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Electrical & Computer Engineering Dr. D. J. Jackson Lecture 5-
ECE380 Digital Logic
Introduction to Logic Circuits:
Design Examples
Design examples
• Logic circuits provide a solution to a
problem
• Some may be complex and difficult to
design
• Regardless of the complexity, the same
basic design issues must be addressed
1. Specify the desired behavior of the circuit
2. Synthesize and implement the circuit
3. Test and verify the circuit
Electrical & Computer Engineering Dr. D. J. Jackson Lecture 5-
Three-way light control
• Assume a room has three doors and a switch
by each door controls a single light in the
room.
- Let x, y, and z denote the state of the switches
- Assume the light is off if all switches are open
- Closing any switch turns the light on. Closing
another switch will have to turn the light off.
- Light is on if any one switch is closed and off if
two (or no) switches are closed.
- Light is on if all three switches are closed
Three-way light control
x
y z f f(x,y,z)=m^1 +m^2 +m^4 +m^7
f(x,y,z)=x’y’z+x’yz’+xy’z’+xyz
This is the simplest sum-of-products form.
Electrical & Computer Engineering Dr. D. J. Jackson Lecture 5-
Multiplexer circuit
s
x (^1)
x (^2)
f=x 1 s’+x 2 s
1 x 2
s f ( s,x 1 ,x 2 )
Graphical symbol Compact truth table
Car safety alarm
• Design a car safety alarm considering four
inputs
- Door closed (D)
- Key in (K)
- Seat pressure (S)
- Seat belt closed (B)
• The alarm (A) should sound if
- The key is in and the door is not closed, or
- The door is closed and the key is in and the driver
is in the seat and the seat belt is not closed
Electrical & Computer Engineering Dr. D. J. Jackson Lecture 5-
Car safety alarm
D
K
S B A
A(D,K,S,B)=Σm(4,5,6,7,14) A(D,K,S,B)=D’KS’B’+D’KS’B+D’KSB’+D’KSB+DKSB’
=D’KS’+D’KS+KSB’
=D’K+KSB’
Adder circuit
• Design a circuit that adds two input bits
together (x,y) and produces two output bits
(s and c)
- S: sum bit
- x=0, y=0 => s=
- x=0, y=1 => s=
- x=1, y=0 => s=
- x=1, y=1 => s=
- C: carry bit
- x=0, y=0 => c=
- x=0, y=1 => c=
- x=1, y=0 => c=
- x=1, y=1 => c=
