91Ó°ÊÓ

Show that the set of gates \\{OR, NOT\\} is functionally complete.

Find the disjunctive normal form of each function and draw the combinatorial circuit corresponding to the disjunctive normal form. $$\begin{array}{ccc|c}\hline x & y & z & f(x, y, z) \\\\\hline 1 & 1 & 1 & 1 \\\1 & 1 & 0 & 1 \\\1 & 0 & 1 & 0 \\\1 & 0 & 0 & 1 \\\0 & 1 & 1 & 0 \\\0 & 1 & 0 & 0 \\\0 & 0 & 1 & 1 \\\0 & 0 & 0 & 1 \\\\\hline\end{array}$$

Prove or disprove the equations. $$ \overline{\bar{x}}=x $$

Design a half-adder circuit using five NAND gates.

How many Boolean functions are there from \(Z_{2}^{n}\) into \(Z_{2}\) ?

Design a half-adder circuit using only NOR gates.

Design a half-adder circuit using five NOR gates.

Design a circuit with three inputs that outputs 1 precisely when two or three inputs have value \(1 .\)