What common function does the following truth table represent?
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A B C X Y Z
0 0 0 → 0 0 0
0 0 1 → 0 0 1
0 1 0 → 0 1 0
0 1 1 → 0 0 1
1 0 0 → 1 0 0
1 0 1 → 0 0 1
1 1 0 → 0 1 0
1 1 1 → 0 0 1
The truth table implements a form of priority encoder:
- Z is set if C is set, otherwise
- Y is set if B is set, otherwise
- X is set if A is set
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In other words, C has the highest priority and A has the lowest. However, unlike conventional priority encoders that produce a binary output, this one produces a “one hot” encoding.
The logic is quite straightforward:
- Z = C
- Y = B & !C
- X = A & !B & !C
