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Q$1.7-$segment LED displays are a very important part of any digital system. For example, for

showing which floor a lift is currently present. Imagine a building with $7$ floors, $1$ ground floor and

$8$ basement floors. To keep the arithmetic simple, the building management system uses $2\text{'}$s

complement binary system of appropriate bit length to store the floor number of the lift $($positive for

floors above ground, $0$ for ground floor and negative for basement floors$).$ For the lift display, we

decide to denote the ground floor as $"0"$ on the $7-$segment display. For floors above the ground floor,

we display the floor number with a $"+"$ sign, and in case of basement floors, we display the floor

number with a $"-"$ sign. We are able to do this using a $2-$segment LED display in front of the $7-$

segment display, as shown in the figure below. Also, just to keep the aesthetics, we decide that when

$"0"$ is displayed, we will keep the $2-$segment display off, because $"+0"$ or $"-0"$ looks weird! Your job

is to design a circuit that takes input from the building management system about the floor number

of the lift, and displays it using the lift display. You can assume that you already have $7447$ decoder

ICs $($BCD to $7-$segment decoder$)$ with you, so you can denote it as a black box. Don't worry about

optimizing the transistor count or the timing.