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 $7$-segment display.
- If no buttons are pressed, $’0’$ is displayed, signifying 'Rs. $0$'.
- If only $P_{1}$ is pressed, $’2’$ is displayed, signifying 'Rs. $2$'.
- If only $P_{2}$ is pressed, $’5’$ is displayed, signifying 'Rs. $5$'.
- If both $P_{1}$ and $P_{2}$ are pressed, ' $\mathrm{E}$ ' is displayed, signifying 'Error'.
The names of the segments in the $7$-segment display, and the glow of the display for $\text{‘0’, ‘2’, ‘5’}$ and $\text{‘E’},$ are shown below.
Consider
- push button pressed/not pressed is equivalent to logic $1 / 0$ respectively,
- a segment glowing / not glowing in the display is equivalent to logic $1 / 0$ respectively.
What are the minimum numbers of NOT gates and $2$-input OR gates required to design the logic of the driver for this $7$-segment display?
- $3$ NOT and $4$ OR
- $2$ NOT and $4$ OR
- $1$ NOT and $3$ OR
- $2$ NOT and $3$ OR