A particular number is written as 132 in radix-4 representation. The same…

Concept: In a positional (radix) number system, a number with digits dk…d1d0 in base b has decimal value Σ di × bi. To express a decimal value in a different base c, divide the value repeatedly by c and read the successive remainders from last to first.

Applying to this question:

1. Expand 132 (radix-4) by place value: 1 × 42 + 3 × 41 + 2 × 40 = 16 + 12 + 2 = 30 in decimal.

2. Convert 30 (decimal) to radix-5 by repeated division: 30 ÷ 5 = 6 remainder 0; 6 ÷ 5 = 1 remainder 1; 1 ÷ 5 = 0 remainder 1.

3. Reading the remainders from the last division to the first gives the radix-5 digits 1, 1, 0 — that is, 110.

Cross-check: Converting 110 (radix-5) back to decimal: 1 × 52 + 1 × 51 + 0 × 50 = 25 + 5 + 0 = 30, matching the decimal value obtained from 132 (radix-4) — confirming the conversion. (An option such as 303 does not correspond to any correct base-4-to-base-5 conversion of this value; 303 in radix-5 equals 3×25 + 0×5 + 3 = 78 in decimal, not 30.)

Answer: 110 (radix-5).