ITPEC FE Morning April 2022 Question 1

NOR Gate Boolean Equivalent — identify the expression equal to NOR(A, B).

NOR = NOT(A OR B) = Ā · B̄ (De Morgan's Law).

Check each option by truth table (NOR = 1 only when A=0 AND B=0):

• •(a) Ā · (A + B̄): 1·(0+1)=1, 1·(0+0)=0, 0·any=0, 0·any=0 → 1,0,0,0 ✓ matches NOR
• •(b) Ā · (Ā + B̄): fails at A=0,B=1 → gives 1 instead of 0
• •(c) B · (A + B̄): fails at A=1,B=1 → gives 1 instead of 0
• •(d) B̄ · (Ā + B̄): fails at A=1,B=0 → gives 1 instead of 0

Answer: (a)

Key rule: NOR = Ā · B̄. Use truth tables when algebraic simplification is tricky — just 4 rows for 2 variables.

AI-generated — may contain errors