91Ó°ÊÓ

How many constant boolean functions can be defined from \(B^{n}\) to \(B\) with \(B\) a two-element boolean algebra?

When will the combinatorial circuit for each boolean expression produce 1 as the output? $$x y$$

Compute the NAND gate output from inputing each pair of bits. $$0,1$$

Simplify the boolean expression represented by each Karnaugh map. $$\begin{aligned}&\begin{array}{lllll}\qquad yz \quad y z^{\prime} \quad y^{\prime} z^{\prime}\quad y^{\prime}z \end{array} \\ &\begin{array}{lllll}wx \\\ wx^{\prime} \\ w^{\prime} x^{\prime}\\\ w^{\prime} x\end{array} \quad\begin{array}{|l|l|l|l|} \hline 1 & d & & \\ \hline d & 1 & & \\ \hline & & d & d \\ \hline & & 1 & 1 \\ \hline \end{array}\end{aligned}$$

Find the number of boolean functions that can be defined from \(B^{n}\) to \(B,\) where \(B\) is a two-element boolean algebra.

Using Example \(12.2,\) evaluate each. $$(2+3) + 5$$

Simplify each boolean expression using the laws of boolean algebra. $$x y+x y^{\prime}+x^{\prime} y^{\prime}$$

Simplify each boolean expression using the laws of boolean algebra. $$x^{\prime} y z+x^{\prime} y^{\prime} z^{\prime}+x^{\prime} y z^{\prime}+x^{\prime} y^{\prime} z$$

Simplify the boolean expression represented by each Karnaugh map. $$\begin{aligned}&\begin{array}{lllll}\qquad yz \quad y z^{\prime} \quad y^{\prime} z^{\prime}\quad y^{\prime}z \end{array} \\ &\begin{array}{lllll}wx \\\ wx^{\prime} \\ w^{\prime} x^{\prime}\\\ w^{\prime} x\end{array} \quad\begin{array}{|c|c|c|c|} \hline d & 1 & 1 & 1 \\ \hline & & & \\ \hline & & & d \\ \hline 1 & & 1 & d \\ \hline \end{array}\end{aligned}$$

Determine if each is a boolean expression, where each variable is boolean. $$\left(\left(x y^{\prime}\right)^{\prime}\right)^{\prime}$$