5-7. Write the Boolean equation for the circuits of Figure P5-7. Simplify the equations, and draw the simplified logic circuit.
5-9. Draw the logic circuit for the following equations. Simplify the equations, and draw the simplified logic circuit.
(a) V = AC + ACD + CD
(b) W = (BCD + C)CD
(c) X = (B + D) (A + C) + ABD
(d) y = AB + BC + ABC
(e) Z = ABC + CD + CDE
5-10. Construct a truth table for each of the simplified equations of Problem 5-9.
5-15. Which two circuits in figure P5-15 produce equivalent output equations?
5-17. Draw the logic circuit for the following equations. Apply De Mor-gan's theorem and Boolean algebra rules to reduce them to equations hav¬ing inversion bars over single variables only. Draw the simplified circuit.
(a) W = AB + A + C
(b) X = AB + C + BC
(c) Y = (AB) + C ± BC
(d) Z = AB + (A + C)
5-27. Complete a truth table for the following simplified Boolean equat
(a) W = AB C + BC + AB
(b) X = A B + ABC + BC
(c) Y = t'D + AB CD + BCD + AC75
(d) Z = A- BCD + AC + CD + BC
5-31. Draw the connections required to convert
(a) A NAND gate into an inverter
(b) A NOR gate into an inverter
5-32. Draw the connections required to construct
(a) An OR gate from two NOR gates
(b) An AND gate from two NAND gates
(c) An AND gate fi-:)m v--:veral NOR gates
(d) A NOR gate from .;:eviral NAND gates
5-35. Identify each of the following Boolean equations as a POS expression, a SOP expression, or both.
(a) U = + BC + AC
(b) V = (A + C)(T3 + CT)
(c) W = AC(ii + C)
(d) X = AB + C + BD
(e) Y = (AB + D) (A + CD)
ka./ c. - 11 LA a-- 1. LA 1/4_, I MLA le I CI LI
5-38. Using mum form in a Karnaugh map, reduce the following equations to a mini-
(a) W = B(CD + AD) -':- BC(A + A D)
(b) X = ABD + B(CP + ACT)) + ABb
(c) Y = A(CD + C D) 1. ABD + A BCD
(d) Z = WED + BCD + C b + Cb(B + A T3)