Chapter B, Problem 38E

Explanation of Solution

Finite-state machine:

Explanation:

• The above diagram describes about the graphical representation of electronic eye. 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 intensity of the light depends on the time and the signals of electronic eye depend on the input value.

Truth table:

Input State			Output State
S0	S1	S2		X	X’
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

Explanation:

• The table describes about the working of electronic eye with the inputs S₀, S₁ and S₂ and the outputs X and X’.
• By comparing the inputs S₀ and S₁, the output X is obtained and by comparing the inputs S₁ and S₂, the output X’ is obtained.
• With consideration of the above values, it can be concluded that left light has the values 00 and 11, middle light has the value 01 and the right light has the value 10.

The logic equations for the outputs X and X’ can be written as follows

$\begin{array}{c}\text{X}\text{=}\overline{{\text{S}}_{\text{0}}}\overline{{\text{S}}_{\text{1}}}\text{+}\overline{{\text{S}}_{\text{0}}}{\text{S}}_{\text{1}}{\text{S}}_{\text{2}}\text{+}{\text{S}}_{\text{0}}{\text{S}}_{\text{1}}\overline{{\text{S}}_{\text{2}}}\text{+}{\text{S}}_{\text{0}}{\text{S}}_{\text{1}}{\text{S}}_{\text{2}}\\ \text{=}\overline{{\text{S}}_{\text{0}}}{\text{S}}_{\text{2}}\text{(}\overline{{\text{S}}_{\text{1}}}\cdot {\text{S}}_{\text{1}}\text{)}\text{+}{\text{S}}_{\text{0}}{\text{S}}_{\text{1}}\text{(}\overline{{\text{S}}_{\text{2}}}\cdot {\text{S}}_{\text{2}}\text{)}\\ \text{=}\end{array}$