If (21121) 3 = (C) 4 , then what is the value of C?

Step 1: Convert (21121) in base 3 to decimal.

2×3^4 + 1×3^3 + 1×3^2 + 2×3^1 + 1×3^0 = 162 + 27 + 9 + 6 + 1 = 205

Step 2: Convert decimal 205 to base 4.

• 4^3 = 64: 205 = 3 × 64 + 13 → digit 3 (most significant)

• 4^2 = 16: remaining 13 = 0 × 16 + 13 → digit 0

• 4^1 = 4: 13 = 3 × 4 + 1 → digit 3

• 4^0 = 1: remainder 1 = 1 × 1 + 0 → digit 1 (least significant)

Reading the base-4 digits from most to least significant gives 3, 0, 3, 1. So the number in base 4 is (3031)_4.