Question

You are working for a World Logic Corporation, your manager have assigned you to a task to design a digital hardware associated with the user interface of a portable tourist guidance device. All input and output signals are described by the following table in the user specification. Signal Type Input Input Description '1' when the main ON button is pressed; else 'O' '1' when the UP arrow button is pressed; else 'O '1' when DOWN arrow button is pressed; else '0' '1' when the device screen light is turned on; else 'O’ '1' when a screenshot (picture) is taken and stored; else Input Output Output S "O The user specification further describes the relationship between inputs and outputs: The main ON button (P) turns on the screen light (L), unless any other button is also pressed simultaneously with it. Pressing UP (U) and DOWN (D) arrow buttons together turns ON the screen light (L) if the ON button (P) is not pressed. Pressing any single input button other than the main ON button (P) does not affect any of the given outputs due to the firmware running on the tourist guidance device. Similarly, the two cases when all three inputs are pressed together and when none of the inputs are pressed are handled by firmware separately. Hence, you do not need to care about these combinations. Pressing the ON button (P) simultaneously with either of the DOWN (D) or UP (U) arrow buttons takes a screenshot (S); otherwise screenshot is OFF. The screen light is turned OFF when a screenshot is taken, to save instantaneous power. a.(12 pts.) Show the truth table that corresponds to the problem description (remember to identify any don't care cases that may exist.) b. (8 pts.) Use Karnaugh maps to derive minimal POS expressions for both outputs. C. (4 pts.) Draw the logic diagram of your implementation.

Answer 1

a)- There are 4 don't care cases here due to which the two ouputs dont have any impact. They are being listed as (X) against the respective input combinations in the truth table below.

P	U	D	L	S
0	0	0	X	X
0	0	1	X	X
0	1	0	X	X
0	1	1	1	0
1	0	0	1	0
1	0	1	0	1
1	1	0	0	1
1	1	1	X	X

b)- From the above truth table, the POS expression of Max terms for the two outputs L and S are given by

$L=(\bar{P}+U+\bar{D})(\bar{P}+\bar{U}+D)=\Pi M(5,6)+d(0,1,2,7)$

$S=(\bar{P}+U+{D})({P}+\bar{U}+\bar{D})=\Pi M(3,4)+d(0,1,2,7)$

On using the K-maps for further minimization, the minimal POS expression for the two outputs upon also using the don't care terms for simplification are-

$L=(D+\bar{U})(\bar{P}+\bar{D})$

S= (D+U) (P+D)

o poo, ol, 11, 10, A 0%, s=( + D) (P+ D) 1 x d

c)- The logic diagram of this implementation is shown below.

PIUIDI