of University Illinois at Chicago Department of Electrical and Computer Engineering ECE 265 - Introduction to Logic Design Summer 2005 Semester
Lab Experiment #4 Simplification of Boolean Functions Using "Don't Care" Conditions
Introduction The diagram below depicts an automobile in an automatic car wash, beginning a wash sequence as it is slowly being pulled through. When the auto first enters Area 1, Sensor 1 detects its presence causing soapy water to be applied by rotating scrubbers. When the auto leaves Area 1, Sensor 1 is no longer activated causing that function to be turned off. Similarly, Sensors 2 through 4 control the other three car washing functions as the auto is pulled through the corresponding areas.
Area 1: Soap Scrub
Area 2: Water Rinse
Area 3: Hot Wax
Area 4: Air Dry
Sensor 1
Sensor 2
Sensor 3
Sensor 4
Input/Output Control Signals Binary variables {S1, S2, S3, S4} are the outputs of Sensors 1 through 4 ( = 1 when the auto is above the sensor, and otherwise = 0). You will simulate these signals using switches, and they will serve as input variables to the circuit that you will design. Binary variables {C1, C2, C3, C4} control the car wash functions. These signals are the outputs of a digital circuit that you will design. For each of these control signals logical "1" activates the corresponding car wash function to be ON, and logical "0" turns the function OFF.
2005
V. Goncharoff
University of Illinois at Chicago
ECE 265 Experiment #4
(page 1/3)
Your task will be to design digital logic circuits that accept input signals {S1, S2, S3, S4} and produce output signals {C1, C2, C3, C4} according to certain design specifications. Method 1 This circuit should produce Ck = Sk (k=1 through 4), with the following exception: As an automobile crosses the boundary between adjacent car wash areas, it is possible that two sensors are simultaneously activated. To prevent any interference between different washing operations, turn off all car wash functions {make C1 = C2 = C3 = C4 = 0} whenever any two adjacent sensor outputs are high. Method 2 Same specifications as in Method 1, except: Make C1 = C2 = C3 = C4 = X (don't care) for any row where any two nonadjacent sensor outputs are high. This to corresponds sensor states that should never occur when a single car is being washed.
Choose the method resulting in fewest gates, build the circuit and demonstrate it to your T.A. Show what happens when (a) only one sensor is high; (b) exactly two adjacent sensors are high, and (c) exactly two non-adjacent sensors are high.
2005
V. Goncharoff
University of Illinois at Chicago
ECE 265 Experiment #4
(page 2/3)
Lab report: The lab report should be neatly written (preferably printed) on clean, stapled sheets of paper. Cover Page (containing the course/lab title, date, your name and signature) Purpose (state the goal of performing this experiment -- i.e. what is intended for the student to learn) Design Method For each of the two methods: State and explain the design specifications (why they make sense) Write a truth table for each output variable {C1, C2, C3, C4} as a function of input variables {S1, S2, S3, S4} Find expressions for each output variable {C1, C2, C3, C4} in canonical SOP and canonical POS forms. Draw K-maps and arrive at simplest expressions for {C1, C2, C3, C4} in SOP form. Draw K-maps and arrive at simplest expressions for {C1, C2, C3, C4} in POS form. Design a digital circuit to compute output variables from input variables having the minimum number of gates. Neatly draw and label a schematic diagram of the circuit....