Title: Chapter 1 Introduction to Digital Systems Design
1Chapter 1 Introduction to Digital Systems Design
2Digital vs. Analog
- Analog systems represent information using
physical quantities - Voltage on a wire, magnetic field strength
- Digital systems represent information using
binary digits, or bits - 1 or 0, high or low, on or off
3Positional Number Systems
- Two discrete values are insufficient for most
applications - We combine bits to represent more values
- We use a positional number system for binary just
like we do in decimal
4Positional Number Systems
- Decimal, base 10, means we have 10 digits (0-9)
- Decimal example
- 103210 1x103 0x102 3x101 2x100
- Hexadecimal, base 16, means we have 16 digits
(0-9, A-F) - Hexadecimal example
- 2A516 2x162 10x161 5x160 512 160 5
677 - Binary, base 2, follows the same pattern
- Binary example
- 10112 1x23 0x22 1x21 1x20 8 0 2 1
11 - Counting in any base is analogous to counting in
decimal
5Digital vs. Analog
- Analog thermometer
- 0V to 10V, could be used to represent 0 to 100
F - Each 1/10th volt represents 1 degree
- Digital thermometer
- 7-bit binary number could be used to represent 0
to 127 F - Seven bits can be used to represent the numbers 0
to 127
6Digital Precision
- How would you represent 10.5 F?
- Analog example 1.05V
- Digital example ????
- 00010102 1010
- 00010112 1110
- We must either add bits or decrease the range
7Digital Precision
- 9-bit thermometer, 0 to 127.75 F
- Each discrete number increase represents 0.25 F
- 10.5 F ? 10.5/0.25 42 1010102
- 7-bit thermometer, 0 to 12.7 F
- Each discrete number represents 12.7/127 0.1
F - 10.5 F ? 10.5/0.1 105 11010012
- It is not possible to represent all values
exactly using digital representation - Example 1/3 cant be represented in binary, just
like it cant be represented in decimal
8Example Analog Photography
- An analog camera uses a chemical reaction in the
film when exposed to light - The amount of exposure is directly related to the
amount of light that hits the film
9Example Digital Photography
- A digital camera uses an array of light-sensitive
receptors that measure the light as a binary
number - Image quality is determined mostly by two
factors - The number of bits per pixel
- The number of pixels per image
10Example Digital Photography
1284x897 pixels, 24-bit color
100x70 pixels, 24-bit color
1284x897 pixels, 6-bit color
100x70 pixels, 6-bit color
11Analog vs. Digital Storage
- Analog storage mediums fade over time due to
gradual physical degradation - Photos turn yellow with time
- Cassette audio tapes lose their clarity
- Digital storage mediums dont fade like analog
- If a 0 or 1 fades it will still be a 0 or 1
- A .jpg image taken 10 years ago is exactly the
same today
12Analog vs. Digital Storage
- Making an analog copy implies measuring the
storage medium - Always introduces some errors
- Copies of copies are even worse
- Making digital copies implies distinguishing 0s
from 1s so copies are exact - Copies can be made without any error
- Copies of copies are identical
13Analog vs. Digital Processing
- Modern computers and digital circuits make it
easy to do extremely complex processing - Digital processing allows precision and error to
be exactly predicted
14Combinational vs. Sequential Circuits
- Digital circuits consist of binary inputs and
outputs - In combinational circuits, the output is a direct
function of its inputs - In sequential circuits the output depends on the
current input and previous inputs - Sequential circuits contain memory that tracks
state - A clock is used to signal when to change states
A
B
X
Y
C
D
15Combinational vs. Sequential
- Combinational example Clock chime
- Inputs seconds and minutes
- Output chime
- Behavior Output chime is 1 if and only if
seconds is 0 and minutes is 0, 15, 30, or 45. - Sequential example Counter
- Inputs inc and clk
- Output count
- Behavior Increment count on clk edge if and only
if inc is 1