Digital Logic
Zach Cashero
Berthoud High School
Berthoud, CO
This program is based upon collaborative work supported by a National Science Foundation Grant No.
0841259; Colorado State University, Thomas Chen, Principal Investigator, Michael A. de Miranda and
Stuart Tobet Co-Principal Investigators. Any opinions, findings, conclusions or recommendations
expressed in this material are those of the author(s) and do not necessarily reflect the views of the
National Science Foundation.
Analog vs. Digital Signals
 Analog - continuous signal
 audio
 Digital - discrete signal, either on or off
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Photo: http://markun.cs.shinshu-u.ac.jp
Digital
 Everything in your computer is represented
as 0’s and 1’s
 0 = OFF = Low voltage = 0 V
 1 = ON = High voltage = +5 V
Why Digital?




Much simpler
More predictable
Able to build more complex functionality
Much easier to design a circuit that has 2
states: OFF and ON
Logic Gates
 NOT - inverts the signal
 0→1
 1→0
 AND
 output is a 1 only if ALL inputs are 1
 OR
 output is a 1 if ANY inputs are 1
Truth Tables
 Mapping of inputs to output value
 Must list all possible combinations of inputs
 How many different combinations are there
for 2 inputs?
Inputs
…
…
Output
.
.
Truth Tables
 Mapping of inputs to output value
 Must list all possible combinations of inputs
 How many different combinations are there
for 2 inputs?
4
 00, 01, 10, 11
Inputs
…
…
Output
.
.
NOT Gate
 1 input, 1 output
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Copyright © 1999-2000 Michael Stutz stutz@dsl.org
AND Gate
 2 inputs, 1 output
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Copyright © 1999-2000 Michael Stutz stutz@dsl.org
OR Gate
 2 inputs, 1 output
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Copyright © 1999-2000 Michael Stutz stutz@dsl.org
Transistor NOT Gate
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Transistor NOT Gate
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Practical Example
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AND Gate Using Transistors
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AND Gate IC
Photo: http://www.physics.mcmaster.ca
Binary Numbers
 All numbers can be represented as a string
of 0’s and 1’s
0
1
2
3
→
→
→
→
.
.
.
.
.
255
00000000
00000001
00000010
00000011
.
.
.
.
.
→
11111111
Full Adder
 Can be tied together to add larger binary numbers
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Inputs
Outputs
A B Cin Cout Sum
0 0 0
0
0
0 0 1
0
1
0 1 0
0
1
0 1 1
1
0
1 0 0
0
1
1 0 1
1
0
1 1 0
1
0
1 1 1
1
1
Summary
Silicon
⇓
Create channels to conduct current (doping and photolithography)
⇓
Transistors
⇓
Analog signal
⇓
Digital signal
⇓
Logic gates
⇓
Logic blocks
⇓
Microprocessor
⇓
Computer