Implementing a Division Program with Conditional Termination

Objective: Execute a program using the Fetch$-$Decode$-$Execute cycle that repeatedly divides a number by $2$ until it drops below a specified minimum threshold, ceasing execution thereafter.

Setup Overview:

The system includes registers: Program Counter $($PC$),$ Instruction Register $($IR$),$ and Accumulator $($AC$).$

The memory $($RAM$)$ is preloaded with the program's instructions and initial values.

Memory Initialization:

Address Content

$1$ LOAD $6$

$2$ DIV $7$

$3$ CMP $8$

$4$ JGE $1$

$5$ HALT

$664$

$72$

$84$

Instructions Explained:

LOAD X: Loads the value from address X into the AC$.$

DIV X: Divides AC's value by the value at address X$,$ updating AC with the result.

CMP X: Compares AC's current value to the value at address X$.$

JGE X: Jumps to address X if the AC's value is Greater than or Equal to compared value.

HALT: Ends the program's execution.

Task:

Analyze the division program's execution to determine the Accumulator's value at specified cycles and to compute the total number of cycles executed before program termination.

Questions:

a$.$ After completing the second execution cycle, what is the value in the Accumulator $($AC$)?$

b$.$ Following $4$ execution cycles, what remains the value at memory address $6?$

c$.$ Calculate the total number of execution cycles the program undergoes before it reaches the HALT instruction.