Chapter B, Problem 43E

Explanation of Solution

• The above diagram describes about the graphical representation of the traffic lights and their codes 00 for red light, 01 and 11 for green light and 10 for yellow light with the time t.
• Firstly, red light is activated and sends the signal to the green light and then to the yellow light and the process continues till the occurrence of any disturbance.
• Here, the mealy method is used to represent the graphical diagram because it is easy to understand and implement.
• The states and their numbers can be known and assigned to the finite state machine.
• The lights are propagated only when the signals are passed and vice versa.

Truth table:

Input			Output
A	B	C		Y1	Y2
0	0	0		0	0
0	0	1		1	1
0	1	0		0	0
0	1	1		1	1
1	0	0		0	1
1	0	1		0	1
1	1	0		1	0
1	1	1		1	0

The above truth table describes about the logic equations of the inputs and outputs. It includes the inputs namely A, B and C and outputs namely, Y₁ and Y₂. The values of the output Y₁ are obtained by using the equation AB= Y₁ and the values of the output Y₂ are obtained by following the equation BC= Y₂.

The logic equations for the outputs Y₁ and Y₂ are calculated as follows

$\begin{array}{c}{\text{Y}}_{\text{1}}\text{=}\overline{\text{A}}\overline{\text{B}}\text{C}\text{+}\overline{\text{A}}\text{BC}\text{+}\text{AB}\overline{\text{C}}\text{+}\text{ABC}\\ \text{=}\text{A(}\overline{\text{B}}\end{array}$