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

2024

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

  1. A.

    64 in radix-10

  2. B.

    100 in radix-8

  3. C.

    50 in radix-16

  4. D.

    121 in radix-7

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Correct answer: A, B, D

Key step: convert 224 (base 5) to decimal: 2×5^2 + 2×5 + 4 = 64.

  • 64 in radix-10 — equals 64 decimal.

  • 100 in radix-8 — equals 64 decimal (1×8^2).

  • 121 in radix-7 — equals 64 decimal (1×7^2 + 2×7 + 1).

Therefore, the representations equal to 224 in base 5 are: 64 in radix-10, 100 in radix-8, and 121 in radix-7. (For reference, 50 in radix-16 equals 80 decimal, so it does not match.)

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