Bit Manipulation — Reasoning Check

Apply the module invariants, traces, and boundary conditions.

Get every question correct to pass this checkpoint. You can review feedback, revise your answers, and submit again.

1. Under this pack's leading-width-preserving AddBinary contract, what string results from "0011" + "0001"? Enter the four binary digits without quotes.

2. Reverse all 32 bit positions of uint32(2), not just its significant digits. What is the result as an unsigned decimal integer?

3. Let x be binary 1101000, or decimal 104. What does one execution of x = x & (x-1) produce?

Select one answer.

Binary 1001000, or decimal 72. Binary 0000000, or decimal 0. Binary 1100000, or decimal 96. Binary 0110100, or decimal 52.

4. Every repeated value appears three times in [5,5,5,7]. Why does XORing the entire array fail to recover the singleton?

Select one answer.

The array must be sorted before duplicate values can cancel under XOR. Three copies of 5 XOR to zero, but XOR cannot preserve the remaining 7. Three copies of 5 XOR to 5, leaving 5 XOR 7 = 2 instead of 7. XOR fails whenever the singleton is positive; it only works for negative values.

5. SingleNumberII reconstructs the 32-bit pattern 0xFFFFFFF9 after taking bit counts modulo three. Under its signed-32-bit result interpretation, what must be returned?

Select one answer.

2147483641. 4294967289. 7. -7.

6. What is the bitwise AND of every integer in the inclusive range [9,11]?

Select one answer.

0, because any interval of three integers clears every bit. 9, because ANDing the two endpoints always equals the full-range AND. 8, because the interior value 10 clears a low bit that both endpoints have set. 11, because all values share the upper endpoint's set bits.

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