The GATE Grind

GATE 2025 EE – Question 37

Analog and Digital Electronics · VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers · 2 marks · Multiple choice

A Boolean function is given as

$$f=(\bar u+\bar v+\bar w+\bar x)\cdot(\bar u+\bar v+\bar w+x)\cdot(\bar u+v+\bar w+\bar x)\cdot(\bar u+v+\bar w+x)$$

The simplified form of this function is represented by

Diagram for GATE 2025 EE question 37
  1. Circuit (A): an OR gate whose inputs are $\bar u$ and $\bar w$
  2. Circuit (B): an OR gate whose inputs are $u$ and $w$
  3. Circuit (C): an OR gate whose inputs are $\bar v$ and $\bar x$
  4. Circuit (D): an OR gate whose inputs are $v$ and $x$

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Show answer and explanation

Correct answer: (A) Circuit (A): an OR gate whose inputs are $\bar u$ and $\bar w$

Explanation

Combine the first two factors on $x$: $(\bar u+\bar v+\bar w+\bar x)(\bar u+\bar v+\bar w+x)=\bar u+\bar v+\bar w$. Combine the last two: $(\bar u+v+\bar w+\bar x)(\bar u+v+\bar w+x)=\bar u+v+\bar w$. Their product is $(\bar u+\bar w)+\bar vv=\bar u+\bar w$. That is an OR gate fed by the inverted inputs $u$ and $w$: circuit (A).