GATE 2018 EC – Question 57
The logic gates shown in the digital circuit below use strong pull-down nMOS transistors for LOW logic level at the outputs. When the pull-downs are off, high-value resistors set the output logic levels to HIGH (i.e. the pull-ups are weak). Note that some nodes are intentionally shorted to implement "wired logic". Such shorted nodes will be HIGH only if the outputs of all the gates whose outputs are shorted are HIGH.
The number of distinct values of $X_3X_2X_1X_0$ (out of the 16 possible values) that give $Y=1$ is ________.
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Correct answer: 8
Explanation
Working through the wired-AND nodes of the figure, $Y$ depends on the inverters of $X_0$ and $X_3$ and the XNOR/XOR of $X_1,X_2$ in such a way that exactly half of the 16 input combinations give $Y=1$, which is 8 (the official key).