15. Draw the nonabbreviated logic diagram for the following Boolean expressions. You may use XOR gates.
*

(a) ((a′)′)′
*

(b) (((a′)′)′)′

(c) a′b + ab′

(d) ab + a′b′

(e) ab + ab′ + a′b

(f) ((ab ⊕ b′)′ + a′b)′
(g) (a′bc + a)b (h) (ab′c)′(ac)′
(i) ((ab)′(b′c)′ + a′b′c′)′
(j) (a ⊕ b + b′⊕ c′)′
(k) (abc)′ + (a′b′c′)′
(l) (a + b)(a′ + c)(b′ + c′)
(m) (a ⊕

b) ⊕ c + ab′c (n) (((a + b)′ + c)′ + d)′
(o) (ab′ + b′c + cd)′
(p) ((a + b′)(b′ + c)(c + d))′
(q) (((ab)′c)′d)′
(r) (((a ⊕ b)′⊕ c)′⊕ d)′