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Evaluate the following Postfix expression using a stack (show detailed steps) 5 y 1 + log x a 5 Note: '. The characters 'y' & 'a' are considered as variables. Finally, 'log, +,-, x,+' are considered as operators.

Evaluate the following Postfix expression using a stack (show detailed steps) 5 y 1 + log x a 5 Note: '. The characters 'y' & 'a' are considered as variables. Finally, 'log, +,-, x,+' are considered as operators.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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--- ### Evaluation of Postfix Expressions Using a Stack #### Problem Statement Evaluate the following postfix expression using a stack (show detailed steps): \[ 5\ y\ 1\ +\ \log\ \times\ a\ 5\ \div\ - \] #### Note: - The characters **'y'** and **'a'** are considered as variables. - The symbols **'log', '+', '-', '×', '÷'** are considered as operators. --- ### Detailed Steps 1. **Initial Stack State:** - **Empty Stack** 2. **Reading from Left to Right:** \[ \begin{array}{|l|c|} \hline \text{Expression Element} & \text{Stack State} \\ \hline \ 5 \ & [5] \\ \hline \ y \ & [5, y] \\ \hline \ 1 \ & [5, y, 1] \\ \hline \ + \ & [5, y + 1] \\ \hline \ \log \ & [5, \log(y + 1)] \\ \hline \ \times \ & [5 \times \log(y + 1)] \\ \hline \ a \ & [5 \times \log(y + 1), a] \\ \hline \ 5 \ & [5 \times \log(y + 1), a, 5] \\ \hline \ \div \ & [5 \times \log(y + 1), a \div 5] \\ \hline \ - \ & [5 \times \log(y + 1) - (a \div 5)] \\ \hline \end{array} \] 3. **Final Stack State:** - **[5 × log(y + 1) - (a ÷ 5)]** The final result of the evaluation process is **\[5 \times \log(y + 1) - (a \div 5)\]**. --- ### Explanation of Operators - **+ :** Addition - **- :** Subtraction - **× :** Multiplication - **÷ :** Division - **log :** Logarithm ---
Transcribed Image Text:--- ### Evaluation of Postfix Expressions Using a Stack #### Problem Statement Evaluate the following postfix expression using a stack (show detailed steps): \[ 5\ y\ 1\ +\ \log\ \times\ a\ 5\ \div\ - \] #### Note: - The characters **'y'** and **'a'** are considered as variables. - The symbols **'log', '+', '-', '×', '÷'** are considered as operators. --- ### Detailed Steps 1. **Initial Stack State:** - **Empty Stack** 2. **Reading from Left to Right:** \[ \begin{array}{|l|c|} \hline \text{Expression Element} & \text{Stack State} \\ \hline \ 5 \ & [5] \\ \hline \ y \ & [5, y] \\ \hline \ 1 \ & [5, y, 1] \\ \hline \ + \ & [5, y + 1] \\ \hline \ \log \ & [5, \log(y + 1)] \\ \hline \ \times \ & [5 \times \log(y + 1)] \\ \hline \ a \ & [5 \times \log(y + 1), a] \\ \hline \ 5 \ & [5 \times \log(y + 1), a, 5] \\ \hline \ \div \ & [5 \times \log(y + 1), a \div 5] \\ \hline \ - \ & [5 \times \log(y + 1) - (a \div 5)] \\ \hline \end{array} \] 3. **Final Stack State:** - **[5 × log(y + 1) - (a ÷ 5)]** The final result of the evaluation process is **\[5 \times \log(y + 1) - (a \div 5)\]**. --- ### Explanation of Operators - **+ :** Addition - **- :** Subtraction - **× :** Multiplication - **÷ :** Division - **log :** Logarithm ---
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