For the given logic gate circuit, which of the following is the correct truth table?

Question

G1 Physics · Accepted Answer

The lower gate is an OR gate with inputs n and m. Therefore its output is n + m. The upper final gate is a NAND gate whose two inputs are n and (n + m). Thus, z = overline[n(n+m)]. Using Boolean algebra, n(n+m) = n·n + n·m = n + nm = n(1+m) = n. Therefore, z = n̄. Hence, if n = 0, z = 1, and if n = 1, z = 0, independent of m. The resulting truth table is n m z 0 0 1 0 1 1 1 1 0 1 0 0. Correct option: D.