The GATE Grind

GATE 2021 EC – Question 21

Digital Circuits · Number Representations · 1 mark · Multiple choice

If $(1235)_x=(3033)_y$, where $x$ and $y$ indicate the bases of the corresponding numbers, then

  1. $x=7$ and $y=5$
  2. $x=8$ and $y=6$
  3. $x=6$ and $y=4$
  4. $x=9$ and $y=7$

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Show answer and explanation

Correct answer: (B) $x=8$ and $y=6$

Explanation

For $x=8$: $(1235)_8=512+2\cdot64+3\cdot8+5=669$. For $y=6$: $(3033)_6=3\cdot216+0+3\cdot6+3=669$. The values are equal. The other pairs give $467\ne393$ for (A), and the other options do not match either.