GATE CS 1990 Q3-i — Combinational Circuits

When the outputs of two or more open-collector gates are tied together, they perform a wired-AND operation. This means the combined output $Y$ is the logical AND of the individual gate outputs.

Let the two NAND gates be $G_1$ and $G_2$:

• The output of the first NAND gate with inputs $A, B, C$ is:
  $$G_1 = \overline{A \cdot B \cdot C}$$
• The output of the second NAND gate with inputs $D, E$ is:
  $$G_2 = \overline{D \cdot E}$$

Since their open-collector outputs are tied together, the resulting output $Y$ is the wired-AND of $G_1$ and $G_2$:

Applying De Morgan's Law ($\overline{X} \cdot \overline{Y} = \overline{X + Y}$):

Therefore, the correct option is B.