A greenhouse irrigation controller has four digital inputs
PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Digital electronics, embedded systems and data acquisition · Digital electronics, embedded systems and data acquisition
Electronics for Measurement, Ch Digital logic and its physical realisation
Problem
A greenhouse irrigation controller has four digital inputs, each equal to 1 when its stated condition holds and 0 otherwise: D (the soil moisture sensor reads dry), T (the daylight sensor indicates daytime), M (the attendant's manual override switch is pressed), E (the tank-level sensor reads empty). The pump output P must switch on whenever the soil is dry during daytime, or whenever the override is pressed, but the tank-empty signal must force the pump off regardless of every other input.
((a)) Write the Boolean expression for P in terms of D, T, M, E. Check it against the truth-table rows D=1,T=1,M=0,E=0 and D=0,T=0,M=1,E=1.
((b)) Use De Morgan's laws to redraw the circuit for P using two-input NAND gates alone, reusing any intermediate signal that already equals a complement a later step needs rather than building it twice. State the total number of NAND gates used.
((c)) Every rising edge of P is counted on a 3-bit synchronous binary counter with outputs Q2Q1Q0 (Q0 least significant), which starts at 000 and increments by one on each clean rising edge of P. Tabulate Q2Q1Q0 after each of the first five rising edges of P, and give the count in decimal after the fifth edge.