Decimal 3 can be written as the sum of powers of 2, namely 2 + 1. In binary, this is represented by having a 1 in the 2's place and a 1 in the 1's place. That pattern is written as 11₂. Therefore, 11 is the correct binary representation of decimal 3.
Option A:
Option A, 1₂, equals 1 in decimal because only the 1's place is set. It does not include the 2's place contribution needed to reach 3.
Option B:
Option B, 10₂, represents 2 in decimal, with a 1 only in the 2's place and 0 in the 1's place. This is still short of 3 and therefore incorrect.
Option C:
Option C, 100₂, is equal to 4 in decimal as it sets the 4's place and zeroes elsewhere. This value is greater than 3, so it cannot be the correct representation for 3.
Option D:
Option D is correct because 11₂ has ones in both the 2's and 1's place, giving 2 + 1 = 3. This satisfies the requirement for the binary equivalent of decimal 3.
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