CSCE 211 Digital Design
Lecture 5
Combinational Components
Topics
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Products-of-Sums Form examples
5 variable and larger Karnaugh Maps
Components: Decoders, Multiplexers
Readings
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September 21, 2015
CSCE 211H Fall 2015
Overview
Last Time:
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Boolean Algebra Continued
Combinational Circuit Analysis
Sums-of-Products Form
Karnaugh Maps 3,4 variable maps
Don’t Care Conditions
Products-of-Sums Form
New:
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–2–
Review Products-of-Sums Form
(5, 6, … variable maps)
Decoders
Multiplexers
Circuits kits on paper
CSCE 211H Fall 2015
Karnaugh Map Simplification
F(W,X,Y,Z) =
X
WX
YZ
00
00
01
11
10
01
Z
11
Y
10
W
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CSCE 211H Fall 2015
Karnaugh Map Simplification
F(W,X,Y,Z) =
X
WX
YZ
00
00
01
11
10
01
Z
11
Y
10
W
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CSCE 211H Fall 2015
Products-of-Sums Simplification
F(W,X,Y,Z) =
X
WX
YZ
00
00
01
11
10
01
Z
11
Y
10
W
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CSCE 211H Fall 2015
5 Variable Map Simplification
F(V, W,X,Y,Z) =
X
X
WX
YZ
00
01
WX
00
01
11
10
0
4
12
8
1
5
13
9
11
3
7
15
11
10
2
6
14
10
Y
YZ
00
01
Z
00
01
11
10
0
4
12
8
1
5
13
9
11
3
7
15
11
10
2
6
14
10
Y
Z
W
W
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CSCE 211H Fall 2015
5 Variable Map Simplification
F(V, W,X,Y,Z) =
X
X
WX
YZ
00
00
01
WX
11
YZ
00
10
00
01
11
10
01
Z
01
Z
11
11
Y
10
Y
10
W
W
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CSCE 211H Fall 2015
6 Variable Map
F(U,V,W,X,Y,Z) =
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
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CSCE 211H Fall 2015
6 Variable Map
F(U,V,W,X,Y,Z) =
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
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CSCE 211H Fall 2015
Combinational Circuits
A combinational circuit is one that
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The outputs are functions strictly of the inputs
There are no feedback loops
CSCE 211H Fall 2015
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CSCE 211H Fall 2015
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CSCE 211H Fall 2015
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CSCE 211H Fall 2015
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CSCE 211H Fall 2015
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CSCE 211H Fall 2015
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CSCE 211H Fall 2015
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CSCE 211H Fall 2015
3x8 Decoder
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CSCE 211H Fall 2015
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CSCE 211H Fall 2015
4x16 decoder from 2x4s
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CSCE 211H Fall 2015
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CSCE 211H Fall 2015
Multiplexers
A multiplexer selects one of its inputs to route to its
outputs.
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CSCE 211H Fall 2015
BreadBoard
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CSCE 211H Fall 2015
Wiring an LED
To wire an led
1. Hook the positive to Vcc
2. Hook the negative to a 330 ohm
resistor
3. Hook the resistor to Gnd
4. Check for loose wires
5. Check for shorts
+
See section 3.7.5 page 129-130 for more details
•
I LED = 10 mA needed to light the LED
•
Voltage drop is about 1.6V
•
303 Ohms
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CSCE 211H Fall 2015
74LS00 – Quad 2 input NAND
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CSCE 211H Fall 2015
74LS04 Hex Inverter
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CSCE 211H Fall 2015
Half adder
1. How many inputs?
2. How many outputs?
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CSCE 211H Fall 2015
6 Variable Map
F(U,V,W,X,Y,Z) =
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
0 4 12 8
1 5 13 9
3 7 15 11
2 6 14 10
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CSCE 211H Fall 2015
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CSCE 211H Fall 2015
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CSCE 211H Fall 2015
Analyze This!
0
0
1
1
F1 = ?
F2 = ?
What are the delays?
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CSCE 211H Fall 2015
Quick What’s This?
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CSCE 211H Fall 2015
What’s This?
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CSCE 211H Fall 2015
8 to 1 Mux from 4x1 Muxes
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CSCE 211H Fall 2015
Big Multiplexers from smaller ones
Show the design of a 32-to-1 Mux from 8-to-1’s and smaller
muxes
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CSCE 211H Fall 2015
BreadBoard
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CSCE 211H Fall 2015
Wiring an LED
To wire an led
1. Hook the positive to Vcc
2. Hook the negative to a 330 ohm
resistor
3. Hook the resistor to Gnd
4. Check for loose wires
5. Check for shorts
+
See section 3.7.5 page 129-130 for more details
•
I LED = 10 mA needed to light the LED
•
Voltage drop is about 1.6V
•
303 Ohms
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CSCE 211H Fall 2015
74LS00 – Quad 2 input NAND
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CSCE 211H Fall 2015
74LS04 Hex Inverter
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CSCE 211H Fall 2015
Two Bit adder
1. How many inputs?
2. How many outputs?
3. Do we have enough chips?
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CSCE 211H Fall 2015
Implementing a Binary Adder Using a Decoder
PC
0
0
0
0
1
1
1
1
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X
0
0
1
1
0
0
1
1
Y
0
1
0
1
0
1
0
1
S
C
PC
X
3x8
Decoder
Y
CSCE 211H Fall 2015
74LS139 Decoder
Dual 2x4 decoder
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CSCE 211H Fall 2015
Using a 74LS139 to implement a Half-adder
X
Y
S
C
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CSCE 211H Fall 2015
74LS157 Dual 4 input Mux
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CSCE 211H Fall 2015
Hardware Description Languages
Hardware description language or HDL is any language
from a class of computer languages for formal
description of electronic circuits
Boolean Algebra was applied to circuits by Shannon 1948.
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http://cm.bell-labs.com/cm/ms/what/shannonday/paper.html
Current HDLs include:
 Verilog HDL
 VHDL – VHSIC HDL
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VHSIC – Very High Speed Integrated Circuits
 ABEL HDL - Advanced Boolean Expression Language
 http://en.wikipedia.org/wiki/Hardware_description_langu
age
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CSCE 211H Fall 2015
Seven Segment Display
 Common anode
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CSCE 211H Fall 2015
Functions for 74LS47 with don’t cares
a(D,C,B,A) = D + A.C + A.B + A’.C’
b(D,C,B,A) = D + (D'*C') + (A'*B') + (A*B)
c <=
d=
e = A(bar) and (B or C(bar))
f = D + A'B' + B'C + A'BC
g=D + B'C + C'B + A'B
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CSCE 211H Fall 2015
Karnaugh Map Simplification
On a real 74LS47 the outputs for 10, …15 are not don’t cares.
They would indicate errors in BCD input. We could use the period for that.
period(D,C,B,A)=SUM(
dc(D,C,B,A) = SUM(
)
)
C
DC
BA
00
00
01
11
10
period(D,C,B,A) =
01
A
11
B
10
D
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CSCE 211H Fall 2015
Transistors
History
1790s Ben Franklin “assigns” negative charge to
electrons
1898 Thompson discovers the electron
1947 Shockley, Bardeen and Brattain “invent”
transistor
1958 first Integrated Circuit, Texas Instruments
1971 Intel 4004, microprocessor, Ted Hoff
Timeline
http://www.pbs.org/transistor/
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CSCE 211H Fall 2015
Hot Batteries
You should regularly check your batteries “slightly
warm” is OK but hot indicates that your circuit has a
short circuit.
Unplug quickly and check.
1.
2.
3.
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Look for direct lines Vcc to GND.
Remember you need 330 ohm resistors in series with LEDs
and that includes segments of the seven segment display.
Recheck sections of the breadboard.
CSCE 211H Fall 2015
Transistor: Water Flow Model
Water flow in B raises the
plunger so that water can
flow from C to E.
Small flow turns on and
off bigger flow.
Put signal on B, transfer
signal C to E
Reference: http://www.satcure-focus.com/tutor/page4.htm
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CSCE 211H Fall 2015
Transistor Terminology
Conductor – electrons easily passed from one atom to
next (copper every atom has loose electron)
Insulator – electrons tightly tied down to atoms, no flow
Semiconductor – by adding impurities (doping) can be
changed to increase conductivity
Silicon wafer – used for IC circuits
N-type - silicon doped with boron (excess electrons)
P-ype - silicon doped with phosphorous (excess
“holes” lack of electrons)
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CSCE 211H Fall 2015
Transistor
Reference: http://www.intel.com/education/transworks/
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CSCE 211H Fall 2015
Transistor
Reference: http://www.intel.com/education/transworks/
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CSCE 211H Fall 2015
Transistor
Put Positive charge
on gate.
This attracts
electrons into gap.
This allows electrons
to pass freely
through the gap.
Reference: http://www.intel.com/education/transworks/
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CSCE 211H Fall 2015
Transistor
Reference: http://www.intel.com/education/transworks/
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CSCE 211H Fall 2015
Transistor
Take positive charge off
Gate
This stops attracting
electrons.
This shuts off the flow.
Reference: http://www.intel.com/education/transworks/
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CSCE 211H Fall 2015
N channel transitor
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CSCE 211H Fall 2015
P channel Transistor
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CSCE 211H Fall 2015
CMOS Inverter
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CSCE 211H Fall 2015
CMOS NAND
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CSCE 211H Fall 2015
What’s This?
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CSCE 211H Fall 2015
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CSCE 211H Fall 2015