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plc boolean - 6.39<br />

4. Convert the truth table below to a Boolean equation, <strong>and</strong> then simplify it. The output is X <strong>and</strong><br />

the inputs are A, B, C <strong>and</strong> D.<br />

A<br />

B<br />

C<br />

D<br />

X<br />

0<br />

0<br />

0<br />

0<br />

0<br />

0<br />

0<br />

0<br />

1<br />

1<br />

1<br />

1<br />

1<br />

1<br />

1<br />

1<br />

0<br />

0<br />

0<br />

0<br />

1<br />

1<br />

1<br />

1<br />

0<br />

0<br />

0<br />

0<br />

1<br />

1<br />

1<br />

1<br />

0<br />

0<br />

1<br />

1<br />

0<br />

0<br />

1<br />

1<br />

0<br />

0<br />

1<br />

1<br />

0<br />

0<br />

1<br />

1<br />

0<br />

1<br />

0<br />

1<br />

0<br />

1<br />

0<br />

1<br />

0<br />

1<br />

0<br />

1<br />

0<br />

1<br />

0<br />

1<br />

0<br />

0<br />

0<br />

1<br />

0<br />

0<br />

0<br />

1<br />

0<br />

0<br />

0<br />

1<br />

1<br />

1<br />

1<br />

1<br />

5. Simplify the following Boolean equation. Convert both the unsimplified <strong>and</strong> simplified equations<br />

to ladder logic.<br />

X =<br />

( ABC) ( A + BC)

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