CprE 281: Digital Logic - Computer Engineering4-1 Multiplexer (Definition) • Has four inputs: w 0...
Transcript of CprE 281: Digital Logic - Computer Engineering4-1 Multiplexer (Definition) • Has four inputs: w 0...
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Instructor: Alexander Stoytchev
http://www.ece.iastate.edu/~alexs/classes/
CprE 281: Digital Logic
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Intro to Verilog
CprE 281: Digital LogicIowa State University, Ames, IACopyright © Alexander Stoytchev
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Administrative Stuff
• HW3 is due on Monday Sep 11 @ 4p
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Administrative Stuff• HW4 is out
• It is due on Monday Sep 18 @ 4pm.
• Please write clearly on the first page (in BLOCK CAPITAL letters) the following three things:
§ Your First and Last Name§ Your Student ID Number§ Your Lab Section Letter
• Also, please § Staple your pages
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Administrative StuffTA Office Hours:
• 5:00 pm - 6:00 pm on Tuesdays (Vahid Sanei-Mehri)Location: 3125 Coover Hall
• 11:10 am-1:10 pm on Wednesdays (Siyuan Lu) Location: TLA (Coover Hall - first floor)
• 5:00 pm - 6:00 pm on Thursdays (Vahid Sanei-Mehri)Location: 3125 Coover Hall
• 10:00 am-12:00 pm on Fridays (Krishna Teja) Location: 3214 Coover Hall
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Administrative Stuff• Midterm Exam #1
• When: Friday Sep 22.
• Where: This classroom
• What: Chapter 1 and Chapter 2 plus number systems
• The exam will be open book and open notes (you can bring up to 3 pages of handwritten notes).
• More details to follow.
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Quick Review
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2-1 Multiplexer (Definition)
• Has two inputs: x1 and x2
• Also has another input line s
• If s=0, then the output is equal to x1
• If s=1, then the output is equal to x2
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Graphical Symbol for a 2-1 Multiplexer
f
s
x 1 x 2
0
1
[ Figure 2.33c from the textbook ]
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Let’s Derive the SOP form
s x1 x2
s x1 x2
s x1 x2
s x1 x2
f (s, x1, x2) = s x1 x2 s x1 x2 s x1 x2 s x1 x2+ + +
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Let’s simplify this expression
f (s, x1, x2) = s x1 x2 s x1 x2 s x1 x2 s x1 x2+ + +
f (s, x1, x2) = s x1 (x2 + x2) s (x1 +x1 )x2+ +
f (s, x1, x2) = s x1 s x2+
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Circuit for 2-1 Multiplexer
f
x 1
x 2s
f
s
x 1 x 2
0
1
(c) Graphical symbol(b) Circuit
[ Figure 2.33b-c from the textbook ]
f (s, x1, x2) = s x1 s x2+
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Analogy: Railroad Switch
http://en.wikipedia.org/wiki/Railroad_switch]
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Analogy: Railroad Switch
http://en.wikipedia.org/wiki/Railroad_switch]
selectx1 x2
f
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Analogy: Railroad Switch
http://en.wikipedia.org/wiki/Railroad_switch]
selectx1 x2
f
This is not a perfect analogy because the trains can go in either direction, while the multiplexer would only allow them to go from top to bottom.
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More Compact Truth-Table Representation
0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 1
(a) Truth table
s x1 x2 f (s, x1, x2)
[ Figure 2.33 from the textbook ]
0
1
f (s, x1, x2)sx1
x2
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4-1 Multiplexer (Definition)
• Has four inputs: w0 , w1, w2, w3
• Also has two select lines: s1 and s0
• If s1=0 and s0=0, then the output f is equal to w0
• If s1=0 and s0=1, then the output f is equal to w1
• If s1=1 and s0=0, then the output f is equal to w2
• If s1=1 and s0=1, then the output f is equal to w3
We’ll talk more about this when we get to chapter 4, but here is a quick preview.
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Graphical Symbol and Truth Table
[ Figure 4.2a-b from the textbook ]
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The long-form truth table
[http://www.absoluteastronomy.com/topics/Multiplexer]
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4-1 Multiplexer (SOP circuit)
[ Figure 4.2c from the textbook ]
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0
w 0 w 1
0
1
w 2 w 3
0
1
f 0
1
s 1
s
Using three 2-to-1 multiplexers to build one 4-to-1 multiplexer
[ Figure 4.3 from the textbook ]
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Analogy: Railroad Switches
http://en.wikipedia.org/wiki/Railroad_switch]
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Analogy: Railroad Switches
http://en.wikipedia.org/wiki/Railroad_switch]
s1
w0
f
w1 w2 w3
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Analogy: Railroad Switches
http://en.wikipedia.org/wiki/Railroad_switch]
s1
w0
f
w1 w2 w3
these two switches are controlled together
s0
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Using three 2-to-1 multiplexers to build one 4-to-1 multiplexer
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Using three 2-to-1 multiplexers to build one 4-to-1 multiplexer
fs1
s0
w0
w1
w2
w3
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That is different from the SOP form of the 4-1 multiplexer shown below, which uses fewer gates
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w 8
w 11
s 1
w 0
s 0
w 3
w 4
w 7
w 12
w 15
s 3
s 2
f
16-1 Multiplexer
[ Figure 4.4 from the textbook ]
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[http://upload.wikimedia.org/wikipedia/commons/2/26/SunsetTracksCrop.JPG]
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7-Segment Display Example
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Display of numbers
[ Figure 2.34 from the textbook ]
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Display of numbers
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Display of numbers
b = 1
e = s0c = s1
f = s1 s0
g = s1 s0a = s0
d = s0
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Intro to Verilog
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History• Created in 1983/1984
• Verilog-95 (IEEE standard 1364-1995)
• Verilog 2001 (IEEE Standard 1364-2001)
• Verilog 2005 (IEEE Standard 1364-2005)
• SystemVerilog
• SystemVerilog 2009 (IEEE Standard 1800-2009).
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HDL
• Hardware Description Language
• Verilog HDL
• VHDL
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Verilog HDL != VHDL
• These are two different Languages!
• Verilog is closer to C
• VHDL is closer to Ada
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[ Figure 2.35 from the textbook ]
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“Hello World” in Verilog
[http://en.wikipedia.org/wiki/Verilog]
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x 1 x 2
x 1 x 2 +
AND gate
x x x 1 x 2
x 1 x 2 •
The Three Basic Logic Gates
[ Figure 2.8 from the textbook ]
OR gateNOT gate
You can build any circuit using only these three gates
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How to specify a NOT gate in Verilog
NOT gate
x x
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x y
How to specify a NOT gate in Verilog
NOT gate
we’ll use the letter y for the output
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x y
How to specify a NOT gate in Verilog
NOT gate
not (y, x)
Verilog code
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How to specify an AND gate in Verilog
AND gate
and (f, x1, x2)
Verilog code
x 1 x 2
x 1 x 2 •f=
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How to specify an OR gate in Verilog
OR gate
or (f, x1, x2)
Verilog code
x 1 x 2
x 1 x 2 + f=
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2-1 Multiplexer
[ Figure 2.36 from the textbook ]
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Verilog Code for a 2-1 Multiplexer
[ Figure 2.37 from the textbook ][ Figure 2.36 from the textbook ]
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Verilog Code for a 2-1 Multiplexer
[ Figure 2.40 from the textbook ][ Figure 2.36 from the textbook ]
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Verilog Code for a 2-1 Multiplexer
[ Figure 2.42 from the textbook ][ Figure 2.36 from the textbook ]
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Verilog Code for a 2-1 Multiplexer
[ Figure 2.43 from the textbook ][ Figure 2.36 from the textbook ]
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Another Example
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Let’s Write the Code for This Circuit
[ Figure 2.39 from the textbook ]
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[ Figure 2.38 from the textbook ]
Let’s Write the Code for This Circuit
module example2 (x1, x2, x3, x4, f, g, h);input x1, x2, x3, x4;output f, g, h;
and (z1, x1, x3);and (z2, x2, x4);or (g, z1, z2);or (z3, x1, ~x3);or (z4, ~x2, x4);and (h, z3, z4);or (f, g, h);
endmodule
[ Figure 2.39 from the textbook ]
![Page 54: CprE 281: Digital Logic - Computer Engineering4-1 Multiplexer (Definition) • Has four inputs: w 0 , w 1, w 2, w 3 • Also has two select lines: s 1and s 0 • If s 1=0 and s 0=0,](https://reader034.fdocuments.in/reader034/viewer/2022052102/603be764296f066b800743d5/html5/thumbnails/54.jpg)
[ Figure 2.41 from the textbook ]
Let’s Write the Code for This Circuit
[ Figure 2.39 from the textbook ]
module example4 (x1, x2, x3, x4, f, g, h);input x1, x2, x3, x4;output f, g, h;
assign g = (x1 & x3) | (x2 & x4);assign h = (x1 | ~x3) & (~x2 | x4);assign f = g | h;
endmodule
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Yet Another Example
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A logic circuit with two modules
[ Figure 2.44 from the textbook ]
![Page 57: CprE 281: Digital Logic - Computer Engineering4-1 Multiplexer (Definition) • Has four inputs: w 0 , w 1, w 2, w 3 • Also has two select lines: s 1and s 0 • If s 1=0 and s 0=0,](https://reader034.fdocuments.in/reader034/viewer/2022052102/603be764296f066b800743d5/html5/thumbnails/57.jpg)
The adder module
[ Figure 2.12 from the textbook ]
![Page 58: CprE 281: Digital Logic - Computer Engineering4-1 Multiplexer (Definition) • Has four inputs: w 0 , w 1, w 2, w 3 • Also has two select lines: s 1and s 0 • If s 1=0 and s 0=0,](https://reader034.fdocuments.in/reader034/viewer/2022052102/603be764296f066b800743d5/html5/thumbnails/58.jpg)
The adder module
[ Figure 2.45 from the textbook ]
![Page 59: CprE 281: Digital Logic - Computer Engineering4-1 Multiplexer (Definition) • Has four inputs: w 0 , w 1, w 2, w 3 • Also has two select lines: s 1and s 0 • If s 1=0 and s 0=0,](https://reader034.fdocuments.in/reader034/viewer/2022052102/603be764296f066b800743d5/html5/thumbnails/59.jpg)
The display module
b = 1
e = s0c = s1
f = s1 s0
g = s1 s0a = s0
d = s0
![Page 60: CprE 281: Digital Logic - Computer Engineering4-1 Multiplexer (Definition) • Has four inputs: w 0 , w 1, w 2, w 3 • Also has two select lines: s 1and s 0 • If s 1=0 and s 0=0,](https://reader034.fdocuments.in/reader034/viewer/2022052102/603be764296f066b800743d5/html5/thumbnails/60.jpg)
The display module
b = 1
e = s0
c = s1
f = s1 s0
g = s1 s0
a = s0
d = s0
[ Figure 2.46 from the textbook ]
![Page 61: CprE 281: Digital Logic - Computer Engineering4-1 Multiplexer (Definition) • Has four inputs: w 0 , w 1, w 2, w 3 • Also has two select lines: s 1and s 0 • If s 1=0 and s 0=0,](https://reader034.fdocuments.in/reader034/viewer/2022052102/603be764296f066b800743d5/html5/thumbnails/61.jpg)
Putting it all together
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Questions?
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THE END