HW3: Problem 4 (1 point) Write the Boolean expression that...

HW3: Problem 4 (1 point) Write the Boolean expression that corresponds to the output of the following circuits: X y Z Instructions for entering Boolean expressions: to make it easier to enter Boolean expressions, please use the prime symbol for complement. For example, $\bar{x}\bar{y}$ can be entered as x'y', while $\bar{xy}$ can be entered as (xy)'.

Derive the Boolean expression and construct a truth table for the switching circuit shown in Fig. $11.6$. Figure 11.6] The parallel circuit $I$ to 2 and 3 to 4 gives $(\Lambda+\bar{B})$ and this is equivalent to a single switching unit between 7 and 2 . The parallel circuit 5 to 6 and 7 to 2 gives $C+(A+\bar{B})$ and this is equivalent to a single switching unit between 8 and 2 . The series circuit 9 to 8 and 8 to 2 gives the output $$ \boldsymbol{Z}=\boldsymbol{B} \cdot[\boldsymbol{C}+(\boldsymbol{A}+\overline{\boldsymbol{B}})] $$ The truth table is shown in Table 11.3. Columns 1 , 2 and 3 give all the possible combinations of $A, B$ and $C$, Column 4 is $\bar{B}$ and is the opposite to column 2. Column 5 is the or-function applied to columns 1 and 4 , giving $(A+\bar{B})$. Column 6 is the or-function applied to columns 3 and 5 giving $C+(A+\bar{B})$. The output is given in column 7 and is obtained by applying the and-function to columns 2 and 6 , giving $Z=B \cdot[C+(A+\bar{B})]$

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