Question 25.SG.Q.8: If segments a to g are considered as functions of P1 and P2 ......
Statement for Linked Answer Questions 8 and 9: Two products are sold from a vending machine, which has two push buttons P_1 and P_2 . When a button is pressed, the price of the corresponding product is displayed in a seven-segment display. If no buttons are pressed, `0’ is displayed, signifying ` ₹0 ’. If only P_1 is pressed, `2’ is displayed, signifying ` ₹2’. If only P_2 is pressed, `5’ is displayed, signifying ` ₹5’. If both P_1 and P_2 are pressed, `E ’ is displayed, signifying `Error’. The names of the segments in the seven-segment display, and the glow of the display for `0’, `2’, `5’ and `E ’ are shown in the following figure.
Consider
i. Push button pressed/not pressed is equivalent to logic 1/0, respectively.
ii. A segment glowing/not glowing in the display is equivalent to logic 1/0, respectively.
If segments a to g are considered as functions of P_1 and P_2 , then which of the following is correct?
(a) g = \bar{P_1} + P_2, d = c +e
(b) g = P_1 + P_2, d = c +e
(c) g = \bar{P_1} + P_2, e = b + c,
(d) g = P_1 + P_2, e = b + c
The truth table can be drawn as follows:
\begin{array}{ccccccccc} \hline P_1 & P_2 & a & b & c & d & e & f & g \\ \hline 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 \\ 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 & 1 \\ 1 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 \\ \hline \end{array}
From the truth table, we can write the simplified Boolean functions for a, b, c, d, e, f and g as follows:
\begin{aligned} & a=1 \\ & b=\bar{P}_2 \\ & c=\bar{P}_1 \\ & d=1 \\ & e=P_1+\bar{P}_2 \\ & f=\bar{P}_1+P_2 \\ & g=P_1+P_2 \end{aligned}
From the above expressions, we get
c + e = 1 = d
and hence the answer.
Ans. (b)