boolean 4.1 boolean logic 4 ©paul godin created september 2007 gmail.com
DESCRIPTION
Boolean 4.3 Solving Logic Problems ◊Digital logic problems are often expressed in a verbal format. ◊“I need a circuit that does this when that happens...” ◊Problem-solving steps generally involve structuring the problem into a logic format, simplifying, designing, simulating, prototyping, constructing and evaluating. ◊There are application software tools available to help with the simplification process (seen later).TRANSCRIPT
Boolean 4.1
Boolean Logic 4
©Paul GodinCreated September 2007
prgodin @ gmail.com
Boolean 4.2
Solving Logic Problems
Boolean 4.3
Solving Logic Problems◊ Digital logic problems are often expressed in a verbal
format.◊ “I need a circuit that does this when that happens...”
◊ Problem-solving steps generally involve structuring the problem into a logic format, simplifying, designing, simulating, prototyping, constructing and evaluating.
◊ There are application software tools available to help with the simplification process (seen later).
Boolean 4.4
First Step: Logic Format
Convert the problem to a structured logic format.
A’C’ + BC + ABC’Truth TableBoolean equation
Timing DiagramA
B
Z
Logic Diagram
A A’ B C Y
0 1 0 0 0
0 1 0 1 0
0 1 1 0 0
0 1 1 1 1
1 0 0 0 1
1 0 0 1 0
1 0 1 0 1
1 0 1 1 0
Boolean 4.5
Second Step: Simplify
Simplify the problem using reduction techniques.
00 01 11 10
00 0 0 0 0
01 1 0 0 1
11 1 0 0 1
10 0 0 0 0
DCBA
(AB+C)+(A+BD)+E
(ABC)+(ABC)+(ABC)+(ABC) = W
Boolean algebraic reduction
K-Mapping
SOP from a Truth Table to Boolean or K-Map
AB'C'+AC'D'+E
Boolean 4.6
Third Step: Design
Create a logic circuit, preferably with simulation software. Consider universal gates.
Logic Circuit Logic Circuit, NAND Only
Boolean 4.7
Fourth Step: Simulate
Analyse the functionality of the simulated circuit.
Input/Output Timing Diagram (Logic Analysis)
Boolean 4.8
Fifth Step: Prototype
Construct a prototype circuit. Select the devices based on electrical, environmental, physical and other requirements.
Boolean 4.9
Sixth Step: Construct and Evaluate
Design and assemble a circuit board. Evaluate the physical circuit’s functionality within the limits of the
environmental operating conditions.
Boolean 4.10
Exercise: Word problem to circuit
◊ A water pump must start if any 2 adjacent sensors of its 4 sensors detects water, or if someone switches on an over-ride switch.
◊ Design and simulate this circuit.
Boolean 4.11
©Paul R. Godinprgodin°@ gmail.com
END1011?
1101!