Solve the Boolean algebraic expression above, showing all the steps and laws used, in English

Question

ScanSolve AI Tutor · Accepted Answer

To obtain the truth table for the function $F = A\bar{B} + \bar{B}C + \bar{A}\bar{C}$ , we need to evaluate the function for all possible combinations of the input variables A, B, and C. Since there are three variables, there will be $2^3 = 8$ rows in the truth table.

List all possible combinations for A, B, and C.
Calculate the inversions $\bar{A}$ , $\bar{B}$ , and $\bar{C}$ .
Calculate each product term
$A\bar{B}$ , $\bar{B}C$ , and $\bar{A}\bar{C}$ .
Calculate the final function F by performing the OR operation on the three product terms
$F = A\bar{B} + \bar{B}C + \bar{A}\bar{C}$ .

Here is the truth table:
$\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline \textbf{A} & \textbf{B} & \textbf{C} & \mathbf{\bar{A}} & \mathbf{\bar{B}} & \mathbf{\bar{C}} & \mathbf{A\bar{B}} & \mathbf{\bar{B}C} & \mathbf{\bar{A}\bar{C}} & \textbf{F} \\ \hline 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 0 & 1 \\ 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 & 1 & 1 \\ 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 \\ 1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 \\ 1 & 1 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \end{array}$
The final truth table for the function $F = A\bar{B} + \bar{B}C + \bar{A}\bar{C}$ is shown above.
$\text{See truth table above}$

Solve the Boolean algebraic expression above, showing all the steps and laws used, in English

Answer

Step-by-step solution

List all possible combinations for A, B, and C.

Calculate the inversions $\bar{A}$ , $\bar{B}$ , and $\bar{C}$ .

Calculate each product term

Calculate the final function F by performing the OR operation on the three product terms

Try one yourself

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More English Questions

Solve the Boolean algebraic expression above, showing all the steps and laws used, in English

Answer

Step-by-step solution

List all possible combinations for A, B, and C.

Calculate the inversions Aˉ\bar{A}Aˉ, Bˉ\bar{B}Bˉ, and Cˉ\bar{C}Cˉ.

Calculate each product term

Calculate the final function F by performing the OR operation on the three product terms

Try one yourself

Still stuck on this one?

More English Questions

Calculate the inversions $\bar{A}$ , $\bar{B}$ , and $\bar{C}$ .