Final answer:
The correct expression for a two-level NOR-only circuit with bubbles for the function f(a, b, c, d) is b) ¬(A · B) + ¬(C · D), as it best represents the NOR operations with the bubble indicating the NOT operation.
Step-by-step explanation:
The student asked for the expression that builds a two-level NOR-only circuit for the function f(a, b, c, d) with bubbles. A NOR gate is the combination of an OR gate followed by a NOT gate. Therefore, to express a function using NOR gates, we need to find a way to represent the function using NOR gates only. Given the options, the correct expression for a NOR-only circuit would be the one that negates the ORs of the inputs, because a NOR gate can be visualized as an OR gate with inverted inputs due to the bubbles at their inputs, which represent negation.
When constructing a NOR-only circuit, we can use the property that the NOR gate is its own inverse, which means that a series of two NOR gates is equivalent to a single OR gate. Consequently, the function f(a, b, c, d) will be structured to have OR (sum) operations at the first level and NOT (inverted) operations at the second level. The correct expression is option b) ¬(A · B) + ¬(C · D), as it represents the OR of NOTs of the products, which is equivalent to a two-level NOR-only circuit with bubbles.