A shaft position encoder has 4 output. The outputs corresponding to each position are given in the table below. It is desired to design a circuit that shaft position between 0 and 210° → the output f=1 at the other position →f=0 The values not determined by the shaft position will be taken as 0. a) Fill the truth table. b) Reduce the output function as sum of minterms using Karnaugh map. c) Realize this function using logic gates. Shaft position 0° -30 30° -60° 60°-90° 90° 120 150 120° 180 - 210 210 - 240° 240 - 270 270-300 - 330⁰ XOOOOOOHHH OOOOHHOH 300 330 - 360 X1 X2 X3 X4 0 0 0 150 - 180° 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 OOOOOO 1 1 1 0 1 0 1 0 10 0 0 1 1 1 0 OOP C 1 1 1 OH 0 1 1 0 1 X1 X₂ X3 X4 f 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 ·lolo 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1
A shaft position encoder has 4 output. The outputs corresponding to each position are given in the table below. It is desired to design a circuit that shaft position between 0 and 210° → the output f=1 at the other position →f=0 The values not determined by the shaft position will be taken as 0. a) Fill the truth table. b) Reduce the output function as sum of minterms using Karnaugh map. c) Realize this function using logic gates. Shaft position 0° -30 30° -60° 60°-90° 90° 120 150 120° 180 - 210 210 - 240° 240 - 270 270-300 - 330⁰ XOOOOOOHHH OOOOHHOH 300 330 - 360 X1 X2 X3 X4 0 0 0 150 - 180° 0 0 0 1 1 1 0 0 1 1 0 1 0 0 1 1 0 0 0 OOOOOO 1 1 1 0 1 0 1 0 10 0 0 1 1 1 0 OOP C 1 1 1 OH 0 1 1 0 1 X1 X₂ X3 X4 f 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 ·lolo 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Question
A shaft position encoder has 4 output. The outputs corresponding to each position are given in the
table below. It is desired to design a circuit that
shaft position between and → the output f=1
at the other position → f=0
The values not determined by the shaft position will be taken as 0.
a) Fill the truth table.
b) Reduce the output function as sum of minterms using Karnaugh map.
c) Realize this function using logic gates.
Transcribed Image Text:A shaft position encoder has 4 output. The outputs corresponding to each position are given in the
table below. It is desired to design a circuit that
shaft position between 0 and 210° → the output f=1
at the other position → f-0
The values not determined by the shaft position will be taken as 0.
a) Fill the truth table.
b) Reduce the output function as sum of minterms using Karnaugh map.
c) Realize this function using logic gates.
Shaft position
0° -30°
30° -60°
60° - 90°
90°
120°
120 150
150 - 180°
180 - 210
210° - 240°
240 - 270
270-300
- 330°
300
330 - 360
X1X2 X3 X4
0
0
OOHOOOOHHH
OOOOHHOH
0
0
1
1
1
0
0
0
1
0
1
1
0 1
0
0
1 0
OOOOOOH
1
1
0
1
0
0 1
0
1 0
1
10
0
0
1
0
1
1
OOP C
0
1
1
OH
0
1
1
0
1
X1 X₂ X3 X4 f
0
0
0 0
0
0
0 1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0 1
0
0
1
1
1
0
1
0
1
1
0 1
0
1
0
1
1
1 1
0
0
1
1
0
1
1
1
1 0
1
1 1
1
·lolo
0
0
OO
0
1
1
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