Transcript Digital Design

Logic Design
Logic design deals with the basic concepts and tools used
to design digital hardware consisting of logic circuits
Digital devices:
airbags, auto-focus cameras, aircraft navigators,
cell phones, credit card readers, digital cameras,
DVD players, personal computers, portable music players, …
1
What Does “Digital” Mean?
• Analog signal
• Digital signal
– Inifinite possible values
• Ex: voltage on a wire
created by microphone
– Finite possible values
• Ex: button pressed on a
keypad
1
2
3
4
2
digital
signal
Possible values:
1.00, 1.01, 2.0000009,
... infinite possibilities
time
value
value
analog
signal
4
3
2
1
0
Possible values:
0, 1, 2, 3, or 4.
That’s it.
time
2
1
0
Digitized version enables
near-perfect save/cpy/trn.
– “Sample” voltage at
particular rate, save
sample using bit encoding
– Voltage levels still not kept
perfectly
– But we can distinguish 0s
from 1s
Let bit encoding be:
1 V: “01”
Digitized signal not
2 V: “10”
perfect re-creation,
but higher sampling
3 V: “11”
rate and more bits per
encoding brings closer.
original signal
time
a2d
1
digitized signal
0
time
01 10 11 10 11
3
2
1
0
received signal
time
How fix -- higher, lower, ?
01 10 11 10 11
Volts
•
2
lengthy transmission
(e.g, cell phone)
– Voltage levels not
saved/copied/transmitted
perfectly
3
lengthy transmission
(e.g, cell phone)
Analog signal (e.g., audio)
may lose quality
Volts
•
Volts
Example of Digitization Benefit
1
0
time
Can fix -- easily distinguish 0s
and 1s, restore
d2a
3
2
1
0
time
3
Digitized Audio: Compression Benefit
• Digitized audio can be
compressed
– e.g., MP3s
– A CD can hold about 20
songs uncompressed,
but about 200
compressed
Example compression scheme:
00 --> 0000000000
01 --> 1111111111
1X --> X
0000000000 0000000000 0000001111 1111111111
00 00 10000001111 01
• Compression also done
on digitized pictures
(jpeg), movies (mpeg),
and more
• Digitization has many
other benefits too
4
Benefits of Digital
• Reliable storage (CD, DVD, …)
• Compression (MP3, JPEG, …)
• Reliable transmission (cell phones, digital TVs, …)
Conversion from Analog to Digital Technology
5
Digital Encodings and
Binary Numbers
We can represent any digital data using only
binary digits (0 and 1), or bits.
ASCII encoding:
A
B
…
01000001
01000010
…
Why binary numbers?
Base ten: decimal numbers (0,1,2,3,4,5,6,7,8,9)
Base two: binary numbers (0,1)
Base eight: octal numbers (0,1,2,3,4,5,6,7)
Base sixteen: hexadecimal numbers
(0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F)
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Converting from Decimal to Binary Numbers:
Subtraction Method Example
• Q: Convert the number “23” from decimal to binary
A: Remaining quantity
Binary Number
23
0 0
32 16
0
8
0
4
0
2
0
1
23
-16
7
0 1
32 16
0
8
0
4
0
2
0
1
7
-4
3
0 1
32 16
0
8
1
4
0
2
0
1
3
-2
1
0 1
32 16
0
8
1
4
1
2
0
1
1
-1
0
0 1
32 16
0
8
1
4
1
2
1
1
8 is more than 7, can’t use
Done! 23 in decimal is 10111 in binary.
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Base Sixteen: Another Base Sometimes Used by
Digital Designers
164
163
8
A
F
162
161
160
8
A
F
1000 1010 1111
hex
binary
hex
binary
0
1
2
3
4
5
6
7
0000
0001
0010
0011
0100
0101
0110
0111
8
9
A
B
C
D
E
F
1000
1001
1010
1011
1100
1101
1110
1111
• Nice because each position
represents four base two positions
– Used as compact means to write
binary numbers
• Known as hexadecimal, or just hex
Q: Write 11110000 in hex
F0
8