What is the minterm notation for the following function? – f(a,b,c) = abc+a'bc+abc'+a'b'c

Question

Design a controller of the parking meter. The controller has two inputs, C and B. C is a one-bit input
from the car detector. If there is a car in the parking spot, C = 1, otherwise C = 0. B is a two-bit input from the money
receiver. If B = 00, no money is dropped into the money receiver. If B = 01, five yuan is dropped. If B = 10, ten yuan
is dropped. B = 11 is an invalid input. The outputs of the controller are R, G, A. R connects to a red light, G connects
to a green light, and A connects to an alarm.
The controller works in a way like this: Initially, no car is in the parking spot, green light is on, red light and
alarm are off. Once a car drives into the spot, the green light turns off, red light turns on, alarm keeps off. If the driver
pays enough money (15 yuan), the green light turns on, red light keeps on, alarm keeps off. If the car leaves without
paying correct parking fee, the red light turns off, the green light turns on, the alarm turns on until the next car drives
in. If the car leaves with correct parking fee paid, the alarm and red light are off, the green light is on.

Answer 1

Paul,

 

This is similar to a traffic light project I did in a digital design class in college at MIT that took two weeks! Nevertheless, here is the way to approach this. You want to express R, G and A as functions of B and C. There's one small catch though: the way that B is defined, you'll need one more state to show when 15 yuan has been paid. Can you check the assignment again?  That will help us define A. I'm just going to assume that B goes back to '00 when the correct amount of money has been paid.

 

At the rate it goes, here is the function:

First the light is green if there isn't a car or the meter's been paid

G=not(C) or nand(B)

The light is red if there's a car and the meter hasn't been paid

R=C and or(B)

The alarm triggers when the meter hasn't been paid and the car's left.

A=not(C) and or(B)

 

This is easier to draw in LaTex but that's just my two cents.

 

Deanna