What is the 2's complement of the binary number 101110?

The correct answer is B, 010010. The 2's complement of a binary number is found in two steps: flip every bit to get the 1's complement, then add 1. Flipping 101110 gives 010001, and 010001 + 1 = 010010. A quick check confirms it: 101110 is 46 and 010010 is 18, and 46 + 18 = 64, which is 2⁶ for a six-bit number, exactly as it should be. Computers use the 2's complement to store negative numbers and to do subtraction by addition, which keeps their circuits simple. A shortcut also works: copy the bits from the right up to and including the first 1, then flip all the rest. A is wrong because 010011 adds 2 instead of 1 to the 1's complement. C is wrong because 110001 leaves the leftmost bit unflipped. D is wrong because 010001 is only the 1's complement; the final +1 is missing. Exam tip: 2's complement = flip all bits, then add 1; a number plus its 2's complement equals 2ⁿ.