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What is the base-10 equivalent of the base-4 number 3013?

A182
B196
C199 ✓ Correct
D190
Correct answer: (C) 199
Explanation

The base-four number 3013 equals 199 in base ten when each digit is weighted by a power of four.

The leftmost 3 sits in the 64s place, contributing 192.

The next 0 sits in the 16s place, contributing nothing.

The 1 sits in the fours place, contributing 4, and the final 3 adds 3 units.

Adding 192, 0, 4, and 3 gives exactly 199.

In base four only the digits 0 to 3 are allowed, each place four times the one to its right.

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