Transcript 1 - godinweb

Introduction to Basic
Digital Logic
©Paul Godin
Updated August 2014
prgodin @ gmail.com
Presentation
1.11
Digital Electronics
1.2
Basic Digital Logic Concepts
Digital Number System
1.3
“Digital”
◊ A Digital World
◊ Many of the things we use every day
are “digital” or “digitized”.
◊ What does “Digital” mean?
◊ Represented by discrete (stepped) or
numerical values rather than analog
(continuous) values.
1.4
Examples
Measure temperature, a continuous value
1.5
Advantages of Digital Systems/Values
◊
◊
◊
◊
◊
◊
◊
◊
◊
Relatively less sensitive to distortion (noise and losses)
Can be reproduced more accurately
Easier to reconstruct a signal
More storage and transfer options
Can be processed mathematically and logically
Easier to standardize
Systems are easier to design electrically (lower voltage / very
low current)
Digital systems can be made small
Encryption available
Many of these concepts will make sense as
we progress through this course.
1.6
Disadvantages of Digital Systems/Values
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Takes time to convert and process values
Digital systems have significant electrical limitations
(cannot handle large current or high voltage)
Can become quite complex with an increase of significant
digits
Not a completely accurate representation of analog
values (rounding errors)
Often need to convert to / from analog systems
More complex circuitry
More sensitive to environmental issues (noise, electrical,
temperature, etc)
1.7
Future of Digital Systems
◊
With advances in semiconductor manufacturing, digital
systems are inexpensive, faster and more complex.
◊
In a mass production society the advantages of digital
systems outweigh the disadvantages.
◊
Digital technology will continue to replace what was
typically the analog or mechanical domain. Examples
include telephone and other communication systems,
broadcast television, sound and video reproduction,
instrumentation, timekeeping, etc...
1.8
Basic Digital Logic Concepts
Number Systems
There are 10 types of people in the world:
Those who understand binary, and those who don’t.
1.9
Number Systems
We use decimal, or “base-10”.
◊ 10 digits (0 to 9)
The decimal numbering system has positional weighing
where each position has a power of 10.
Example: 56310
Least Significant Digit
(LSD)
Most Significant Digit
(MSD)
5 6 3
5 x 102 + 6 x 101
+ 3 x 100
5 hundreds + 6 tens + 3 ones
1.10
Binary Signals
◊
Decimal values are difficult to represent in electrical
systems. It is easier to use two voltage values than ten.
◊
Binary Signals have two basic states:
1 (logic “high”, or H, or “on”, or “True”)
0 (logic “low”, or L, or “off”, or “False”)
◊
A good example of binary states is a light (only on or off)
on
off
1.11
Binary
The base value is the
number of digits in the
counting system. It is also
known as the radix.
Example: the radix of 01102 is 2.
Base 2 = Base 10
Binary to Decimal
In Binary there are only 0’s
and 1’s. These numbers are
called “Base-2”.
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
=
=
=
=
=
=
=
=
=
=
0
1
2
3
4
5
6
7
8
9
1.12
Binary digits
Bit: single binary digit
Byte: 8 binary digits
Bit
100101112
Radix
Byte
1.13
Converting Binary to Decimal
Each position represents a numerical “weight”
10112
23
22
21
20
23+21+20= 8+2+1 = 11 in decimal
1.14
Easy Conversion from Binary
◊ The easiest way to convert from binary to
decimal is to remember the positional values:
Base 2 = Base 10
00000 = 0
00001 = 1
00010 = 2
00100 = 4
01000 = 8
10000 = 16
10001 = 16 + 1 = 17
01111 = 10000 – 1 = 16 -1 = 15
01010 = 8 + 2 = 10
1.15
Hexadecimal
◊
Hexadecimal is used to simplify dealing with large binary
values:
◊ Base-16, or Hexadecimal, has 16 characters: 0-9, A-F
◊ Represent a 4-bit binary value: 00002 (0) to 11112 (F)
◊ Easier than using ones and zeros for large binary values
◊ Commonly used in computer applications
◊
Examples:
◊ 11002 = 1210 = C16
◊ 1010 0110 1100 00102 = A6 C216
Hex values can be followed by an “H” to indicate base-16.
Example: A6 C2 H
1.16
Hex Values in Computers
1.17
Decimal to Hexadecimal
Decimal
Hex
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
A
11
B
12
C
13
D
14
E
15
F
1.18
Conversion Binary to Hexadecimal
1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0
1010 = 10
1100 = 12
A
C
0001 = 1
1
0110 = 6
6
1.19
BCD
◊ BCD (Binary-Coded Decimal) values are used
to represent a decimal value in binary.
◊ BCD values allow for the easy conversion from
binary to decimal.
◊ Exclude values beyond ‘9’ (10102 to 11112).
◊ 00002 to 10012
1.20
Conversion
Chart
Binary
BCD
Decimal
Octal
Hex
0000
0
0
0
0
0001
1
1
1
1
0010
2
2
2
2
0011
3
3
3
3
0100
4
4
4
4
0101
5
5
5
5
0110
6
6
6
6
0111
7
7
7
7
1000
8
8
x
8
1001
9
9
x
9
1010
x
10
x
A
1011
x
11
x
B
1100
x
12
x
C
1101
x
13
x
D
1110
x
14
x
E
1111
x
15
x
F
1.21
Binary in everyday life
Ever wonder why computer-related values seem to follow a
pattern of: 32, 64, 128, 256, 512,…?
It is because they are related to binary values.
214=16,364 = 16k
215=32,768 = 32k
216=65,536 = 64k
217=131,072= 128k
218=262,144= 256k
219=524,288= 512k
220=1,048,576= 1M
…
Every bit added to the binary
number doubles the unique
values it can represent
1.22
Review 1
◊ Define:
◊ Binary
◊ Decimal
◊ Hexadecimal
◊ Convert 10102 to:
◊ Decimal
◊ Hexadecimal
1.23
Binary as Electrical Values
Electrical Representation of
Binary Values.
1.24
Binary as a Voltage
Voltages are used to represent logic values:
A voltage present (called Vcc or Vdd) = 1
Zero Volts or ground (called gnd or Vss) = 0
The voltage for a popular family of devices is 5 Volts.
Many digital device families function at other voltages.
1.25
A Simple Switch
A simple switch provides a logic value:
Vcc
Vcc
Vcc, or 1
Gnd, or 0
There are other, better ways to connect a switch in digital circuits.
1.26
Digital Waveform
Ideal Digital
Waveform
Logic 1
Logic 0
Waveform to
Digital value
0
1
1
0
1
0
1.27
Analog versus Digital
Distorted Analog signal
Original Analog signal
000000100000010000101000
101000011010010011001110
101000100000101000101000
011010010011001110101000
100000001000010100000010
000101000101000011010010
011001110101000100001010
000110100100110011101010
001010111011011010001001
Binary signal
1.28
Analog to Digital
Original Analog signal
A to D Conversion
The voltage is converted to a
binary value at regular intervals.
Animated
000100110111101010001
000111000000100000010
011100101001001011101
011110010101010010101
010101001001010101001
000101001010101111010
000001001011101011101
000000010101110101010
000000000001001111010
000000000000111111010
000000000001010101010
000000000001011011101
000000000001101101100
000000001100010111010
000000100011111010110
000001001010101000100
000001010111101111000
000011001101010100101
000110111000010100101
…
Binary signal
1.29
Digital to Analog
000100110111101010001
000111000000100000010
011100101001001011101
011110010101010010101
010101001001010101001
000101001010101111010
000001001011101011101
000000010101110101010
000000000001001111010
000000000000111111010
000000000001010101010
000000000001011011101
000000000001101101100
000000001100010111010
000000100011111010110
000001001010101000100
000001010111101111000
000011001101010100101
000110111000010100101
…
Digital signal
Animated
D to A Conversion
Analog signal
The binary value is converted to
a voltage at regular intervals.
1.30
Parallel versus Serial
◊ Serial communications:
provides a binary number as
a sequence of binary digits,
one after another, through
one data line.
◊ Parallel communications:
provides a binary number as
binary digits through multiple
data lines at the same time.
1.31
Exercise
◊
Name some advantages of digital signals over analog
signals.
◊
Discussion: Why have today’s standards gone toward
serial communications instead of parallel
communications?
END
1.32