Problem Background Information: Gray code is an alternate form of binary where only one bit changes at a time. This can be useful when trying to measure a binary signal in the real world. Take, for...

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Problem Background Information: Gray code is an alternate form of binary where only one bit changes at a time. This can be useful when trying to measure a binary signal in the real world. Take, for instance, a rotary position encoder. The encoder is comprised of some sort of sensor (optical in many cases) and a disk that contains an encoding. The disk is partitioned into separate slices (kind of like a pie being cut into slices). Each slice has a binary code that radiates out from the center. The coloring of the pattern represents the value of that position. For instance, a dark band may represent a '1' and a light band may represent a '0'. The disk is rotated past an array of sensors. A separate sensor is used to read each bit of the position encoding. If a normal binary pattern is used to encode the position, small displacements in position between the sensors can cause the position to be misread. If a gray code is used, the position cannot be misread since only one bit changes at a time.

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Answered Same Day Dec 24, 2021

Solution

David answered on Dec 24 2021

129 Votes

Solution:
a)
Truth Table:
B3 B2 B1 B0 G3 G2 G1 G0
0 0 0 0 1 0 0 0
0 0 0 1 1 0 0 1
0 0 1 0 1 0 1 1
0 0 1 1 1 0 1 0
0 1 0 0 1 1 1 0
0 1 0 1 1 1 1 1
0 1 1 0 1 1 0 1
0 1 1 1 1 1 0 0
1 0 0 0 0 1 0 0
1 0 0 1 0 1 0 1
1 0 1 0 0 1 1 1
1 0 1 1 0 1 1 0
1 1 0 0 0 0 1 0
1 1 0 1 0 0 1 1
1 1 1 0 0 0 0 1...

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Problem Background Information: Gray code is an alternate form of binary where only one bit changes at a time. This can be useful when trying to measure a binary signal in the real world. Take, for...

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