Using a single type of universal gate in a two-level realization, which logic…

Concept

A Product of Sums (POS) expression is an AND (product) of two or more OR (sum) terms. Thus, its direct mixed-gate realization is an OR-AND network: OR gates form the sum terms and an AND gate combines those terms.

For the standard homogeneous two-level realization, De Morgan’s theorem converts that OR-AND structure into a NOR-NOR network. This is the canonical single-gate-family association used in the official examination key.

Application

Take the representative POS expression F = (A + B)(C + D).

1. Apply double complementation without changing the function: F = [(A + B)(C + D)]''.

2. Apply De Morgan’s theorem to the complemented product: [(A + B)(C + D)]' = (A + B)' + (C + D)'. Therefore, F = [(A + B)' + (C + D)']'.

3. Each inner complemented sum is a NOR output: (A + B)' = NOR(A, B) and (C + D)' = NOR(C, D).

4. The outer complemented sum is another NOR operation: F = NOR(NOR(A, B), NOR(C, D)). Hence the homogeneous two-level realization uses NOR gates.

Cross-check

Expanding the derived network gives [(A + B)' + (C + D)']' = (A + B)''(C + D)'' = (A + B)(C + D), which reproduces the original POS expression exactly.

Contrast

• EX-OR implements parity or inequality of inputs; it is not the standard two-level realization associated with POS.

• AND performs the outer product in a direct OR-AND implementation, so it describes one stage rather than the homogeneous gate family asked for in this PYQ.

• OR forms each inner sum term in a direct OR-AND implementation, so it likewise describes one stage rather than the homogeneous gate family.

• NOR gates implement both levels after De Morgan conversion, giving the standard NOR-NOR realization of POS.

Result

The official DSSSB key for this exact question marks NOR gate. The learner’s OR-AND observation is valid for the direct mixed-gate circuit, while the keyed answer refers to the standard single-gate-family realization.