Question

The table below represents a stack stored in a contiguous block of memory cells, as discussed in the text. If the base of the stack is at address \(0 \times 10\) and the stack pointer contains the value \(0 \times 12\), what value is retrieved by a pop instruction? What value is in the stack pointer after the pop operation? $$ \begin{array}{cc} \text { Address } & \text { Contents } \\ 0 \times 10 & ' F^{\prime} \\ 0 \times 11 & ' C \text { ' } \\ 0 \times 12 & \text { 'A' } \\ 0 \times 13 & \text { 'B' } \\ 0 \times 14 & \text { 'E' } \end{array} $$

Short answer

Popped value is 'A'; new stack pointer is at address 0×11.

Step-by-step solution

Identify the Current Position of Stack Pointer

The stack pointer currently holds the value \( 0 \times 12 \). This means that the value at this address in memory is the top item of the stack that will be popped.

Check Contents at Stack Pointer Address

According to the table, the content at address \( 0 \times 12 \) is \('A'\). This is the value that will be retrieved by the pop instruction.

Update Stack Pointer After Pop Operation

After a pop operation, the stack pointer must be decremented to point to the next item below the top of the stack. Since it is currently at \( 0 \times 12 \), it will move one address back to \( 0\times 11 \).

Key concepts

Stack Operations

Stacks are fundamental data structures used in computing for managing collections of elements in a last-in, first-out (LIFO) manner. This means the last item added is the first one to be removed. One of the key operations in stack management is the "pop" operation, which removes and returns the top element from the stack.

In the given problem, the stack is implemented using memory addresses, creating a clear and straightforward way to visualize how elements are stored and retrieved in a stack. The stack pointer is a crucial part of stack operations; it points to the current top of the stack. Here, a pop operation was used to remove the top element at address \(0\times 12\), which contained \'A\'. Upon retrieval, the stack pointer must be updated to reflect the new top of the stack, which is the element previously below the one just popped, at address \(0\times 11\).

The operations involve accessing the current memory address, retrieving its value, and then adjusting the pointer to the next address in line. This movement is essential in maintaining the integrity of stack operations, ensuring all subsequent actions are performed correctly.

Memory Management

Memory management is the efficient handling of computer memory resources. When dealing with data structures such as stacks, memory management is crucial to ensure that data is stored and accessed optimally.

Stacks stored in contiguous memory blocks benefit from simple and efficient memory manipulation. Because each element of the stack is right next to the other, calculating the next or previous item involves simple address arithmetic. In this problem, the stack's base address is \(0\times 10\), and each subsequent element is stored in sequential addresses. This method significantly simplifies accessing and managing the stack's contents since you can easily predict where the next stack element will be.

With each pop operation, the stack pointer moves to the next lower memory address, reflecting the LIFO nature of the stack. Managing memory addresses efficiently ensures that the stack's data integrity and performance are maintained without requiring complex calculations or operations. This is vital since poorly managed memory can lead to errors like stack overflow and other critical failures.

Problem Solving

Problem-solving with data structures, such as stacks, often involves understanding how data is organized and how operations affect this organization. The original problem required us to perform a pop operation and understand its impact on the stack pointer. This task necessitated a clear comprehension of how stack pointers work and how memory addresses are used to store stack data.

Approaching this problem involves several systematic steps:

• Identify the position of the stack pointer and its role in accessing stack elements.
• Determine the value retrieved by performing a pop by checking the content at the pointer’s address.
• Correctly update the stack pointer to reflect the stack’s new state after the pop.

By systematically analyzing each component, students can develop a deeper understanding of both the specific problem and the general mechanisms at play in stack operations. Mastering these concepts can significantly enhance one's problem-solving skills in computer science and programming.