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Conditional expressions are the backbone of decision making in programming. They allow programs to respond differently to various inputs or states. At its most basic, a conditional expression evaluates to either true or false and is often used within an 'if statement'.

For instance, take the exercise prompt, which requires writing a conditional statement to assign a value to the variable 'x' based on the condition of the variable 'y' being equal to zero. The conditional expression would be written in code as y == 0. If 'y' indeed equals zero, the expression evaluates to true, prompting the subsequent code block within the if statement to execute. In this case, that action is to assign the value 100 to 'x'. If 'y' does not equal zero, the condition is false, and the assignment does not occur.

The assignment operator, depicted as '=', is a fundamental element used to assign values to variables in programming languages. It acts like a directive that tells the computer to store a particular value in a variable.

In the provided solution, x = 100 is the line where the assignment operator comes into play. This line does not evaluate as a condition; instead, it instructs the program to store the value 100 in the variable 'x'. It is crucial to distinguish the assignment operator '=' from the equality operator '==', which is used to compare values for equality.

Programming logic is the systematic method of addressing a problem through a sequence of instructions given to the computer. It includes understanding how to use control structures, such as if statements, loops, and functions, to create a desired outcome. The logic flow ensures that instructions are executed under the correct conditions and in the right order.

In the context of the exercise, we see programming logic at work when we first check a condition before performing an action. The if statement 'if y == 0:' is followed by an indented block where 'x = 100' is only executed if the condition is true, demonstrating how programming logic controls the flow of the program.