gate 2002_
Duration: 2 min
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The video presents a detailed solution to a Boolean algebra problem from the GATE 2002 examination, taught by Sanchit Jain Sir of Knowledge Gate Educator. The problem asks to simplify the expression f(f(x + y, y), z) given the function definition f(A, B) = A' + B. The screen displays four options: (A) x' + z, (B) xyz, (C) xy' + z, and (D) None of these. The instructor begins by writing the generalized function f(a, b) = a' + b to clarify the substitution logic. He then proceeds to evaluate the inner function f(x + y, y) first. By substituting the arguments, he derives the expression (x + y)' + y. Next, he substitutes this result back into the outer function, creating the expression f( (x + y)' + y , z ). Applying the function definition again, the first argument is complemented and the second argument 'z' is added, resulting in [ (x + y)' + y ]' + z. He then simplifies the complex term [ (x + y)' + y ]' using De Morgan's laws and Boolean algebra identities. Specifically, he simplifies it to xy'. Finally, combining this with the remaining term, the simplified expression becomes xy' + z. The instructor identifies this result as matching option (C) and circles it on the screen.
Chapters
0:00 – 1:47 00:00-01:47
The video opens with the text "Q Let f(A, B) = A' + B. Simplified expression for function f(f(x + y, y), z) is : (GATE-2002) (2 Marks)". The options (A) x' + z, (B) xyz, (C) xy' + z, (D) None of these are visible. The instructor writes f(a, b) = a' + b. He then writes f(x + y, y) and derives (x + y)' + y. He writes the outer function f( (x + y)' + y , z ). He expands this to [ (x + y)' + y ]' + z. He simplifies the term [ (x + y)' + y ]' using De Morgan's law to (x + y)y' which becomes xy'. The final result xy' + z is circled as option (C).
The lecture demonstrates a systematic approach to nested Boolean functions. By breaking down the problem into inner and outer layers, the instructor shows how to apply the function definition recursively. The key takeaway is the correct application of De Morgan's laws and simplification rules like (A + A'B = A + B), leading to the final answer xy' + z. The visual progression from the initial problem statement to the final circled answer (C) provides a clear, step-by-step guide for students to follow when dealing with similar functional composition problems in digital logic design.