Question

A particular number is written as $132$ in radix-$4$ representation. The same number in radix-$5$ representation is ________

Hint:

To convert between different bases, always first go through base 10 (decimal) unless a direct pattern is obvious. Divide by the target base and collect remainders bottom-up.

Answer 1

Step 1: Expand the base-4 number using powers of 4

The number 132₄ can be written as:

1×4² + 3×4¹ + 2×4⁰

= 16 + 12 + 2 = 30

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Step 2: Express 30 using powers of 5

Find coefficients of powers of 5:

30 = 1×5² + 1×5¹ + 0×5⁰

So the digits in base-5 are 1, 1, 0.

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Final Answer:

132₄ = 110₅