Skip to content
Question of 37

Q.[FIGURE: A logic circuit made of three NOR gates only. Input A is connected to both inputs of the first NOR gate; input B is connected to both inputs of the second NOR gate. The outputs of these two NOR gates are fed as the two inputs of a third NOR gate, whose output is Y.] Write the truth table for the circuit given in the figure, consisting of NOR gates only.

Uttarakhand UbseUttarakhand Board Intermediate (Class 12) 2023Subjective· 3mImportance★★★★★est
0% · 0/37 Questions
🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Two NOR gates used as inverters (NOT A, NOT B) feeding a third NOR gate produce Y=A⋅BY = A \cdot B — an AND gate.

Each of the first two NOR gates has both its inputs tied together — to AA for the first gate and to BB for the second. A NOR gate with both inputs the same acts as a NOT gate: output =A+A‾=A‾= \overline{A+A} = \overline{A}, and similarly the second gate gives B‾\overline{B}.

These two outputs, A‾\overline{A} and B‾\overline{B}, are fed into the third NOR gate:

Y=A‾+B‾‾Y = \overline{\overline{A}+\overline{B}}

By De Morgan's theorem, A‾+B‾‾=A⋅B\overline{\overline{A}+\overline{B}} = A\cdot B. So Y=A⋅BY = A\cdot B — this all-NOR circuit realizes the AND function.

Truth table:

ABA‾\overline{A}B‾\overline{B}Y=A‾+B‾‾Y=\overline{\overline{A}+\overline{B}}
00110
01100
10010

Unlock everything free for 14 days

  • Full step-by-step solutions
  • Concept-first explanations
  • Methods, shortcuts & mistakes
  • PYQ mapping + timed mock tests

Full access for 14 days. No credit card required.