Expression Evaluation

Question

44. Evaluate each of these expressions.

a) 1 1000 ∧ (0 1011 ∨ 1 1011)

b) (0 1111 ∧ 1 0101) ∨ 0 1000

c) (0 1010 ⊕ 1 1011) ⊕ 0 1000

d) (1 1011 ∨ 0 1010) ∧ (1 0001 ∨ 1 1011)

Answer 1

In this we have to perform bitwise oprations like bitwise OR, bitwise AND, bitwise Ex-OR.

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a) 1 1000 ∧ (0 1011 ∨ 1 1011)

0 1011 ∨ 1 1011 = 1 1011

1 1000 $\wedge$ 1 1011 = 1 1000

So, 1 1000 ∧ (0 1011 ∨ 1 1011) = 1 1000

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b) (0 1111 ∧ 1 0101) ∨ 0 1000

0 1111 ∧ 1 0101 = 0 0101

0 0101 $\vee$ 0 1000 = 0 1101

So, (0 1111 ∧ 1 0101) ∨ 0 1000 = 0 1101

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c) (0 1010 ⊕ 1 1011) ⊕ 0 1000

0 1010 ⊕ 1 1011 = 1 0001

1 0001 ⊕ 0 1000 = 1 1001

So, (0 1010 ⊕ 1 1011) ⊕ 0 1000 = 1 1001

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d) (1 1011 ∨ 0 1010) ∧ (1 0001 ∨ 1 1011)

1 1011 ∨ 0 1010 = 1 1011

1 0001 ∨ 1 1011 = 1 1011

1 1011 $\wedge$ 1 1011 = 1 1011

So, (1 1011 ∨ 0 1010) ∧ (1 0001 ∨ 1 1011) = 1 1011

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