How can Y=(A+B)·C be implemented only from NAND gates?
This is shown in Fig. 1.21.
Show that the distributive laws: A·(B+C)=A·B+A·C and A+(B·C)=(A+B)·(A+C) are duals.
Draw the circuits that will perform the functions described by both sides of the first of De Morgan’s theorems (Equation 1.16) given in Table 1.4, and also demonstrate the theorem is true using a truth table.
What type of expression is Y=(A+B)·(A+B), what sum terms are included in it, and what is its expanded form?
Use De Morgan’s theorem to express Y= A+B, the OR operation, in a different form.
Use Boolean algebra and de Morgan’s theorem for two variables, A + B=A· B, to show that the form given in Equation 1.16 for three variables is also true.
How can an AND gate be implemented from NOR gates?
The courtesy light of a car must go off when the door is closed and the light switch is off. What gate is required to implement this and what is the alternative way of looking at this circuit?
A circuit is needed to give an output of 1 when any of its three inputs are 0. Draw the truth table for this circuit and state what single gate could implement this circuit. Then derive its dual and state which gives the most appropriate desription of the circuit’s operation.
Draw a NAND gate and its dual and describe their outputs in terms of assertion level logic.
Draw the circuit for Y=A·(B+C) and produce alternative representations of it using only a three-input AND and three-input OR gate (assuming NOT gates are also available). Also obtain the same expressions using Boolean algebra, and write out the truth table of these functions.