Barracks logic is built out of sleeping soldiers covered by electric blankets. Each blanket has a control switch with discrete control settings ranging in S-degree (Fahrenheit) intervals from 0 to SO degrees. The temperature of a soldier covered by one or more electric blankets will be the sum of the ambient temperature in the barracks plus the setting on the controller for each blanket. Each soldier has a preferred sleeping temperature, which varies from individual to individual but is always within the range of 60 to 80 degrees, inclusive. If a soldier's temperature departs from his preferred temperature, he will wake up once every minute and adjust the control by one 5-degree increment in the direction he would like his temperature to be modified (if he is cold, he will increase the setting on his control, and vice versa). He will continue these adjustments by S-degree increments until he once again reaches his preferred temperature (and goes to sleep) or runs out of settings (in which case he grumbles angrily in bed). If every soldier is allowed to control his own blanket, each will soon reach his preferred temperature and slide into nocturnal bliss (assuming a suitable ambient temperature). The interesting aspects of barracks logic result from switching the controls of the various blankets to different soldiers. Inputs to the system are accomplished by placing a few controls in the hands of outsiders, and outputs are read from the control settings of certain soldiers designated by the logic designer.
A. Draw the graph of output control setting vs. input control setting for a typical soldier in steady state. Assume an ambient temperature of 40 degrees. Mark your graph with good choices of the valid regions for the two logical values, the forbidden zone, and the noise margins. Let logical 0 be when a control is completely off and logical 1 be when the control is completely on (or at the highest setting).
B. List some sources of noise that justify the need for noise margins.
C. Even though it is the middle of February, a sudden warm spell raises the ambient temperature in our barracks logic system to 55 degrees. Sketch a new graph of output control setting vs. input control setting in the warmer barracks.
D. Over what range of ambient temperatures will barracks logic function reliably?
E. Does the following arrangement perform a useful function? What is it?
F. A model HOT-l electric blanket control can power 1200 W of blankets. A model HOT-BED electric blanket requires 275 W. What is the fanout of a HOTl? What might happen if this rating is exceeded? Is there more danger of exceeding the rating at an output value of logical 0 or logical l?
G. To create a system with multiple inputs, we allow several blankets to be placed over a single soldier. What is the maximum fanin possible in barracks logic if 170 degrees is the highest temperature a soldier can tolerate without his characteristics being permanently altered?
H. Show how to build a NOR gate and an AND gate in barracks logic.
I. Explain what causes rise time, fall time, and propagation delay in barracks logic. Give worst-case numerical values for each of these parameters for the barracks logic inverter. (Let rise time be the time from when an output leaves the valid logical 0 range until it enters the valid logical 1 range, and vice versa for fall time. For propagation delay, use the time from when the input switches to a valid logic level to the time when the output switches to a valid logic level.)