Question

An engine operates with four essential variables controlling its operation. For the engine to be operating properly, at least two of its control variables must be present at the same time. However, when the machine is not operating correctly, we wish to have some signal to alert us to the problem. Design a circuit to implement the state when the alarm signal is present

Answer 1

An engine operates with four essential variables controlling its operation.

=> a,b,c,b are the variables

For the engine to be operating properly, at least two of its control variables must be present at the same time.

=> among a,b,c,d, if at least two variables are 1 then the system works fine (y)

However, when the machine is not operating correctly, we wish to have some signal to alert us to the problem.

=> signal is generated when none or one of the variables are one

=> negation of y

Design a circuit to implement the state when the alarm signal is present

Control signals	Output
a	b	c	d	y	y'
0	0	0	0	0	1
0	0	0	1	0	1
0	0	1	0	0	1
0	0	1	1	1	0
0	1	0	0	0	1
0	1	0	1	1	0
0	1	1	0	1	0
0	1	1	1	1	0
1	0	0	0	0	1
1	0	0	1	1	0
1	0	1	0	1	0
1	0	1	1	1	0
1	1	0	0	1	0
1	1	0	1	1	0
1	1	1	0	1	0
1	1	1	1	1	0

alarm will be generated whenever y' = 1

Using K-map (POS) we can find the expression

	c'd'	c'd	cd	cd'
a'b'	1	1	0	1
a'b	1	0	0	0
ab	0	0	0	0
ab'	1	0	0	0

y' = (a'c'd')+(a'b'c')+(a'b'd')+(b'c'd')