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1.X = AB

A B AB 0 0 0 0 1 0 1 0 0 1 1 1

AND means that only when all situations are ture will the result be ture.

2.X = A OR B

A A A OR B 0 0 0 0 1 1 1 0 1 1 1 0

XOR means that if both two events are ture or fauls , the output will be false, or the output will be ture.

3.

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4.

A B A’ AB AB OR A’ 0 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0 0 1

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5.
(AB)’:

A B AB (AB)’ 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0

A’+B’:

A B A’ B’ A’+B’ 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 1 1 0 0 0

so (AB)’ = A’+B’

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6.

7.
i. (X₈X₇X₆X₅1111)₂

ii.(X₈X₇X₆X₅X’₄X’₃X’₂X’₁)₂

iii.
(X₈X₇X₆X₅X’₄X’₃X’₂X’₁)₂