ELE 632 Lecture 12: BME632. February 9,2017 (5)

Implement the following multiple output combinational logic circuit using a 4 line to

16-line decoder: F1= ∑m (0, 1, 4, 7, 12, 14, 15) F3= ∑m (2, 3, 7, 8, 10)

 F2= ∑m (1, 3, 6, 9, 12) F4= ∑m (1, 3, 5)

Find y as a function of t if

y(0)=9,y′(0)=6.

Let
H = {f : R → R | f(x) = ax + b; a, b ∈ R; a > 0}.
H1 = {f : R → R | f(x) = ax; a ∈ R; a > 0}.
H2 = {f : R → R | f(x) = x + b; b ∈ R}.
(a) Prove that H1 and H2 are subgroups of H.
(b) Determine whether each is a normal subgroup of H.