Assume that 0 and 1 are considered as Boolean constants, and A, B, C are…
2026
Assume that 0 and 1 are considered as Boolean constants, and A, B, C are Boolean variables. Answer the following questions based on Boolean Logic, where:
"+" (plus sign) represents the OR operation
"." (dot sign) represents the AND operation
" ' " (apostrophe) represents the NOT (Complement/Inverter) operation
(A) Which Boolean operator or logic gate is equivalent to the expression:
A' . B + A . B'
(B) Simplify the following expression:
A . (A + B')
(C) If A ⊕ B = C, then evaluate A ⊕ C and B ⊕ C in terms of A, B and C, where ⊕ represents XOR operator.
(D) Write the Boolean expression corresponding to any one of De Morgan’s Laws.
Attempted by 64 students.
Show answer & explanation
(A) A'·B + A·B' represents XOR operation ⇒ Equivalent gate is XOR (Exclusive OR).
Example: XOR gives 1 when inputs differ.
(B) A·(A + B') = A (using Absorption Law: A(A + X) = A).
(C) Given A ⊕ B = C:
A ⊕ C = A ⊕ (A ⊕ B) = B
B ⊕ C = B ⊕ (A ⊕ B) = A
(using XOR properties).
(D) De Morgan’s Law: (A·B)' = A' + B'.
Conclusion: Boolean laws and XOR properties simplify expressions and help design efficient logic circuits.