GATE CS 2024 Set 2 | Question 49

MSQ · 2 marks

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

  1. Option A: 64 in radix-10 (correct)
  2. Option B: 100 in radix-8 (correct)
  3. Option C: 50 in radix-16
  4. Option D: 121 in radix-7 (correct)

Answer

(A), (B), (D)

Explanation

Convert every numeral to decimal using its place values.

  • \(224_5 = 2 \times 5^{2} + 2 \times 5 + 4 = 50 + 10 + 4 = 64\).
  • (A) \(64_{10} = 64\): equal.
  • (B) \(100_8 = 1 \times 8^{2} = 64\): equal.
  • (C) \(50_{16} = 5 \times 16 = 80\): not equal.
  • (D) \(121_7 = 1 \times 7^{2} + 2 \times 7 + 1 = 49 + 14 + 1 = 64\): equal.

So three of the four numerals name the same value, 64; only the hexadecimal one differs.

Answer: A, B, D