For the following sets of functions, design a system
i. using a rom
ii. using a pla with the number of product terms shown
iii. using a pal

a. f(a, b,c, d) = σm(1,2,6,7,8,9,12,13)
g(a, b,c, d) = σm(1,8,9,10,11,13,15)
h(a, b,c, d) = σm(1,6,7,8,11,12,14,15)

b. w(a, b, c) = σm(0, 1, 4)
x(a, b, c)= σm(0, 3, 4, 7)
y(a, b, c) = σm(l, 2, 6)
z(a, b, c)= σ(2, 3, 6, 7)

c. f(a, b, c, d)= σm(5, 6, 7, 8, 11,13, 14,15)
g(a, b, c, d)= σm(0, 1, 5, 6, 8, 9, 11,13, 14)

d. f(a, b, c)= σm(1, 2, 6, 7, 8, 9, 12, 13)
g(a, b, c, d)= σm(l, 8, 9, 10, 11, 13, 15)
h(a, b, c, d) =σm(6, 7, 8,11, 12,14, 15)