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Number Representation and Arithmetic

GATE CSE 2024 Set 2 · Q49

MSQ2 marksEasy

Time

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

Select all that applyOne or more correct

Pick every correct option

Solution

Step-by-step verified solution

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

Number Representation and Arithmetic

To find which options are equivalent, convert (224)5(224)_5 into decimal (radix-10):

(224)5=2×52+2×51+4×50=2×25+2×5+4×1=50+10+4=6410(224)_5 = 2 \times 5^2 + 2 \times 5^1 + 4 \times 5^0 = 2 \times 25 + 2 \times 5 + 4 \times 1 = 50 + 10 + 4 = 64_{10}

Now, convert each option to decimal:

  • Option A: 6464 in radix-10 is 641064_{10}. *(Matches)*

  • Option B: (100)8=1×82+0×81+0×80=6410(100)_8 = 1 \times 8^2 + 0 \times 8^1 + 0 \times 8^0 = 64_{10}. *(Matches)*

  • Option C: (50)16=5×161+0×160=8010≠6410(50)_{16} = 5 \times 16^1 + 0 \times 16^0 = 80_{10} \neq 64_{10}. *(Does not match)*

  • Option D: (121)7=1×72+2×71+1×70=49+14+1=6410(121)_7 = 1 \times 7^2 + 2 \times 7^1 + 1 \times 7^0 = 49 + 14 + 1 = 64_{10}. *(Matches)*

Therefore, options A, B, and D are correct.

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This Number Representation and Arithmetic previous year question is Q49 of the GATE CSE 2024 Set 2 paper. Find more GATE CSE PYQs on Number Representation and Arithmetic in Digital Logic, or browse all GATE CSE PYQs.

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Number Representation and Arithmetic in GATE CSE

Number Representation and Arithmetic has 33 GATE CSE PYQs across 20 papers from 2012 to 2026. 2 of them are 2-mark MSQs like this one, and GATE CSE 2024 Set 2 has 2.

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

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.