Homeworks
for E2011
1 Problem 1
Prove de Morgan’s laws,
X + Y = X Y
XY = X + Y
using truth tables and set theory.
2 Problem 2
Given the logic circuit below, find the implemented function, simplify it and reimplement the simplified
form.
3 Problem 3
Let [ai], i = 1, . . . , N, N ≥ 3 be a real-valued vector. Write the pseudocode to
• let the user input the values for [ai]
• compute a new vector [si] defined as
si =
0 i ∈ {1, N}
ai+1−ai−1
2 0 < i < N
,
• display (output) the result
1
4 Problem 4
Consider a polynomial of degree n specified by its coefficients a0, a1, . . . , an, P(X) = anXn
+
an−1Xn−1
+ · · · + a1X + a0. Write the pseudocode for computing P(x) for any given x ∈ R and for
computing P′
(x) where P′
is the first derivative of P.
2