The rear lights of a car are to be controlled by digital logic. There is a single lamp in...

(a)

Consider that, \(B R\) overrides EM. \(L T\) and \(R T\) override \(B R\).

It is already known that, EM(Emergency Lights) triggers \(B L\) (Blinking light) and both \(L T\) and \(R T\) also trigger \(B L\).

The equation for both \(L R\) and \(R R\) are derived as follows:

- As EM triggers \(B L\), the expression is: \(E M \cdot B L\)

For left lamp LR :

- As \(L T\) triggers \(B L\), the expression is: \(L T . B L\)

- As \(L T\) overrides \(B R\), the expression is: \(\overline{L T} \cdot B R\)

For right lamp RR :

- As \(R T\) triggers \(B L\), the expression is: \(R T . B L\)

- As \(R T\) overrides \(B R\), the expression is: \(\overline{R T} . B R\)

On combining all the expressions of \(L R\) with expression of emergency flasher the equation of \(L R\) is obtained as follows:

\(L R=E M . B L+L T . B L+\overline{L T} . B R\)

On combining all the expressions of \(R R\) with expression of emergency flasher the equation of \(R R\) is obtained as follows:

\(R R=E M . B L+R T . B L+\overline{R T}, B R\)

(b)

To implement each function, we first must make a truth table of all possible combinations for both LR and RR.

Using LT , EM , RR , and BL as inputs the truth tables for both LR and RR are as follows:

Truth table for LR :

Truth table for RR :

Now, directly apply the truth values of LR and RR to the 4x16 decoder. The outputs of the decoder will be wired into OR gates to output LR and RR.

The logic diagram for output LR is as follows:

The logic diagram for output RR is as follows: