Boolean 4.1 Boolean Logic 4 ©Paul Godin Created September 2007 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 Table Boolean equation Timing Diagram A B Z Logic Diagram AA’BCY

Boolean 4.5 Second Step: Simplify Simplify the problem using reduction techniques DC BA (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. Godin prgodin gmail.com END 1011? 1101!