Tutorial 1

Universal Gates

$$\begin{array}{r}\overline{AB}=\bar{A}+\bar{B}\\ AB=\overline{\bar{A}+\bar{B}}\end{array}$$

Q1

$$\begin{array}{rl}Q=AB+(B+C)\cdot (BC)& =AB+BBC+CBC\\ & =AB+BC+CB\\ & =AB+BC\\ & =B(A+C)\end{array}$$

Q2

Q3

$$\begin{array}{rl}AB+\overline{AB}CD+\overline{CD}EF& =(AB+\overline{AB})(AB+CD)+\overline{CD}EF\\ & =AB+CD+\overline{CD}EF\\ & =AB+(CD+\overline{CD})(CD+EF)\\ & =AB+CD+EF\end{array}$$

X/YZ	00	01	11	10
0		1	1	1
1	1	1	1	1