The GATE Grind

GATE 2024 CS (CS2) – Question 49

Digital Logic · Number Representation and Arithmetic · 2 marks · Multiple select

Which of the following is/are EQUAL to 224 in radix-5 (i.e., base-5) notation?

  1. 64 in radix-10
  2. 100 in radix-8
  3. 50 in radix-16
  4. 121 in radix-7

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Correct answer: (A) 64 in radix-10; (B) 100 in radix-8; (D) 121 in radix-7

Explanation

224 in base 5 = 2·25 + 2·5 + 4 = 64. 100 in base 8 = 64; 50 in base 16 = 80; 121 in base 7 = 49+14+1 = 64. So A, B, D.