Question

Assume that the variables \(a\) and \(b\) are stored in memory locations 300 and 301 , respectively. Also assume that the three integer values \(+1\), \(-1\), and 0 are stored in memory locations 400 , 401 , and 402 , respectively. Finally, assume that the code sequence you are writing begins in memory location 50 . Using any of the machine language instructions shown in Section 5.2.4, translate the following algorithmic operations into their machine language equivalents. a. Set \(a\) to the value of \(a+b-1\) b. if \(a>0\) Set \(b\) to the value \(+1\)

Short answer

Calculate \( a = a + b - 1 \); if \( a > 0 \), then set \( b = +1 \).

Step-by-step solution

Initialize Variables

Load the value of variable \(a\) from memory location 300 into the CPU register.

Add Variable

Use the machine instruction to add the value of variable \(b\) from memory location 301 to the CPU register value. The result will be \(a + b\).

Subtract One

Subtract the value stored in memory location 401 (which is \(-1\)) from the CPU register. Since subtracting \(-1\) is equivalent to adding \(1\), it completes the operation \(a + b + 1 - 1 = a + b - 1\).

Store Result

Store the result from the CPU register back into memory location 300 to update variable \(a\).

Compare with Zero

Load the updated value of \(a\) from memory location 300 into the CPU register. Compare this value with the zero stored in memory location 402 using a compare instruction.

Conditional Assignment

If the comparison in Step 5 shows \(a > 0\), use a conditional jump/branch instruction to jump to the instruction that loads \(+1\) from memory location 400 into the CPU register and store it in memory location 301 to set \(b\) to \(+1\).

Key concepts

Algorithmic Operations

Algorithmic operations refer to a series of steps or procedures carried out to perform a specific task or solve a problem. In computing, these operations often transform input data into a desired output. In the context of machine language, algorithmic operations are broken down into basic instructions that the CPU can execute directly. For the given exercise, we have two main algorithmic operations: computing the value of \(a + b - 1\) and conditionally setting the value of \(b\) based on the result of this computation.

• Set \(a\) to the value of \(a + b - 1\): This involves adding two numbers and adjusting the result by subtracting one. It is implemented through a series of load, add, and subtract instructions.
• Conditionally set \(b\) to \(+1\) if \(a > 0\): Here, a comparison operation is performed, followed by a conditional instruction that executes only if the condition is met.

Memory Locations

Memory locations are specific addresses in a computer's memory used to store data or instructions. Each location has a unique address that the CPU uses to read or write data. In our example, the variables \(a\) and \(b\) are stored in memory locations 300 and 301, respectively. The integer constants \(+1\), \(-1\), and 0 are stored in memory locations 400, 401, and 402.

• Memory Location 300: Initially holds the variable \(a\), which will be modified during execution.
• Memory Location 301: Initially holds the variable \(b\), which may be updated conditionally.
• Memory Locations 400, 401, 402: Contain constants used in calculations and comparisons.

Understanding these addresses helps in organizing and accessing data efficiently during algorithm execution.

CPU Register

A CPU Register is a small, fast storage location within the CPU that holds data temporarily during processing. Registers play a crucial role in performing computations as they can be accessed much faster than data in memory.

• Loading Data: Registers are used to temporarily hold the values of variables like \(a\) while calculations are performed.
• Arithmetic Operations: During the execution of our algorithm, calculations, such as addition and subtraction, are conducted directly on register values for speed.
• Intermediate Storage: Once computations are done, the results may be stored back to memory or further processed within registers.

In our example, the register holds the intermediate results of \(a + b\) and \(a + b - 1\), facilitating quick and efficient processing of the algorithmic instructions.

Conditional Instructions

Conditional instructions are commands that determine whether a certain piece of code should be executed based on a condition, commonly involving comparison operations. In assembly or machine languages, these are often implemented as jump or branch instructions.

In the given problem, a conditional instruction is used after comparing the result of \(a + b - 1\) with zero:

• Comparison: Check if \(a > 0\) by loading \(a\) from memory and comparing it with the zero in memory location 402.
• Conditional Branch: If the condition \(a > 0\) is true, the CPU executes a branch instruction to load \(+1\) into \(b\).

This mechanism allows the program to take different paths, leading to varied outcomes based on the data values, thus enabling dynamic and flexible programming solutions.