The GATE Grind

GATE 2015 EE – Question 48

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

$f(A, B, C, D) = \Pi M(0, 1, 3, 4, 5, 7, 9, 11, 12, 13, 14, 15)$ is a maxterm representation of a Boolean function $f(A, B, C, D)$ where $A$ is the MSB and $D$ is the LSB. The equivalent minimized representation of this function is

  1. $(A + \bar{C} + D)(\bar{A} + B + D)$
  2. $A\bar{C}D + \bar{A}BD$
  3. $\bar{A}C\bar{D} + A\bar{B}\bar{C}D$
  4. $(B + \bar{C} + D)(A + \bar{B} + \bar{C})(\bar{A} + \bar{B} + \bar{C} + D)$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $(A + \bar{C} + D)(\bar{A} + B + D)$

Explanation

The function equals 0 at the 12 listed maxterms and 1 at the four cells 2, 6, 8 and 10. Option A is the product of two sum terms, and it is the minimized product-of-sums form that the official key gives for this function.