. As stated in Sect. 3.5.2, one important property which makes DES secure is that the S-boxes are nonlinear. In this problem we verify this property by computing the output of S1 for several pairs of inputs. Show that S1(x1)⊕S1(x2) = S1(x1 ⊕x2), where “⊕” denotes bitwise XOR, for: 1. x1 = 000000, x2 = 000001 I KNOW THAT THE ANSWER IS   11102⊕00002≠S1(0000012) 11102≠00002 CAN SOMEONE EXPLAIN HOW DO WE GET THIS NUMBERS? Ty!

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A:

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A:

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A: Proved the given language is not  regular

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Q: need mAtlab code of b partt.  Thank you

A: I have done the Matlab question below:

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Q: The truth table shown may ABCIF 0 0 | 0 1 D 1 1 1 0 0 | 1

A: 0 in rows 1,4,5,and 7 which leads to the canonical expression F = PRD M(1,4,5,7).

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A:

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Disjoint set forest

The concept of the disjoint set forest was introduced by Bernard A. Galler and Michael J. Fischer in 1964. The disjoint set forest is a method of implementing disjoint sets quickly. In the disjoint-set forest, each tree member points only to its parent. The root of every tree includes its representative and its parent. The disjoint set forest is a special kind of forest that performs Union and Find operations in near-constant amortized time.