ECE 265 Lab3 - LAB 3 PDF

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Summary

LAB 3...

Description

The aim of this experiment is to design a simplified logic circuit that uses operator generated input variables that produce output control signals. These signals are then used to actually control the logic specified in the truth table. For the circuit to work properly when two input variables are true two corresponding output signals will latch a warning light otherwise the condition will be false and the light will be off. In the event all three input variables are true an alert will broadcast letting the operator know the switches are misconfigured. The logic will force all output signals off thereby preventing an unsafe condition.

Truth Table: X1 0 0 0 0 1 1 1 1

X2 0 0 1 1 0 0 1 1

X3 0 1 0 1 0 1 0 1

Y1 0 0 0 0 1 1 1 0

Y2 0 0 1 1 0 0 1 0

Y3 0 1 0 1 0 1 0 0

Warning 0 0 0 1 0 1 1 0

Alert 0 0 0 0 0 0 0 1

Warning: Product of Sum: W = (Y1 + Y2 + Y3) (Y1 + Y2 + Y3’) (Y1 + Y2’ + Y3) (Y1’ +Y2 + Y3) (Y1’ + Y2’ + Y3’) Simplified:

(Y2 + Y3)(Y1 + Y2)(Y1 + Y3) (Y1’ + Y2’ + Y3’) (Y1Y2Y3’) + (Y1Y2’Y3) + (Y1’Y2Y3)

Sum of Product: W = (Y1’Y2Y3) + (Y1Y2’Y3) + (Y1Y2Y3’)

Alert: Product of Sum: A = (X1 + X2 + X3)(X1 + X2 + X3’)(X1 + X2’ + X3)(X1 + X2’ + X3’)(X1’ + X2 + X3)(X1’ + X2 +X3’) (X1’ +X2’ + X3) Simplified: Sum of Product: A = X1X2X3

(X1 + X2 +X3)

Circuit Diagram:

Questions: 1. Assuming that an output A already exists (but all other outputs do not), write expressions for {Y1, Y2, Y3, W} in terms of {X1, X2, X3 and A}. Do this using your common sense, a truth table solution is not required.

A = X1X2X3 Y1 = A’X1 Y2 = A’X2 Y3 = A’X3 W = A’[(X1X2) + (X2X3) + (X1X3)]

Q2. Draw a simplified circuit that obtains output signals {Y1, Y2, Y3, W, A} from input signals {X1, X2, X3} based on your results in Q1. You may choose to build this circuit instead of the one derived in M3 for demonstration purposes.

See above Circuit Diagram

It should be noted that in the circuit above the actual control of the lock is by the associated logic gate and not the operator. The operator is only needed to input the parameters that agree with the logic. If the parameters are misconfigured the logic of the network shuts off. This fail safe device embedded in the circuit prevents an illogical relationship in accordance with the parameters set-forth in the truth table. All this proves is that humans err, and the automation designed into the circuit is there to prevent it. In summation, the premise of this experiment was met and exceeded after the logic gates were reduced to their simplest form. Because logic gates contribute either a true or a false input a complex circuit with multiple variables can be simplified by using Boolean algebraic manipulation. This approach is minimalistic yet efficient when designing circuits. When the redundant logic is eliminated from the network a proportional decrease in size and power use will be the effect. This methodology is invaluable when designing the most cost effective yet efficient product giving the desired specifications. The switching of the logic from human controlled to circuit controlled is so irreplaceable that the main principles learned during the course of this laboratory will be expounded upon for future use as the technology becomes more capable. As of now the quality is determined by the needs of the network which impart the main objective of this experiment....