advantages
signals represented digitally can be transmittedwithout degradation due to noise.
For example, a continuous audio signal,
transmitted as a sequence of 1s and 0s, can bereconstructed without error provided the noisepicked up in transmission is not enough toprevent identification of the 1s and 0s.
An hour of music can be stored on a compactdisc as about 6 billion binary digits.
-
7/28/2019 w9 Sfe3013 Digital Sv
9/37
-
7/28/2019 w9 Sfe3013 Digital Sv
10/37
In an analog system, additional resolution
requires fundamental improvements in thelinearity and noise characteristics of eachstep of the signal chain.
In an analog system, noise from aging andwear degrade the information stored.
In a digital system, as long as the total noiseis below a certain level, the information canbe recovered perfectly.
-
7/28/2019 w9 Sfe3013 Digital Sv
11/37
ANALOG vs DIGITAL
In analog representation a quantity isrepresented by a voltage, current, ormeter movement that is proportional tothe value of that quantity
--> CONTINUOS VALUE
In digital representation the quantitiesare represented not by proportionalquantities but by symbols called digits.--> 0 or 1 --> DISCRETE VALUE
-
7/28/2019 w9 Sfe3013 Digital Sv
12/37
ANALOG DIGITAL
-
7/28/2019 w9 Sfe3013 Digital Sv
13/37
In digital circuits, a logic level is one of a finite
number of states that a signal can have.
Logic levels are usually represented by the
voltage difference between the signal and
ground.
The range of voltage levels that represents eachstate depends on the logic family being used.
The two levels are logical high and logical low,
which generally correspond to a binary 1 and 0respectively.
-
7/28/2019 w9 Sfe3013 Digital Sv
14/37
Technology L voltage H voltage Notes
CMOS 0V to VCC/2 VCC/2 to VCCVCC = supply
voltage
TTL 0V to 0.8V 2V to VCC VCC = 5V 10%
ECL VEE to 1.4V 1.2V to 0V
VEE is about
5.2V;VCC=Ground
Examples of binary logic levels:
-
7/28/2019 w9 Sfe3013 Digital Sv
15/37
2. NUMBERS and CODING SYSTEMS
A number system is a code that uses
symbols to refer to a number of items.
Decimal, binary, hexadecimal (HEX),
octal, binary coded decimal (BCD),
Gray code, ASCII code.
-
7/28/2019 w9 Sfe3013 Digital Sv
16/37
2. NUMBERS and CODING SYSTEMS
TheDecimal system is a base-ten system0,1,2,3,4,5,6,7,8,9.
The binary system is a base-two system.0 and 1
The octal system is a base-eight system.0,1,2,3,4,5,6,7.
-
7/28/2019 w9 Sfe3013 Digital Sv
17/37
The Hexadecimal system is a base-sixteensystem. 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F.
The position of a digit indicates its weight, or valuewithin the number.
The weights are based on powers of .. 10 in a decimal number (10 )
2 in a binary number (2 )
8 in a octal number (8 ) 16 in a Hex number (16 )
Where n is a digit position. n = -2, -1, 0, 1, 2,
..
n
n
n
n
-
7/28/2019 w9 Sfe3013 Digital Sv
18/37
Decimal System Weight
-
7/28/2019 w9 Sfe3013 Digital Sv
19/37
Binary System weight
The position of each digit (bit) in a
binary number can be assigned a
weight
1 0 1 1 1 0 1.
22 21 20 2-1 2-2 2-3
-
7/28/2019 w9 Sfe3013 Digital Sv
20/37
OCTAL and HEX
-
7/28/2019 w9 Sfe3013 Digital Sv
21/37
Octal Binary
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111
Binary is also easily converted to the octal
numeral system, since octal uses a radix of 8
-
7/28/2019 w9 Sfe3013 Digital Sv
22/37
Example: Converting from
(a) octal to binary
658 = 110 101217
8= 001 111
2
(b) binary to octal:
1011002 = 101 1002 grouped = 54810011
2= 010 011
2grouped with padding = 23
8
(c) octal to decimal:
658 = (6 81) + (5 80) = (6 8) + (5 1) = 5310
1278
= (1 82) + (2 81) + (7 80) = (1 64) + (2
8) + (7 1) = 8710
-
7/28/2019 w9 Sfe3013 Digital Sv
23/37
decimal to binary conversion
A systematic method of converting whole numbers fromdecimal to binary is the repeated division-by-2 process.
-
7/28/2019 w9 Sfe3013 Digital Sv
24/37
BINARY TO DECIMAL CONVERSION
-
7/28/2019 w9 Sfe3013 Digital Sv
25/37
Conversion Code - Chart
DECIMAL 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
HEX 0 1 2 3 4 5 6 7 8 9 A B C D E F
BINARY 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111
http://easycalculation.com/hex-converter.php
-
7/28/2019 w9 Sfe3013 Digital Sv
26/37
Question 1:
-
7/28/2019 w9 Sfe3013 Digital Sv
27/37
Question 1:
Counting practice: count from zero to thirty-one in binary, octal,
and hexadecimal:
-
7/28/2019 w9 Sfe3013 Digital Sv
28/37
Convert decimal 54 to binary number
54 /2 = 27 Remainder = 0
27 /2 = 13 Remainder = 1
13 /2 = 6 Remainder = 1
6 /2 = 3 Remainder = 0
3 /2 = 1 Remainder = 1
1 /2 = 0 Remainder = 1
ANSWER: 5410 = 1101102
-
7/28/2019 w9 Sfe3013 Digital Sv
29/37
-
7/28/2019 w9 Sfe3013 Digital Sv
30/37
BINARY TO HEXADECIMAL CONVERSION
Convert 10110111.12
to hexadecimal
Solution:
Group the bits in four's, from the binary point
left, and from the binary point right, adding
zeros as necessary to make complete 4-bit
groups.
Answer: 10110111.12 = B7.816
-
7/28/2019 w9 Sfe3013 Digital Sv
31/37
HEXADECIMAL TO BINARY CONVERSION
Convert C316
to binary number
Solution:
Each HEX digit is converted to its 4-bit binary
equivalent.
C16 = 11002 316 = 00112
Answer: C316 = 110000112
-
7/28/2019 w9 Sfe3013 Digital Sv
32/37
Exercise 4
Convert the number1128 DECIMAL to HEXADECIMAL
Ans: 46816
Convert octal 32 to binary
Convert octal 53.7 to binary
Ans: 011010
-
7/28/2019 w9 Sfe3013 Digital Sv
33/37
Binary Addition
The four basic rules for adding binary digits (bits)
are as follows:
0 + 0 = 0 Sum of 0 with a carry of 0
0 + 1 = 1 Sum of 1 with a carry of 0
1 + 0 = 1 Sum of 1 with a carry of 0
1 + 1 = 0 Sum of 0 with a carry of 1
[Excercise] Add 1111 and 1100.
Ans: 11011
-
7/28/2019 w9 Sfe3013 Digital Sv
34/37
-
7/28/2019 w9 Sfe3013 Digital Sv
35/37
The ASCII (pronounced ask-E) code assigns binary
patterns forNumbers 0 to 9
All the letters of English alphabet, uppercase and
lowercase
Many control codes and punctuation marks
The ASCII system uses 7 bits to represent each code
Hex Symbol Hex Symbol
5A Z 7A z
59 Y 79 y
... ... ... 44 D 64 d
43 C 63 c
42 B 62 b
41 A 61 a
ASCII CODE
-
7/28/2019 w9 Sfe3013 Digital Sv
36/37
HOMEWORK
Perform hex subtraction:
59F 2B8
-
7/28/2019 w9 Sfe3013 Digital Sv
37/37
THE END